1. K. Giannokostas, Moschopoulos

Advanced constitutive modeling of the thixotropic elasto-visco-plastic behavior of blood: Description of the model and rheological predictions Journal Article

In: Materials , 13(18) , pp. 4184, 2020.

Abstract | Links | BibTeX | Tags: blood, blood relaxation time, blood viscoelasticity, constitutive modeling, elastoviscoplastic, extensional rheometry, hemorheology, LAOS, personalize parametrization, shear rheometry, TEVP, thixotropic index, thixotropy

@article{Giannokostas2020,

title = {Advanced constitutive modeling of the thixotropic elasto-visco-plastic behavior of blood: Description of the model and rheological predictions},

author = {Giannokostas, K., Moschopoulos, P., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.},

doi = {10.3390/ma13184184},

year = {2020},

date = {2020-09-20},

journal = {Materials },

volume = {13(18)},

pages = {4184},

abstract = {This work focuses on the advanced modeling of the thixotropic nature of blood, coupled with an elasto-visco-plastic formulation by invoking a consistent and validated model for TEVP materials. The proposed model has been verified for the adequate description of the rheological behavior of suspensions, introducing a scalar variable that describes dynamically the level of internal microstructure of rouleaux at any instance, capturing accurately the aggregation and disaggregation mechanisms of the RBCs. Also, a non-linear fitting is adopted for the definition of the model’s parameters on limited available experimental data of steady and transient rheometric flows of blood samples. We present the predictability of the new model in various steady and transient rheometric flows, including startup shear, rectangular shear steps, shear cessation, triangular shear steps and LAOS tests. Our model provides predictions for the elasto-thixotropic mechanism in startup shear flows, demonstrating a non-monotonic relationship of the thixotropic index on the shear-rate. The intermittent shear step test reveals the dynamics of the structural reconstruction, which in turn is associated with the aggregation process. Moreover, our model offers robust predictions for less examined tests such as uniaxial elongation, in which normal stress was found to have considerable contribution. Apart from the integrated modeling of blood rheological complexity, our implementation is adequate for multi-dimensional simulations due to its tensorial formalism accomplished with a single time scale for the thixotropic effects, resulting in a low computational cost compared to other TEVP models.},

keywords = {blood, blood relaxation time, blood viscoelasticity, constitutive modeling, elastoviscoplastic, extensional rheometry, hemorheology, LAOS, personalize parametrization, shear rheometry, TEVP, thixotropic index, thixotropy},

pubstate = {published},

tppubtype = {article}

}

This work focuses on the advanced modeling of the thixotropic nature of blood, coupled with an elasto-visco-plastic formulation by invoking a consistent and validated model for TEVP materials. The proposed model has been verified for the adequate description of the rheological behavior of suspensions, introducing a scalar variable that describes dynamically the level of internal microstructure of rouleaux at any instance, capturing accurately the aggregation and disaggregation mechanisms of the RBCs. Also, a non-linear fitting is adopted for the definition of the model’s parameters on limited available experimental data of steady and transient rheometric flows of blood samples. We present the predictability of the new model in various steady and transient rheometric flows, including startup shear, rectangular shear steps, shear cessation, triangular shear steps and LAOS tests. Our model provides predictions for the elasto-thixotropic mechanism in startup shear flows, demonstrating a non-monotonic relationship of the thixotropic index on the shear-rate. The intermittent shear step test reveals the dynamics of the structural reconstruction, which in turn is associated with the aggregation process. Moreover, our model offers robust predictions for less examined tests such as uniaxial elongation, in which normal stress was found to have considerable contribution. Apart from the integrated modeling of blood rheological complexity, our implementation is adequate for multi-dimensional simulations due to its tensorial formalism accomplished with a single time scale for the thixotropic effects, resulting in a low computational cost compared to other TEVP models.2. P. Moschopoulos, Syrakos

Dynamics of viscoplastic filament stretching Journal Article

In: Journal of Non-Newtonian Fluid Mechanics, 284 (104371), 2020.

Abstract | Links | BibTeX | Tags: Filament stretching, Penalized Augmented Langrangian method, Pinching dynamics, Slender filament-2D comparison, viscoplastic materials

@article{Moschopoulos2020b,

title = {Dynamics of viscoplastic filament stretching},

author = {Moschopoulos, P., Syrakos, A., Dimakopoulos, Y., Tsamopoulos, J.},

doi = {10.1016/j.jnnfm.2020.104371},

year = {2020},

date = {2020-08-11},

journal = {Journal of Non-Newtonian Fluid Mechanics},

volume = {284},

number = {104371},

abstract = {We use numerical simulations to study the stretching and pinching of a viscoplastic material that is confined by two coaxial disks when they are pulled apart. The material initially forms a cylindrical bridge between the disks, follows the Heschel-Bulkley model and yields according to the von Mises criterion. We solve the governing equations numerically in their 2D, axisymmetric form using the PAL algorithm (Dimakopoulos et al. (2018)) and the slender filament approximation using the Bercovier and Engelman (1980) regularization. This approximation is valid when the disk radius to the initial length of the bridge, is small, but it is often used even when this aspect ratio is O(1). The results from the 2D solution agree with the experiments of Balmforth et al. (2010) for both a Carbopol gel and a Kaolin suspension, which can be classified as materials of medium and high viscoplasticity, respectively. Depending on the values of the aspect ratio and the yield stress of the material, we show that stretching can or cannot be accurately described by the slender filament approximation. By varying the yield stress and the pulling velocity, we find that discrepancies arise when the viscoplastic character of the flow increases, even though . The inaccuracy of the slender filament approximation stems from the omission of the shear component of the rate of strain tensor from the calculation of its magnitude in the von Mises criterion. This causes a significant overestimation of the effective viscosity, since this component can be comparable to or greater than the normal components outside the filament neck. Thus, larger unyielded regions are predicted by this approximation and the remaining yielded ones carry the burden of the deformation leading to much shorter pinching times. Our results for the pinching process of viscoplastic filaments show the minor role of the yield stress, in agreement with Balmforth et al. (2010). In particular, the process is almost the same as that of power-law fluids with the same value of the shear-thinning exponent n. Our simulations include cases with n < 0.54, where the slender filament approximation is known to fail, and also a case where inertia is accounted for. Still, we confirm that the behavior is similar to that of power-law fluids.},

keywords = {Filament stretching, Penalized Augmented Langrangian method, Pinching dynamics, Slender filament-2D comparison, viscoplastic materials},

pubstate = {published},

tppubtype = {article}

}

We use numerical simulations to study the stretching and pinching of a viscoplastic material that is confined by two coaxial disks when they are pulled apart. The material initially forms a cylindrical bridge between the disks, follows the Heschel-Bulkley model and yields according to the von Mises criterion. We solve the governing equations numerically in their 2D, axisymmetric form using the PAL algorithm (Dimakopoulos et al. (2018)) and the slender filament approximation using the Bercovier and Engelman (1980) regularization. This approximation is valid when the disk radius to the initial length of the bridge, is small, but it is often used even when this aspect ratio is O(1). The results from the 2D solution agree with the experiments of Balmforth et al. (2010) for both a Carbopol gel and a Kaolin suspension, which can be classified as materials of medium and high viscoplasticity, respectively. Depending on the values of the aspect ratio and the yield stress of the material, we show that stretching can or cannot be accurately described by the slender filament approximation. By varying the yield stress and the pulling velocity, we find that discrepancies arise when the viscoplastic character of the flow increases, even though . The inaccuracy of the slender filament approximation stems from the omission of the shear component of the rate of strain tensor from the calculation of its magnitude in the von Mises criterion. This causes a significant overestimation of the effective viscosity, since this component can be comparable to or greater than the normal components outside the filament neck. Thus, larger unyielded regions are predicted by this approximation and the remaining yielded ones carry the burden of the deformation leading to much shorter pinching times. Our results for the pinching process of viscoplastic filaments show the minor role of the yield stress, in agreement with Balmforth et al. (2010). In particular, the process is almost the same as that of power-law fluids with the same value of the shear-thinning exponent n. Our simulations include cases with n < 0.54, where the slender filament approximation is known to fail, and also a case where inertia is accounted for. Still, we confirm that the behavior is similar to that of power-law fluids.3. S. Varchanis, Syrakos

PEGAFEM-V: A new petrov-galerkin finite element method for free surface viscoelastic flows Journal Article

In: Journal of Non-Newtonian Fluid Mechanics, 284 , pp. 104365, 2020.

Abstract | Links | BibTeX | Tags: finite element method, free surface, petrov-galerkin, Viscoelastic flows

@article{Varchanis2020c,

title = {PEGAFEM-V: A new petrov-galerkin finite element method for free surface viscoelastic flows},

author = {Varchanis, S., Syrakos, A., Dimakopoulos, Y., Tsamopoulos, J.},

doi = {10.1016/j.jnnfm.2020.104365},

year = {2020},

date = {2020-08-07},

journal = {Journal of Non-Newtonian Fluid Mechanics},

volume = {284},

pages = {104365},

abstract = {The recently proposed finite element (FE) formulation for viscoelastic flows that allows the use of equal order linear interpolants for all variables and simultaneously does not suffer from the high Weissenberg number problem, is extended to free surface flows. The coupling of this Petrov-Galerkin stabilized FE formulation with the quasi-elliptic mesh generator allows us to obtain stable numerical solutions in highly deformed meshes and for very high values of the Weissenberg number (Wi). We present benchmark solutions in three free surface flows: the axisymmetric filament stretching, the elastocapillary-driven formation of bead-on-a-string, and the 2-dimensional, planar extrudate swell flow. In all cases, we attain converged solutions for values of Wi that have never been reached before by FE. The accuracy and robustness of the proposed numerical scheme are illustrated by achieving mesh and time step convergence under extreme mesh deformation conditions such as the bead-on-a-string (BOAS) formation during filament stretching. The formulation is enriched further with a discontinuity capturing scheme that enhances the quality of the solution around singularities dramatically. Finally, our simulations reveal for the first time the existence of lip-vortices in the steady planar extrudate-swell flow of Oldroyd-B fluids, which converge with mesh refinement.},

keywords = {finite element method, free surface, petrov-galerkin, Viscoelastic flows},

pubstate = {published},

tppubtype = {article}

}

The recently proposed finite element (FE) formulation for viscoelastic flows that allows the use of equal order linear interpolants for all variables and simultaneously does not suffer from the high Weissenberg number problem, is extended to free surface flows. The coupling of this Petrov-Galerkin stabilized FE formulation with the quasi-elliptic mesh generator allows us to obtain stable numerical solutions in highly deformed meshes and for very high values of the Weissenberg number (Wi). We present benchmark solutions in three free surface flows: the axisymmetric filament stretching, the elastocapillary-driven formation of bead-on-a-string, and the 2-dimensional, planar extrudate swell flow. In all cases, we attain converged solutions for values of Wi that have never been reached before by FE. The accuracy and robustness of the proposed numerical scheme are illustrated by achieving mesh and time step convergence under extreme mesh deformation conditions such as the bead-on-a-string (BOAS) formation during filament stretching. The formulation is enriched further with a discontinuity capturing scheme that enhances the quality of the solution around singularities dramatically. Finally, our simulations reveal for the first time the existence of lip-vortices in the steady planar extrudate-swell flow of Oldroyd-B fluids, which converge with mesh refinement.4. Simon J. Haward Stylianos Varchanis, Cameron C. Hopkins; Tsamopoulos, John

Transition between solid and liquid state of yield-stress fluids under purely extensional deformations Journal Article

In: PNAS (Proceedings of the National Academy of Sciences of the United States of America), 117 (23) , pp. 12611-12617, 2020.

Abstract | Links | BibTeX | Tags: elastoviscoplastic materials, extensional flow, viscoplastic materials, yield strain, Yield stress

@article{Varchanis2020b,

title = {Transition between solid and liquid state of yield-stress fluids under purely extensional deformations},

author = { Stylianos Varchanis, Simon J. Haward, Cameron C. Hopkins, Alexandros Syrakos, Amy Q. Shen, Yannis Dimakopoulos, and John Tsamopoulos},

editor = {David A. Weitz},

doi = {10.1073/pnas.1922242117},

year = {2020},

date = {2020-05-20},

journal = {PNAS (Proceedings of the National Academy of Sciences of the United States of America)},

volume = { 117 (23)},

pages = {12611-12617},

abstract = {We report experimental microfluidic measurements and theoretical modeling of elastoviscoplastic materials under steady, planar elongation. Employing a theory that allows the solid state to deform, we predict the yielding and flow dynamics of such complex materials in pure extensional flows. We find a significant deviation of the ratio of the elongational to the shear yield stress from the standard value predicted by ideal viscoplastic theory, which is attributed to the normal stresses that develop in the solid state prior to yielding. Our results show that the yield strain of the material governs the transition dynamics from the solid state to the liquid state. Finally, given the difficulties of quantifying the stress field in such materials under elongational flow conditions, we identify a simple scaling law that enables the determination of the elongational yield stress from experimentally measured velocity fields.},

keywords = {elastoviscoplastic materials, extensional flow, viscoplastic materials, yield strain, Yield stress},

pubstate = {published},

tppubtype = {article}

}

We report experimental microfluidic measurements and theoretical modeling of elastoviscoplastic materials under steady, planar elongation. Employing a theory that allows the solid state to deform, we predict the yielding and flow dynamics of such complex materials in pure extensional flows. We find a significant deviation of the ratio of the elongational to the shear yield stress from the standard value predicted by ideal viscoplastic theory, which is attributed to the normal stresses that develop in the solid state prior to yielding. Our results show that the yield strain of the material governs the transition dynamics from the solid state to the liquid state. Finally, given the difficulties of quantifying the stress field in such materials under elongational flow conditions, we identify a simple scaling law that enables the determination of the elongational yield stress from experimentally measured velocity fields.5. S. Varchanis, Hopkins

Asymmetric flows of complex fluids past confined cylinders: A comprehensive numerical study with experimental validation Journal Article

In: Physics of Fluids, 32(5) (0008783), 2020.

Abstract | Links | BibTeX | Tags: Complex fluids, Flow instabilities, Fluid dynamics, Fluid flows, Rheological properties, Shear thinning, Velocimetry, Viscoelastic flows, Viscosity

@article{Varchanis2020,

title = {Asymmetric flows of complex fluids past confined cylinders: A comprehensive numerical study with experimental validation},

author = {Varchanis, S., Hopkins, C.C., Shen, A.Q., Tsamopoulos, J., Haward, S.J.},

doi = {10.1063/5.0008783},

year = {2020},

date = {2020-05-08},

journal = {Physics of Fluids},

volume = {32(5)},

number = {0008783},

abstract = {Three non-Newtonian constitutive models are employed to investigate how fluid rheological properties influence the development of laterally asymmetric flows past confined cylinders. First, simulations with the shear-thinning but inelastic Carreau–Yasuda model are compared against complementary flow velocimetry experiments on a semidilute xanthan gum solution, showing that shear-thinning alone is insufficient to cause flow asymmetry. Next, simulations with an elastic but non-shear-thinning finitely extensible non-linear elastic dumbbell model are compared with experiments on a constant viscosity solution of poly(ethylene oxide) (PEO) in an aqueous glycerol mixture. The simulations and the experiments reveal the development of an extended downstream wake due to elastic stresses generated at the stagnation point but show no significant lateral asymmetries of the flow around the sides of the cylinder. Finally, the elastic and shear-thinning linear Phan–Thien–Tanner (l-PTT) model is compared with experimental velocimetry on a rheologically similar solution of PEO in water. Here, at low flow rates, lateral symmetry is retained, while the growth of a downstream elastic wake is observed, in qualitative similarity to the non-shear-thinning elastic fluids. However, above a critical flow rate, the flow bifurcates to one of the two stable and steady laterally asymmetric states. Further parameter studies with the l-PTT model are performed by varying the degrees of shear-thinning and elasticity and also modifying the confinement of the cylinder. These tests confirm the importance of the coupling between shear-thinning and elasticity for the onset of asymmetric flows and also establish stability and bifurcation diagrams delineating the stable and unstable flow states.

},

keywords = {Complex fluids, Flow instabilities, Fluid dynamics, Fluid flows, Rheological properties, Shear thinning, Velocimetry, Viscoelastic flows, Viscosity},

pubstate = {published},

tppubtype = {article}

}

Three non-Newtonian constitutive models are employed to investigate how fluid rheological properties influence the development of laterally asymmetric flows past confined cylinders. First, simulations with the shear-thinning but inelastic Carreau–Yasuda model are compared against complementary flow velocimetry experiments on a semidilute xanthan gum solution, showing that shear-thinning alone is insufficient to cause flow asymmetry. Next, simulations with an elastic but non-shear-thinning finitely extensible non-linear elastic dumbbell model are compared with experiments on a constant viscosity solution of poly(ethylene oxide) (PEO) in an aqueous glycerol mixture. The simulations and the experiments reveal the development of an extended downstream wake due to elastic stresses generated at the stagnation point but show no significant lateral asymmetries of the flow around the sides of the cylinder. Finally, the elastic and shear-thinning linear Phan–Thien–Tanner (l-PTT) model is compared with experimental velocimetry on a rheologically similar solution of PEO in water. Here, at low flow rates, lateral symmetry is retained, while the growth of a downstream elastic wake is observed, in qualitative similarity to the non-shear-thinning elastic fluids. However, above a critical flow rate, the flow bifurcates to one of the two stable and steady laterally asymmetric states. Further parameter studies with the l-PTT model are performed by varying the degrees of shear-thinning and elasticity and also modifying the confinement of the cylinder. These tests confirm the importance of the coupling between shear-thinning and elasticity for the onset of asymmetric flows and also establish stability and bifurcation diagrams delineating the stable and unstable flow states.

6. Pettas, D; Dimakopoulos, Y; Tsamopoulos, J

Steady flow of a viscoelastic film over an inclined plane featuring periodic slits Journal Article

In: Journal of Non-Newtonian Fluid Mechanics, pp. 104243, 2020, ISSN: 0377-0257.

Abstract | Links | BibTeX | Tags: Cassie-Baxter state, flow hysteresis, flow over variable topography, hydrophilic surfaces, Viscoelastic films, wetting length

@article{PETTAS2020104243,

title = {Steady flow of a viscoelastic film over an inclined plane featuring periodic slits},

author = {D Pettas and Y Dimakopoulos and J Tsamopoulos},

url = {http://www.sciencedirect.com/science/article/pii/S0377025720300112},

doi = {https://doi.org/10.1016/j.jnnfm.2020.104243},

issn = {0377-0257},

year = {2020},

date = {2020-01-01},

journal = {Journal of Non-Newtonian Fluid Mechanics},

pages = {104243},

abstract = {We consider the steady flow of a viscoelastic film over an inclined plane featuring a periodic arrangement of slits, which are oriented normal to the main direction of flow. The film creates a second gas-liquid interface connecting the two hydrophilic sidewalls of a slit. This interface forms two three-phase contact lines and supports a widely varying amount of liquid under different physical and geometrical conditions. We develop a computational model and carry out detailed numerical simulations, based on the finite element method to investigate this flow. To this end, we solve the two-dimensional momentum and mass conservation equations, while employing the Phan-Thien-Tanner (PTT) constitutive model to account for the rheology of the viscoelastic material. An elliptic grid generation scheme is used to follow the large deformation of the film shape. We perform a thorough parametric analysis to investigate the combined effects of elastic, inertia, capillary and viscous forces on the characteristics of the steady flow. The results of our simulations indicate that increasing fluid elasticity decreases the two wetting lengths along each side wall of a slit. On the contrary, the wetting of the slit is enhanced by the shear-thinning of the fluid. Multiple steady solutions connected by turning points forming a hysteresis loop and transcritical bifurcations as well as isolated solution branches are revealed by pseudo-arc-length continuation. In particular, it is predicted that under certain conditions, the transition from the capillary to the inertia regime is not smooth; instead a hysteresis loop arises. This is the signature of an abrupt decrease of the film penetration with increasing flow rate since higher deformations cannot be sustained. Additionally, we have performed calculations for a wide range of the geometrical characteristics of the substrate. We find that the elastic effects of the fluid become more pronounced when the slits are closer together in their periodic arrangement and of width decreasing to become almost comparable to the capillary length of the liquid. These can lead to almost no wetting of the slit, i.e. the Cassie-Baxter state, even in a hydrophilic surface.},

keywords = {Cassie-Baxter state, flow hysteresis, flow over variable topography, hydrophilic surfaces, Viscoelastic films, wetting length},

pubstate = {published},

tppubtype = {article}

}

We consider the steady flow of a viscoelastic film over an inclined plane featuring a periodic arrangement of slits, which are oriented normal to the main direction of flow. The film creates a second gas-liquid interface connecting the two hydrophilic sidewalls of a slit. This interface forms two three-phase contact lines and supports a widely varying amount of liquid under different physical and geometrical conditions. We develop a computational model and carry out detailed numerical simulations, based on the finite element method to investigate this flow. To this end, we solve the two-dimensional momentum and mass conservation equations, while employing the Phan-Thien-Tanner (PTT) constitutive model to account for the rheology of the viscoelastic material. An elliptic grid generation scheme is used to follow the large deformation of the film shape. We perform a thorough parametric analysis to investigate the combined effects of elastic, inertia, capillary and viscous forces on the characteristics of the steady flow. The results of our simulations indicate that increasing fluid elasticity decreases the two wetting lengths along each side wall of a slit. On the contrary, the wetting of the slit is enhanced by the shear-thinning of the fluid. Multiple steady solutions connected by turning points forming a hysteresis loop and transcritical bifurcations as well as isolated solution branches are revealed by pseudo-arc-length continuation. In particular, it is predicted that under certain conditions, the transition from the capillary to the inertia regime is not smooth; instead a hysteresis loop arises. This is the signature of an abrupt decrease of the film penetration with increasing flow rate since higher deformations cannot be sustained. Additionally, we have performed calculations for a wide range of the geometrical characteristics of the substrate. We find that the elastic effects of the fluid become more pronounced when the slits are closer together in their periodic arrangement and of width decreasing to become almost comparable to the capillary length of the liquid. These can lead to almost no wetting of the slit, i.e. the Cassie-Baxter state, even in a hydrophilic surface.7. Moschopoulos, P; Dimakopoulos, Y; Tsamopoulos, J

Electro-osmotic flow of electrolyte solutions of PEO in microfluidic channels Journal Article

In: Journal of Colloid and Interface Science, 563 , pp. 381-393, 2020, ISSN: 00219797, (cited By 0).

Abstract | Links | BibTeX | Tags: Chain scission criterion, Electro-osmosis, Electrolytic solution, Microchannel, Polyethylene oxide, Polymeric Depletion Layer (PDL)

@article{Moschopoulos2020381,

title = {Electro-osmotic flow of electrolyte solutions of PEO in microfluidic channels},

author = {P Moschopoulos and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85077088954&doi=10.1016%2fj.jcis.2019.12.052&partnerID=40&md5=96da36dadabf6c83ad6acc3b582723e0},

doi = {10.1016/j.jcis.2019.12.052},

issn = {00219797},

year = {2020},

date = {2020-01-01},

journal = {Journal of Colloid and Interface Science},

volume = {563},

pages = {381-393},

abstract = {Hypothesis: We investigate if the shear-stress exerted on the wall of a glass microchannel can be a robust and accurate criterion for the safe electro-osmotic transfer of polyethylene oxide (PEO) chains dissolved in a NaCl aquatic solvent. To this end, a comprehensive multiscale formulation based on the rheological and electrochemical modeling of the PEO dynamics is proposed. Phenomena that occur in microscale, e.g., the migration of PEO to the core region of the channel and Polymeric Depletion Layer (PDL) formation, and in nanoscale, e.g., the development of an electric double layer on the glass surface and ionic steric effects, are included. Experimental arrangement: We study the electro-osmotic flow of PEO solutions (0.1–0.5%), flowing in a glass microchannel of rectangle shape, with dimensions of 300 μm in length and 75 μm in height. We vary the externally applied electric field (300–500 V/cm), and the bulk ionic concentration (0.001–10 mM). Findings: We find that all features of our formulation are indeed essential to reproduce the experimental data of Huang, Chen, Wong, Liow, Soft Matter, (2016) precisely. Although the PDL formation preserves the fragile nature of biopolymers, the dominant stress is the normal stress, and the critical value is at the PDL interface. A new design criterion for microdevices is proposed. © 2019 Elsevier Inc.},

note = {cited By 0},

keywords = {Chain scission criterion, Electro-osmosis, Electrolytic solution, Microchannel, Polyethylene oxide, Polymeric Depletion Layer (PDL)},

pubstate = {published},

tppubtype = {article}

}

Hypothesis: We investigate if the shear-stress exerted on the wall of a glass microchannel can be a robust and accurate criterion for the safe electro-osmotic transfer of polyethylene oxide (PEO) chains dissolved in a NaCl aquatic solvent. To this end, a comprehensive multiscale formulation based on the rheological and electrochemical modeling of the PEO dynamics is proposed. Phenomena that occur in microscale, e.g., the migration of PEO to the core region of the channel and Polymeric Depletion Layer (PDL) formation, and in nanoscale, e.g., the development of an electric double layer on the glass surface and ionic steric effects, are included. Experimental arrangement: We study the electro-osmotic flow of PEO solutions (0.1–0.5%), flowing in a glass microchannel of rectangle shape, with dimensions of 300 μm in length and 75 μm in height. We vary the externally applied electric field (300–500 V/cm), and the bulk ionic concentration (0.001–10 mM). Findings: We find that all features of our formulation are indeed essential to reproduce the experimental data of Huang, Chen, Wong, Liow, Soft Matter, (2016) precisely. Although the PDL formation preserves the fragile nature of biopolymers, the dominant stress is the normal stress, and the critical value is at the PDL interface. A new design criterion for microdevices is proposed. © 2019 Elsevier Inc.8. Syrakos, A; Dimakopoulos, Y; Tsamopoulos, J

A finite volume method for the simulation of elastoviscoplastic flows and its application to the lid-driven cavity case Journal Article

In: Journal of Non-Newtonian Fluid Mechanics, 275 , 2020, ISSN: 03770257, (cited By 0).

Abstract | Links | BibTeX | Tags: Benchmark problem, Carbopol, Elastoviscoplastic flow, Finite Volume method, Flow cessation, Lid-driven cavity

@article{Syrakos2020,

title = {A finite volume method for the simulation of elastoviscoplastic flows and its application to the lid-driven cavity case},

author = {A Syrakos and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85076172172&doi=10.1016%2fj.jnnfm.2019.104216&partnerID=40&md5=91473f41ebd36091adf437a2da72f783},

doi = {10.1016/j.jnnfm.2019.104216},

issn = {03770257},

year = {2020},

date = {2020-01-01},

journal = {Journal of Non-Newtonian Fluid Mechanics},

volume = {275},

abstract = {We propose a Finite Volume Method for the simulation of elastoviscoplastic (EVP) flows, modelled after the extension to the Herschel-Bulkley model by Saramito [J. Non-Newton. Fluid Mech. 158 (2009) 154–161]. The method is applicable to cell-centred grids of arbitrary geometry by the introduction of new stabilisation techniques of the “momentum interpolation” and “both sides diffusion” types, for pressure and velocity, respectively. Adaptive time stepping is employed. The method is used to perform benchmark simulations of lid-driven cavity flow, which also serve to explore certain aspects of this EVP constitutive equation in a two-dimensional setting. The model parameters are chosen so as to represent Carbopol, and simulations are performed for different lid velocities and with either slip or no-slip wall boundaries. The results are compared against those obtained with the classic Herschel-Bulkley model. It is noticed that different initial conditions for stress lead to different steady states. Furthermore, we investigate the cessation of the flow, once the lid is suddenly halted; it is found that, contrary to the classic Herschel-Bulkley predictions, the EVP flow does not cease in finite time. Rather, the flow decays very slowly while the material oscillates as kinetic energy is converted to elastic energy and vice versa. Flow decay is much faster under slip conditions due to the friction between the material and the walls. © 2019 Elsevier B.V.},

note = {cited By 0},

keywords = {Benchmark problem, Carbopol, Elastoviscoplastic flow, Finite Volume method, Flow cessation, Lid-driven cavity},

pubstate = {published},

tppubtype = {article}

}

We propose a Finite Volume Method for the simulation of elastoviscoplastic (EVP) flows, modelled after the extension to the Herschel-Bulkley model by Saramito [J. Non-Newton. Fluid Mech. 158 (2009) 154–161]. The method is applicable to cell-centred grids of arbitrary geometry by the introduction of new stabilisation techniques of the “momentum interpolation” and “both sides diffusion” types, for pressure and velocity, respectively. Adaptive time stepping is employed. The method is used to perform benchmark simulations of lid-driven cavity flow, which also serve to explore certain aspects of this EVP constitutive equation in a two-dimensional setting. The model parameters are chosen so as to represent Carbopol, and simulations are performed for different lid velocities and with either slip or no-slip wall boundaries. The results are compared against those obtained with the classic Herschel-Bulkley model. It is noticed that different initial conditions for stress lead to different steady states. Furthermore, we investigate the cessation of the flow, once the lid is suddenly halted; it is found that, contrary to the classic Herschel-Bulkley predictions, the EVP flow does not cease in finite time. Rather, the flow decays very slowly while the material oscillates as kinetic energy is converted to elastic energy and vice versa. Flow decay is much faster under slip conditions due to the friction between the material and the walls. © 2019 Elsevier B.V.9. Pettas, D; Karapetsas, G; Dimakopoulos, Y; Tsamopoulos, J

Viscoelastic film flows over an inclined substrate with sinusoidal topography. II. Linear stability analysis Journal Article

In: Physical Review Fluids, 4 (8), 2019, ISSN: 2469990X, (cited By 1).

Abstract | Links | BibTeX | Tags:

@article{Pettas2019,

title = {Viscoelastic film flows over an inclined substrate with sinusoidal topography. II. Linear stability analysis},

author = {D Pettas and G Karapetsas and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85072033020&doi=10.1103%2fPhysRevFluids.4.083304&partnerID=40&md5=b33029e0b661b509151e1b4077eb48ff},

doi = {10.1103/PhysRevFluids.4.083304},

issn = {2469990X},

year = {2019},

date = {2019-01-01},

journal = {Physical Review Fluids},

volume = {4},

number = {8},

abstract = {The linear hydrodynamic stability of a film of viscoelastic fluid flowing down an inclined wavy surface is studied. We investigate the stability of the flow with respect to infinitesimal two- A nd three-dimensional (2D and 3D) disturbances and employ the Floquet-Bloch theory to examine the effect of periodic disturbances of any wavelength. The study is based on the numerical solution of the momentum equations along with the Phan-Thien-Tanner (PTT) model to account for material viscoelasticity. The generalized eigenvalue problem is solved using Arnoldi's algorithm, in a Newton-like implementation in order to calculate faster the critical conditions for the onset of the instability. Our results are in excellent agreement with the previous experimental and theoretical results in the case of Newtonian liquids flowing over flat and undulating substrates and viscoelastic liquids over flat substrates. We present detailed stability maps for finite amplitude of the wall corrugations and a wide range of material parameters. Our calculations indicate that fluid elasticity is primarily stabilizing, while shear thinning of the fluid tends to destabilize the fluid flow. In order to investigate the mechanisms involved, we perform an energy analysis of the flow under long-wave disturbances indicating that the convection of stress-gradient disturbances provides an additional viscoelastic mechanism for the destabilization of the flow, in contrast to the base state stress gradients which contribute to stabilization of the flow. Besides the usual long-wave instability, conditions are identified which lead to unstable disturbances of wavelength equal or smaller than the wavelength of the substrate. Experimental observations for Newtonian liquids have indicated that these short-wave instabilities will dominate and a similar behavior is predicted for viscoelastic liquids. Sometimes, before the short-wave instabilities, a hysteresis loop in the steady flow can be identified, which leads to a sharp change in the critical frequency. Finally, we examine the stability of the flow when subjected to disturbances in the spanwise direction and show that for highly elastic liquids 3D instabilities may arise. © 2019 American Physical Society.},

note = {cited By 1},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

The linear hydrodynamic stability of a film of viscoelastic fluid flowing down an inclined wavy surface is studied. We investigate the stability of the flow with respect to infinitesimal two- A nd three-dimensional (2D and 3D) disturbances and employ the Floquet-Bloch theory to examine the effect of periodic disturbances of any wavelength. The study is based on the numerical solution of the momentum equations along with the Phan-Thien-Tanner (PTT) model to account for material viscoelasticity. The generalized eigenvalue problem is solved using Arnoldi's algorithm, in a Newton-like implementation in order to calculate faster the critical conditions for the onset of the instability. Our results are in excellent agreement with the previous experimental and theoretical results in the case of Newtonian liquids flowing over flat and undulating substrates and viscoelastic liquids over flat substrates. We present detailed stability maps for finite amplitude of the wall corrugations and a wide range of material parameters. Our calculations indicate that fluid elasticity is primarily stabilizing, while shear thinning of the fluid tends to destabilize the fluid flow. In order to investigate the mechanisms involved, we perform an energy analysis of the flow under long-wave disturbances indicating that the convection of stress-gradient disturbances provides an additional viscoelastic mechanism for the destabilization of the flow, in contrast to the base state stress gradients which contribute to stabilization of the flow. Besides the usual long-wave instability, conditions are identified which lead to unstable disturbances of wavelength equal or smaller than the wavelength of the substrate. Experimental observations for Newtonian liquids have indicated that these short-wave instabilities will dominate and a similar behavior is predicted for viscoelastic liquids. Sometimes, before the short-wave instabilities, a hysteresis loop in the steady flow can be identified, which leads to a sharp change in the critical frequency. Finally, we examine the stability of the flow when subjected to disturbances in the spanwise direction and show that for highly elastic liquids 3D instabilities may arise. © 2019 American Physical Society.10. Pettas, D; Karapetsas, G; Dimakopoulos, Y; Tsamopoulos, J

Viscoelastic film flows over an inclined substrate with sinusoidal topography. I. Steady state Journal Article

In: Physical Review Fluids, 4 (8), 2019, ISSN: 2469990X, (cited By 1).

Abstract | Links | BibTeX | Tags:

@article{Pettas2019b,

title = {Viscoelastic film flows over an inclined substrate with sinusoidal topography. I. Steady state},

author = {D Pettas and G Karapetsas and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85072020975&doi=10.1103%2fPhysRevFluids.4.083303&partnerID=40&md5=53c62696c0d11b09addd72217dc04ec7},

doi = {10.1103/PhysRevFluids.4.083303},

issn = {2469990X},

year = {2019},

date = {2019-01-01},

journal = {Physical Review Fluids},

volume = {4},

number = {8},

abstract = {We consider the steady flow of a viscoelastic liquid film over an inclined wall with sinusoidal corrugations of arbitrary wavelength and depth. We develop a computational model and carry out detailed numerical simulations based on the finite-element method to investigate this flow. To this end, we solve the two-dimensional momentum and mass conservation equations while employing the Phan-Thien-Tanner (PTT) constitutive model to account for the rheology of the viscoelastic material. An elliptic grid generation scheme is used to follow the large deformations of the liquid film. We perform a thorough parametric analysis to investigate the combined effects of elasticity, inertia, and capillary and viscous forces on the characteristics of the steady flow. The results of our simulations indicate that fluid elasticity suppresses interfacial deformation at low flow rates, whereas at moderate values of Re it enhances the deformation considerably. In the latter case, elastic forces may even give rise to the formation of a static hump and a cusp at the free surface, the size of which increases with the relaxation time of the liquid. The resonance of the liquid film with the substrate undulations is also enhanced by shear thinning. Interestingly, it is predicted that under certain conditions the transition to the inertia regime is not smooth and a hysteresis loop arises, which is the signature of an abrupt change of the film shape, since its high deformations cannot be sustained. Additionally, we have performed calculations for a wide range of different geometrical characteristics of the substrate. We find that viscoelastic effects become more pronounced in the case of long-wavelength wall undulations, while for substrates with short wavelengths the effect of shear thinning is less significant due to the presence of vortices inside the corrugations. © 2019 American Physical Society.},

note = {cited By 1},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

We consider the steady flow of a viscoelastic liquid film over an inclined wall with sinusoidal corrugations of arbitrary wavelength and depth. We develop a computational model and carry out detailed numerical simulations based on the finite-element method to investigate this flow. To this end, we solve the two-dimensional momentum and mass conservation equations while employing the Phan-Thien-Tanner (PTT) constitutive model to account for the rheology of the viscoelastic material. An elliptic grid generation scheme is used to follow the large deformations of the liquid film. We perform a thorough parametric analysis to investigate the combined effects of elasticity, inertia, and capillary and viscous forces on the characteristics of the steady flow. The results of our simulations indicate that fluid elasticity suppresses interfacial deformation at low flow rates, whereas at moderate values of Re it enhances the deformation considerably. In the latter case, elastic forces may even give rise to the formation of a static hump and a cusp at the free surface, the size of which increases with the relaxation time of the liquid. The resonance of the liquid film with the substrate undulations is also enhanced by shear thinning. Interestingly, it is predicted that under certain conditions the transition to the inertia regime is not smooth and a hysteresis loop arises, which is the signature of an abrupt change of the film shape, since its high deformations cannot be sustained. Additionally, we have performed calculations for a wide range of different geometrical characteristics of the substrate. We find that viscoelastic effects become more pronounced in the case of long-wavelength wall undulations, while for substrates with short wavelengths the effect of shear thinning is less significant due to the presence of vortices inside the corrugations. © 2019 American Physical Society.11. Corato, M De; Dimakopoulos, Y; Tsamopoulos, J

The rising velocity of a slowly pulsating bubble in a shear-thinning fluid Journal Article

In: Physics of Fluids, 31 (8), 2019, ISSN: 10706631, (cited By 1).

Abstract | Links | BibTeX | Tags:

@article{DeCorato2019,

title = {The rising velocity of a slowly pulsating bubble in a shear-thinning fluid},

author = {M De Corato and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85071089054&doi=10.1063%2f1.5108812&partnerID=40&md5=c57c0bdde158d1a4d1c508e5931da8c2},

doi = {10.1063/1.5108812},

issn = {10706631},

year = {2019},

date = {2019-01-01},

journal = {Physics of Fluids},

volume = {31},

number = {8},

abstract = {We study the rising motion of small bubbles that undergo contraction, expansion, or oscillation in a shear-thinning fluid. We model the non-Newtonian response of the fluid using the Carreau-Yasuda constitutive equation, under the assumptions that the inertia of the fluid and the bubble is negligible and that the bubble remains spherical. These assumptions imply that the rising velocity of the bubble is instantaneously proportional to the buoyancy force, with the proportionality constant given by the inverse of the friction coefficient. Instead of computing the rising velocity for a particular radial dynamics of the bubble, we evaluate its friction coefficient as a function of the rheological parameters and of the instantaneous expansion/contraction rate. To compute the friction coefficient, we impose a translational motion and we linearize the governing equations around the expansion/contraction dynamics of the bubble, which we solve using a perturbation expansion along with the finite element method. Our results show that the radial motion of the bubble reduces the viscosity of the surrounding fluid and may thus markedly decrease the friction coefficient of the bubble. We use the friction coefficient to compute the average rise velocity of a bubble with periodic variations of its radius, which we find to be strongly increased by the radial pulsations. Finally, we compare our predictions with the experiments performed by Iwata et al. ["Pressure-oscillation defoaming for viscoelastic fluid," J. Non-Newtonian Fluid Mech. 151(1-3), 30-37 (2008)], who found that the rise velocity of bubbles that undergo radial pulsations is increased by orders of magnitude compared to the case of bubbles that do not pulsate. Our results shed light on the mechanism responsible for enhanced bubble release in shear-thinning fluids, which has implications for bubble removal from complex fluids. © 2019 Author(s).},

note = {cited By 1},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

We study the rising motion of small bubbles that undergo contraction, expansion, or oscillation in a shear-thinning fluid. We model the non-Newtonian response of the fluid using the Carreau-Yasuda constitutive equation, under the assumptions that the inertia of the fluid and the bubble is negligible and that the bubble remains spherical. These assumptions imply that the rising velocity of the bubble is instantaneously proportional to the buoyancy force, with the proportionality constant given by the inverse of the friction coefficient. Instead of computing the rising velocity for a particular radial dynamics of the bubble, we evaluate its friction coefficient as a function of the rheological parameters and of the instantaneous expansion/contraction rate. To compute the friction coefficient, we impose a translational motion and we linearize the governing equations around the expansion/contraction dynamics of the bubble, which we solve using a perturbation expansion along with the finite element method. Our results show that the radial motion of the bubble reduces the viscosity of the surrounding fluid and may thus markedly decrease the friction coefficient of the bubble. We use the friction coefficient to compute the average rise velocity of a bubble with periodic variations of its radius, which we find to be strongly increased by the radial pulsations. Finally, we compare our predictions with the experiments performed by Iwata et al. ["Pressure-oscillation defoaming for viscoelastic fluid," J. Non-Newtonian Fluid Mech. 151(1-3), 30-37 (2008)], who found that the rise velocity of bubbles that undergo radial pulsations is increased by orders of magnitude compared to the case of bubbles that do not pulsate. Our results shed light on the mechanism responsible for enhanced bubble release in shear-thinning fluids, which has implications for bubble removal from complex fluids. © 2019 Author(s).12. Varchanis, S; Makrigiorgos, G; Moschopoulos, P; Dimakopoulos, Y; Tsamopoulos, J

Modeling the rheology of thixotropic elasto-visco-plastic materials Journal Article

In: Journal of Rheology, 63 (4), pp. 609-639, 2019, ISSN: 01486055, (cited By 1).

Abstract | Links | BibTeX | Tags: elasto-visco-plastic, EVP, materials, rheology, SAOS

@article{Varchanis2019609,

title = {Modeling the rheology of thixotropic elasto-visco-plastic materials},

author = {S Varchanis and G Makrigiorgos and P Moschopoulos and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85066807729&doi=10.1122%2f1.5049136&partnerID=40&md5=2852b6137d879bf29a4d75dab0888ded},

doi = {10.1122/1.5049136},

issn = {01486055},

year = {2019},

date = {2019-01-01},

journal = {Journal of Rheology},

volume = {63},

number = {4},

pages = {609-639},

abstract = {To describe the macroscopic rheological behavior of thixotropic elasto-visco-plastic (TEVP) materials, phenomena that take place in their microstructure must be accounted for. To this end, we couple the tensorial constitutive model by Saramito for EVP materials with thixotropy, extending the ideas of isotropic hardening, and with kinematic hardening (KH), to account for back stresses. We use a scalar variable that describes the level of structure at any instance and a modified Armstrong-Frederick KH equation, thus providing rules governing the dynamics of the apparent yield stress. The material viscosity, yield stress, and back stress modulus feature a nonlinear dependence on the structural parameter, enabling the model to make accurate predictions with a single structural parameter. To avoid unphysical stress evolution in both shear and extensional flows, we propose a modified back stress constitutive equation that keeps the components of the stress tensor bounded. The predictions of the new model are compared to experimental data and predictions of previously proposed TEVP models in simple rheometric flows, including steady and step-shear tests, flow reversal, intermittent step tests, small amplitude oscillatory shear (SAOS) and large amplitude oscillatory shear. In most cases, the proposed model reproduces more accurately these experimental data than the other models, highlighting its predictive capabilities. Moreover, SAOS illustrates that introducing viscoplasticity via the Saramito model necessarily reduces G″ to zero in the linear strain regime. This calls for model adjustments in the solid state. Finally, we examined the proposed model in uniaxial elongation and concluded that it is important to include this flow in the rheological characterization and modeling of such systems. © 2019 The Society of Rheology.},

note = {cited By 1},

keywords = {elasto-visco-plastic, EVP, materials, rheology, SAOS},

pubstate = {published},

tppubtype = {article}

}

To describe the macroscopic rheological behavior of thixotropic elasto-visco-plastic (TEVP) materials, phenomena that take place in their microstructure must be accounted for. To this end, we couple the tensorial constitutive model by Saramito for EVP materials with thixotropy, extending the ideas of isotropic hardening, and with kinematic hardening (KH), to account for back stresses. We use a scalar variable that describes the level of structure at any instance and a modified Armstrong-Frederick KH equation, thus providing rules governing the dynamics of the apparent yield stress. The material viscosity, yield stress, and back stress modulus feature a nonlinear dependence on the structural parameter, enabling the model to make accurate predictions with a single structural parameter. To avoid unphysical stress evolution in both shear and extensional flows, we propose a modified back stress constitutive equation that keeps the components of the stress tensor bounded. The predictions of the new model are compared to experimental data and predictions of previously proposed TEVP models in simple rheometric flows, including steady and step-shear tests, flow reversal, intermittent step tests, small amplitude oscillatory shear (SAOS) and large amplitude oscillatory shear. In most cases, the proposed model reproduces more accurately these experimental data than the other models, highlighting its predictive capabilities. Moreover, SAOS illustrates that introducing viscoplasticity via the Saramito model necessarily reduces G″ to zero in the linear strain regime. This calls for model adjustments in the solid state. Finally, we examined the proposed model in uniaxial elongation and concluded that it is important to include this flow in the rheological characterization and modeling of such systems. © 2019 The Society of Rheology.13. Corato, M De; Saint-Michel, B; Makrigiorgos, G; Dimakopoulos, Y; Tsamopoulos, J; Garbin, V

Oscillations of small bubbles and medium yielding in elastoviscoplastic fluids Journal Article

In: Physical Review Fluids, 4 (7), 2019, ISSN: 2469990X, (cited By 1).

Abstract | Links | BibTeX | Tags:

@article{DeCorato2019b,

title = {Oscillations of small bubbles and medium yielding in elastoviscoplastic fluids},

author = {M De Corato and B Saint-Michel and G Makrigiorgos and Y Dimakopoulos and J Tsamopoulos and V Garbin},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85070286492&doi=10.1103%2fPhysRevFluids.4.073301&partnerID=40&md5=2b55cb1fa519ac78a2f3dc2915c807ef},

doi = {10.1103/PhysRevFluids.4.073301},

issn = {2469990X},

year = {2019},

date = {2019-01-01},

journal = {Physical Review Fluids},

volume = {4},

number = {7},

abstract = {We investigate the radial oscillations of small gas bubbles trapped in yield-stress fluids and driven by an acoustic pressure field. We model the rheological behavior of the yield-stress fluid using the recently developed elastoviscoplastic constitutive equation that takes into account the elastic and viscoplastic deformations of the material [Saramito, J. Non-Newton. Fluid Mech. 158, 154 (2009)JNFMDI0377-025710.1016/j.jnnfm.2008.12.001]. Assuming that the bubble remains spherical during the pressure driving, we reduce the problem to a set of ordinary differential equations and an integrodifferential equation, which we solve numerically for the case of two yield-stress fluids, i.e., a soft Carbopol gel and a stiffer kaolin suspension. We find that depending on the amplitude and frequency of the pressure field, the radial oscillations of the bubble produce elastic stresses that may or may not suffice to yield the surrounding material. We evaluate the critical amplitude of the acoustic pressure required to achieve yielding and we find a good agreement between numerical simulations and an analytical formula derived under the assumption of linear deformations. Finally, we examine the bubble oscillation amplitude for a very wide range of applied pressures both below and above the critical value to assess the impact of yielding on the bubble dynamics. This analysis could be used to identify a signature of yielding in experiments where the radial dynamics of a bubble is measured. More generally, these results can be used to rationalize the optimal conditions for pressure-induced bubble release from yield-stress fluids, which is relevant to various biomedical and industrial applications, including the oil industry and food processing. © 2019 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.},

note = {cited By 1},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

We investigate the radial oscillations of small gas bubbles trapped in yield-stress fluids and driven by an acoustic pressure field. We model the rheological behavior of the yield-stress fluid using the recently developed elastoviscoplastic constitutive equation that takes into account the elastic and viscoplastic deformations of the material [Saramito, J. Non-Newton. Fluid Mech. 158, 154 (2009)JNFMDI0377-025710.1016/j.jnnfm.2008.12.001]. Assuming that the bubble remains spherical during the pressure driving, we reduce the problem to a set of ordinary differential equations and an integrodifferential equation, which we solve numerically for the case of two yield-stress fluids, i.e., a soft Carbopol gel and a stiffer kaolin suspension. We find that depending on the amplitude and frequency of the pressure field, the radial oscillations of the bubble produce elastic stresses that may or may not suffice to yield the surrounding material. We evaluate the critical amplitude of the acoustic pressure required to achieve yielding and we find a good agreement between numerical simulations and an analytical formula derived under the assumption of linear deformations. Finally, we examine the bubble oscillation amplitude for a very wide range of applied pressures both below and above the critical value to assess the impact of yielding on the bubble dynamics. This analysis could be used to identify a signature of yielding in experiments where the radial dynamics of a bubble is measured. More generally, these results can be used to rationalize the optimal conditions for pressure-induced bubble release from yield-stress fluids, which is relevant to various biomedical and industrial applications, including the oil industry and food processing. © 2019 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.14. Varchanis, S; Syrakos, A; Dimakopoulos, Y; Tsamopoulos, J

A new finite element formulation for viscoelastic flows: Circumventing simultaneously the LBB condition and the high-Weissenberg number problem Journal Article

In: Journal of Non-Newtonian Fluid Mechanics, 267 , pp. 78-97, 2019, ISSN: 03770257, (cited By 1).

Abstract | Links | BibTeX | Tags: Equal order interpolation, Finite elements, High Weissenberg number problem, Log-conformation, Non-Newtonian fluid simulations, PSPG, SUPG, Viscoelastic fluid flow

@article{Varchanis201978,

title = {A new finite element formulation for viscoelastic flows: Circumventing simultaneously the LBB condition and the high-Weissenberg number problem},

author = {S Varchanis and A Syrakos and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85064452819&doi=10.1016%2fj.jnnfm.2019.04.003&partnerID=40&md5=4adc73be737baec9168e2275531fb81b},

doi = {10.1016/j.jnnfm.2019.04.003},

issn = {03770257},

year = {2019},

date = {2019-01-01},

journal = {Journal of Non-Newtonian Fluid Mechanics},

volume = {267},

pages = {78-97},

abstract = {In this paper, we propose a new, fully consistent and highly stable finite element formulation for the simulation of viscoelastic flows. In our method, we have implemented equal order interpolants for all variables and a combination of classical finite element stabilization techniques (PSPG/DEVSS-TG/SUPG) with the log-conformation representation of the constitutive equation that has allowed us to obtain numerically stable solutions at high Weissenberg numbers. The validity of the presented FEM framework is testified by comparing the numerical results of our method to those of the literature in three benchmark tests: the 2-dimensional flows of a viscoelastic fluid in a square lid-driven cavity and past a cylinder in a channel, and the 3-dimensional flow in a cubic lid-driven cavity. We consider both direct steady-state and transient calculations using the Oldroyd-B and linear PTT models. In all cases, we can reach, and in some cases surpass, the maximum Weissenberg number values attainable by mixed finite element methods, but at a considerably lower computational cost and programming effort. In addition, we perform mesh-convergence tests illustrating that the proposed method is convergent and features almost 2nd order accuracy in space. © 2019},

note = {cited By 1},

keywords = {Equal order interpolation, Finite elements, High Weissenberg number problem, Log-conformation, Non-Newtonian fluid simulations, PSPG, SUPG, Viscoelastic fluid flow},

pubstate = {published},

tppubtype = {article}

}

In this paper, we propose a new, fully consistent and highly stable finite element formulation for the simulation of viscoelastic flows. In our method, we have implemented equal order interpolants for all variables and a combination of classical finite element stabilization techniques (PSPG/DEVSS-TG/SUPG) with the log-conformation representation of the constitutive equation that has allowed us to obtain numerically stable solutions at high Weissenberg numbers. The validity of the presented FEM framework is testified by comparing the numerical results of our method to those of the literature in three benchmark tests: the 2-dimensional flows of a viscoelastic fluid in a square lid-driven cavity and past a cylinder in a channel, and the 3-dimensional flow in a cubic lid-driven cavity. We consider both direct steady-state and transient calculations using the Oldroyd-B and linear PTT models. In all cases, we can reach, and in some cases surpass, the maximum Weissenberg number values attainable by mixed finite element methods, but at a considerably lower computational cost and programming effort. In addition, we perform mesh-convergence tests illustrating that the proposed method is convergent and features almost 2nd order accuracy in space. © 201915. Karapetsas, G; Photeinos, D; Dimakopoulos, Y; Tsamopoulos, J

Dynamics and motion of a gas bubble in a viscoplastic medium under acoustic excitation Journal Article

In: Journal of Fluid Mechanics, 865 , pp. 381-413, 2019, ISSN: 00221120, (cited By 2).

Abstract | Links | BibTeX | Tags: bubble dynamics

@article{Karapetsas2019381,

title = {Dynamics and motion of a gas bubble in a viscoplastic medium under acoustic excitation},

author = {G Karapetsas and D Photeinos and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85061900293&doi=10.1017%2fjfm.2019.49&partnerID=40&md5=bdaeaffda8e91b6fe98c6861539d6cbb},

doi = {10.1017/jfm.2019.49},

issn = {00221120},

year = {2019},

date = {2019-01-01},

journal = {Journal of Fluid Mechanics},

volume = {865},

pages = {381-413},

abstract = {We investigate the dynamics of the buoyancy-driven rise of a bubble inside a viscoplastic material when it is subjected to an acoustic pressure field. To this end, we develop a simplified model based on the Lagrangian formalism assuming a pulsating bubble with a spherical shape. Moreover, to account for the effects of a deformable bubble, we also perform detailed two-dimensional axisymmetric simulations. Qualitative agreement is found between the simplified approach and the detailed numerical simulations. Our results reveal that the acoustic excitation enhances the mobility of the bubble, by increasing the size of the yielded region that surrounds the bubble, thereby decreasing the effective viscosity of the liquid and accelerating the motion of the bubble. This effect is significantly more pronounced at the resonance frequency, and it is shown that bubble motion takes place even for Bingham numbers (Bn) that can be orders of magnitude higher than the critical Bn for bubble entrapment in the case of a static pressure field. © 2019 Cambridge University Press.},

note = {cited By 2},

keywords = {bubble dynamics},

pubstate = {published},

tppubtype = {article}

}

We investigate the dynamics of the buoyancy-driven rise of a bubble inside a viscoplastic material when it is subjected to an acoustic pressure field. To this end, we develop a simplified model based on the Lagrangian formalism assuming a pulsating bubble with a spherical shape. Moreover, to account for the effects of a deformable bubble, we also perform detailed two-dimensional axisymmetric simulations. Qualitative agreement is found between the simplified approach and the detailed numerical simulations. Our results reveal that the acoustic excitation enhances the mobility of the bubble, by increasing the size of the yielded region that surrounds the bubble, thereby decreasing the effective viscosity of the liquid and accelerating the motion of the bubble. This effect is significantly more pronounced at the resonance frequency, and it is shown that bubble motion takes place even for Bingham numbers (Bn) that can be orders of magnitude higher than the critical Bn for bubble entrapment in the case of a static pressure field. © 2019 Cambridge University Press.16. Dimakopoulos, Y; Makrigiorgos, G; Georgiou, G C; Tsamopoulos, J

The PAL (Penalized Augmented Lagrangian) method for computing viscoplastic flows: A new fast converging scheme Journal Article

In: Journal of Non-Newtonian Fluid Mechanics, 256 , pp. 23-41, 2018, ISSN: 03770257, (cited By 13).

Abstract | Links | BibTeX | Tags: Augmented Lagrangian method, Bubble rise, Filament, Lid-driven cavity, Papanastasiou regularization; Penalty method, stretching, Viscoplastic fluids

@article{Dimakopoulos201823,

title = {The PAL (Penalized Augmented Lagrangian) method for computing viscoplastic flows: A new fast converging scheme},

author = {Y Dimakopoulos and G Makrigiorgos and G C Georgiou and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85044113517&doi=10.1016%2fj.jnnfm.2018.03.009&partnerID=40&md5=46144d6483fc39fdf658de1f3f65dd06},

doi = {10.1016/j.jnnfm.2018.03.009},

issn = {03770257},

year = {2018},

date = {2018-01-01},

journal = {Journal of Non-Newtonian Fluid Mechanics},

volume = {256},

pages = {23-41},

abstract = {Computation of viscoplastic fluid flows has always been a challenging task. Viscoplastic models are intrinsically discontinuous at the yielded-unyielded interface, which leads to numerical difficulties, because of the singularity in the Jacobian matrix of the resulting discretized equations. For this reason, several modeling or numerical approaches have been proposed, the most popular being the Papanastasiou regularization (PR) and the Augmented Lagrangian (AL) methods, respectively. Recently, studies on AL methods have focused on developing accelerated algorithms, since the required computational cost of using AL is extremely high. In the present work, a fast converging and efficient algorithm is proposed for tracking the yield surface and predicting the flow field of viscoplastic fluids accurately. The numerical procedure is the Penalized Augmented Lagrangian (PAL) method, which is based on a monolithic Newton solver for AL, where the governing equations of the Lagrange-multiplier tensor for both the rate-of-strain projection and the extra-stress tensors are penalized. To test the efficiency of our algorithm, five benchmark flow-problems with fixed, free and moving boundaries are studied. First, the problem of the steady rise of a bubble in a viscoplastic medium is addressed validating the new algorithm with the findings by Dimakopoulos et al. (2013). Then the entrance flow in a rectangular channel is solved, where a primary unyielded region is found around the centerline in the developed part of the flow and secondary unyielded regions near the entrance. In addition, the lid-driven cavity problem is solved, which is an often used test for various numerical algorithms and the results are compared to relevant studies for viscoplastic fluids such as those of Syrakos et al. (2013, 2014) and Treskatis et al. (2016). Furthermore, the developed flow in a square duct is examined, similarly to Saramito (2016). Finally, the transient filament stretching of a shear-thinning, yield stress fluid is examined, and the results are compared to those by Balmforth et al. (2010). In all cases, either steady or transient, the algorithm captures the yield surfaces correctly, while maintaining a low computational cost, because the convergence of the method requires only a few (i.e. 5–30) Newton iterations. Based on these extensive tests, PAL is found to be superior combining accuracy and speed to all existing solution methods for viscoplastic fluids. © 2018 Elsevier B.V.},

note = {cited By 13},

keywords = {Augmented Lagrangian method, Bubble rise, Filament, Lid-driven cavity, Papanastasiou regularization; Penalty method, stretching, Viscoplastic fluids},

pubstate = {published},

tppubtype = {article}

}

Computation of viscoplastic fluid flows has always been a challenging task. Viscoplastic models are intrinsically discontinuous at the yielded-unyielded interface, which leads to numerical difficulties, because of the singularity in the Jacobian matrix of the resulting discretized equations. For this reason, several modeling or numerical approaches have been proposed, the most popular being the Papanastasiou regularization (PR) and the Augmented Lagrangian (AL) methods, respectively. Recently, studies on AL methods have focused on developing accelerated algorithms, since the required computational cost of using AL is extremely high. In the present work, a fast converging and efficient algorithm is proposed for tracking the yield surface and predicting the flow field of viscoplastic fluids accurately. The numerical procedure is the Penalized Augmented Lagrangian (PAL) method, which is based on a monolithic Newton solver for AL, where the governing equations of the Lagrange-multiplier tensor for both the rate-of-strain projection and the extra-stress tensors are penalized. To test the efficiency of our algorithm, five benchmark flow-problems with fixed, free and moving boundaries are studied. First, the problem of the steady rise of a bubble in a viscoplastic medium is addressed validating the new algorithm with the findings by Dimakopoulos et al. (2013). Then the entrance flow in a rectangular channel is solved, where a primary unyielded region is found around the centerline in the developed part of the flow and secondary unyielded regions near the entrance. In addition, the lid-driven cavity problem is solved, which is an often used test for various numerical algorithms and the results are compared to relevant studies for viscoplastic fluids such as those of Syrakos et al. (2013, 2014) and Treskatis et al. (2016). Furthermore, the developed flow in a square duct is examined, similarly to Saramito (2016). Finally, the transient filament stretching of a shear-thinning, yield stress fluid is examined, and the results are compared to those by Balmforth et al. (2010). In all cases, either steady or transient, the algorithm captures the yield surfaces correctly, while maintaining a low computational cost, because the convergence of the method requires only a few (i.e. 5–30) Newton iterations. Based on these extensive tests, PAL is found to be superior combining accuracy and speed to all existing solution methods for viscoplastic fluids. © 2018 Elsevier B.V.17. Syrakos, A; Dimakopoulos, Y; Tsamopoulos, J

Theoretical study of the flow in a fluid damper containing high viscosity silicone oil: Effects of shear-thinning and viscoelasticity Journal Article

In: Physics of Fluids, 30 (3), 2018, ISSN: 10706631, (cited By 8).

Abstract | Links | BibTeX | Tags:

@article{Syrakos2018,

title = {Theoretical study of the flow in a fluid damper containing high viscosity silicone oil: Effects of shear-thinning and viscoelasticity},

author = {A Syrakos and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85042218368&doi=10.1063%2f1.5011755&partnerID=40&md5=7f2626f1158b8895ae6f35b83514187f},

doi = {10.1063/1.5011755},

issn = {10706631},

year = {2018},

date = {2018-01-01},

journal = {Physics of Fluids},

volume = {30},

number = {3},

abstract = {The flow inside a fluid damper where a piston reciprocates sinusoidally inside an outer casing containing high-viscosity silicone oil is simulated using a finite volume method, at various excitation frequencies. The oil is modeled by the Carreau-Yasuda (CY) and Phan-Thien and Tanner (PTT) constitutive equations. Both models account for shear-thinning, but only the PTT model accounts for elasticity. The CY and other generalised Newtonian models have been previously used in theoretical studies of fluid dampers, but the present study is the first to perform full two-dimensional (axisymmetric) simulations employing a viscoelastic constitutive equation. It is found that the CY and PTT predictions are similar when the excitation frequency is low, but at medium and higher frequencies, the CY model fails to describe important phenomena that are predicted by the PTT model and observed in experimental studies found in the literature, such as the hysteresis of the force-displacement and force-velocity loops. Elastic effects are quantified by applying a decomposition of the damper force into elastic and viscous components, inspired from large amplitude oscillatory shear theory. The CY model also overestimates the damper force relative to the PTT model because it underpredicts the flow development length inside the piston-cylinder gap. It is thus concluded that (a) fluid elasticity must be accounted for and (b) theoretical approaches that rely on the assumption of one-dimensional flow in the piston-cylinder gap are of limited accuracy, even if they account for fluid viscoelasticity. The consequences of using lower-viscosity silicone oil are also briefly examined. © 2018 Author(s).},

note = {cited By 8},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

The flow inside a fluid damper where a piston reciprocates sinusoidally inside an outer casing containing high-viscosity silicone oil is simulated using a finite volume method, at various excitation frequencies. The oil is modeled by the Carreau-Yasuda (CY) and Phan-Thien and Tanner (PTT) constitutive equations. Both models account for shear-thinning, but only the PTT model accounts for elasticity. The CY and other generalised Newtonian models have been previously used in theoretical studies of fluid dampers, but the present study is the first to perform full two-dimensional (axisymmetric) simulations employing a viscoelastic constitutive equation. It is found that the CY and PTT predictions are similar when the excitation frequency is low, but at medium and higher frequencies, the CY model fails to describe important phenomena that are predicted by the PTT model and observed in experimental studies found in the literature, such as the hysteresis of the force-displacement and force-velocity loops. Elastic effects are quantified by applying a decomposition of the damper force into elastic and viscous components, inspired from large amplitude oscillatory shear theory. The CY model also overestimates the damper force relative to the PTT model because it underpredicts the flow development length inside the piston-cylinder gap. It is thus concluded that (a) fluid elasticity must be accounted for and (b) theoretical approaches that rely on the assumption of one-dimensional flow in the piston-cylinder gap are of limited accuracy, even if they account for fluid viscoelasticity. The consequences of using lower-viscosity silicone oil are also briefly examined. © 2018 Author(s).18. Varchanis, S; Dimakopoulos, Y; Tsamopoulos, J

Evaluation of tube models for linear entangled polymers in simple and complex flows Journal Article

In: Journal of Rheology, 62 (1), pp. 25-47, 2018, ISSN: 01486055, (cited By 9).

Abstract | Links | BibTeX | Tags:

@article{Varchanis201825,

title = {Evaluation of tube models for linear entangled polymers in simple and complex flows},

author = {S Varchanis and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85032919948&doi=10.1122%2f1.5009197&partnerID=40&md5=f489419839c6a0f33febeb740be45b8b},

doi = {10.1122/1.5009197},

issn = {01486055},

year = {2018},

date = {2018-01-01},

journal = {Journal of Rheology},

volume = {62},

number = {1},

pages = {25-47},

abstract = {We present a systematic analysis of the predictions of two tube-theory based constitutive models: Marrucci and Ianniruberto and Rolie-Poly models. These models are tested in their single-mode form in rheometric flows and in their multimode form in transient, one-dimensional channel flow and steady, two-dimensional, contraction-expansion slit flow. Monodisperse and polydisperse polymers are considered, respectively. As these models predict infinite elongational viscosity, a finite chain extensibility factor is necessary to obtain physically meaningful results in uniaxial extension. A thorough investigation of Warner and Cohen nonlinear spring laws revealed that the latter law may lead to a nonphysical solution multiplicity, where two stable solutions, with a positive definite conformation tensor, arise. All the numerical results are compared with experimental observations and the predictions of Giesekus and Phan-Thien and Tanner models. Characteristic features measured experimentally in the benchmark flows are described well by all models although the tube-theory models perform, in general, more satisfactorily with respect to both the rheological data and the inhomogeneous flow data. © 2017 The Society of Rheology.},

note = {cited By 9},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

We present a systematic analysis of the predictions of two tube-theory based constitutive models: Marrucci and Ianniruberto and Rolie-Poly models. These models are tested in their single-mode form in rheometric flows and in their multimode form in transient, one-dimensional channel flow and steady, two-dimensional, contraction-expansion slit flow. Monodisperse and polydisperse polymers are considered, respectively. As these models predict infinite elongational viscosity, a finite chain extensibility factor is necessary to obtain physically meaningful results in uniaxial extension. A thorough investigation of Warner and Cohen nonlinear spring laws revealed that the latter law may lead to a nonphysical solution multiplicity, where two stable solutions, with a positive definite conformation tensor, arise. All the numerical results are compared with experimental observations and the predictions of Giesekus and Phan-Thien and Tanner models. Characteristic features measured experimentally in the benchmark flows are described well by all models although the tube-theory models perform, in general, more satisfactorily with respect to both the rheological data and the inhomogeneous flow data. © 2017 The Society of Rheology.19. Varchanis, S; Dimakopoulos, Y; Wagner, C; Tsamopoulos, J

How viscoelastic is human blood plasma? Journal Article

In: Soft Matter, 14 (21), pp. 4238-4251, 2018, ISSN: 1744683X, (cited By 14).

Abstract | Links | BibTeX | Tags:

@article{Varchanis20184238,

title = {How viscoelastic is human blood plasma?},

author = {S Varchanis and Y Dimakopoulos and C Wagner and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85047921796&doi=10.1039%2fc8sm00061a&partnerID=40&md5=0dcc502f7f8b818d3120dc4c87db6720},

doi = {10.1039/c8sm00061a},

issn = {1744683X},

year = {2018},

date = {2018-01-01},

journal = {Soft Matter},

volume = {14},

number = {21},

pages = {4238-4251},

abstract = {Blood plasma has been considered a Newtonian fluid for decades. Recent experiments (Brust et al., Phys. Rev. Lett., 2013, 110) revealed that blood plasma has a pronounced viscoelastic behavior. This claim was based on purely elastic effects observed in the collapse of a thin plasma filament and the fast flow of plasma inside a contraction-expansion microchannel. However, due to the fact that plasma is a solution with very low viscosity, conventional rotational rheometers are not able to stretch the proteins effectively and thus, provide information about the viscoelastic properties of plasma. Using computational rheology and a molecular-based constitutive model, we predict accurately the rheological response of human blood plasma in strong extensional and constriction complex flows. The complete rheological characterization of plasma yields the first quantitative estimation of its viscoelastic properties in shear and extensional flows. We find that although plasma is characterized by a spectrum of ultra-short relaxation times (on the order of 10-3-10-5 s), its elastic nature dominates in flows that feature high shear and extensional rates, such as blood flow in microvessels. We show that plasma exhibits intense strain hardening when exposed to extensional deformations due to the stretch of the proteins in its bulk. In addition, using simple theoretical considerations we propose fibrinogen as the main candidate that attributes elasticity to plasma. These findings confirm that human blood plasma features bulk viscoelasticity and indicate that this non-Newtonian response should be seriously taken into consideration when examining whole blood flow. ©2018 The Royal Society of Chemistry.},

note = {cited By 14},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

Blood plasma has been considered a Newtonian fluid for decades. Recent experiments (Brust et al., Phys. Rev. Lett., 2013, 110) revealed that blood plasma has a pronounced viscoelastic behavior. This claim was based on purely elastic effects observed in the collapse of a thin plasma filament and the fast flow of plasma inside a contraction-expansion microchannel. However, due to the fact that plasma is a solution with very low viscosity, conventional rotational rheometers are not able to stretch the proteins effectively and thus, provide information about the viscoelastic properties of plasma. Using computational rheology and a molecular-based constitutive model, we predict accurately the rheological response of human blood plasma in strong extensional and constriction complex flows. The complete rheological characterization of plasma yields the first quantitative estimation of its viscoelastic properties in shear and extensional flows. We find that although plasma is characterized by a spectrum of ultra-short relaxation times (on the order of 10-3-10-5 s), its elastic nature dominates in flows that feature high shear and extensional rates, such as blood flow in microvessels. We show that plasma exhibits intense strain hardening when exposed to extensional deformations due to the stretch of the proteins in its bulk. In addition, using simple theoretical considerations we propose fibrinogen as the main candidate that attributes elasticity to plasma. These findings confirm that human blood plasma features bulk viscoelasticity and indicate that this non-Newtonian response should be seriously taken into consideration when examining whole blood flow. ©2018 The Royal Society of Chemistry.20. Varchanis, S; Dimakopoulos, Y; Tsamopoulos, J

Steady film flow over a substrate with rectangular trenches forming air inclusions Journal Article

In: Physical Review Fluids, 2 (12), 2017, ISSN: 2469990X, (cited By 7).

Abstract | Links | BibTeX | Tags:

@article{Varchanis2017,

title = {Steady film flow over a substrate with rectangular trenches forming air inclusions},

author = {S Varchanis and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85040062857&doi=10.1103%2fPhysRevFluids.2.124001&partnerID=40&md5=353814ef50d6f689828fac65eba01629},

doi = {10.1103/PhysRevFluids.2.124001},

issn = {2469990X},

year = {2017},

date = {2017-01-01},

journal = {Physical Review Fluids},

volume = {2},

number = {12},

abstract = {Film flow along an inclined, solid substrate featuring periodic rectangular trenches may either completely wet the trench floor (Wenzel state) or get pinned on the entrance and exit corners of the trench (Cassie state) or assume other configurations in between these two extremes. Such intermediate configurations are examined in the present study. They are bounded by a second gas-liquid interface inside the trench, which adheres to its walls forming two three-phase contact lines, and encloses a different amount of air under different physical conditions. The Galerkin finite-element method is used to solve the Navier-Stokes equations in a physical domain, which is adaptively remeshed. Multiple steady solutions, connected by turning points and transcritical bifurcations as well as isolated solution branches, are revealed by pseudo-arc-length continuation. Two possible configurations of a single air inclusion inside the trench are examined: the inclusion either surrounds the upstream convex corner or is attached to the upstream trench wall. The penetration of the liquid inside the trench is enhanced primarily by increasing either the wettability of the substrate or capillary over viscous forces or by decreasing the flow rate. Flow hysteresis may occur when the liquid wetting of the upstream wall decreases abruptly, leading to drastically different flow patterns for the same parameter values. The interplay of inertia, viscous, gravity, and capillary forces along with substrate wettability determines the volume of the air encapsulated in the trench and the extent of deformation of the outer free surface. © 2017 American Physical Society.},

note = {cited By 7},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

Film flow along an inclined, solid substrate featuring periodic rectangular trenches may either completely wet the trench floor (Wenzel state) or get pinned on the entrance and exit corners of the trench (Cassie state) or assume other configurations in between these two extremes. Such intermediate configurations are examined in the present study. They are bounded by a second gas-liquid interface inside the trench, which adheres to its walls forming two three-phase contact lines, and encloses a different amount of air under different physical conditions. The Galerkin finite-element method is used to solve the Navier-Stokes equations in a physical domain, which is adaptively remeshed. Multiple steady solutions, connected by turning points and transcritical bifurcations as well as isolated solution branches, are revealed by pseudo-arc-length continuation. Two possible configurations of a single air inclusion inside the trench are examined: the inclusion either surrounds the upstream convex corner or is attached to the upstream trench wall. The penetration of the liquid inside the trench is enhanced primarily by increasing either the wettability of the substrate or capillary over viscous forces or by decreasing the flow rate. Flow hysteresis may occur when the liquid wetting of the upstream wall decreases abruptly, leading to drastically different flow patterns for the same parameter values. The interplay of inertia, viscous, gravity, and capillary forces along with substrate wettability determines the volume of the air encapsulated in the trench and the extent of deformation of the outer free surface. © 2017 American Physical Society.