Stress-gradient induced migration of polymers in complex geometries
We study the flow of a dilute polymer solution in a wavy channel under steady-state flow conditions by employing the non-equilibrium thermodynamics two-fluid model (Mavrantzas-Beris, 1992), allowing for the coupling between polymer concentration and polymer stresses. The resulting highly complex sys...
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nemertes-10889-88292022-09-05T14:03:55Z Stress-gradient induced migration of polymers in complex geometries Μετανάστευση πολυμερούς που προκαλείται από τη βαθμίδα των τάσεων σε σύνθετες γεωμετρίες Τσούκα, Σοφία Τσαμόπουλος, Ιωάννης Τσαμόπουλος, Ιωάννης Δημακόπουλος, Ιωάννης Μαυραντζάς, Βλάσης Τσούκα, Σοφία Polymers Fluid mechanics Computational FEM Viscoelastic Rheology Πολυμερή Ρευστομηχανική Υπολογιστική Πεπερασμένα στοιχεία Ιξωδοελαστικό Ρεολογία 532.51 We study the flow of a dilute polymer solution in a wavy channel under steady-state flow conditions by employing the non-equilibrium thermodynamics two-fluid model (Mavrantzas-Beris, 1992), allowing for the coupling between polymer concentration and polymer stresses. The resulting highly complex system of partial differential equations describing inhomogeneous transport phenomena in the fluid are solved with an efficient implementation of the mixed finite-element method. We present numerical results for polymer concentration, stress, velocity and fluxes of polymer as a function of the non-dimensional parameters of the problem (the Deborah number , the Peclet number , the Reynolds number , the ratio of the solvent viscosity to the total fluid viscosity , and the constriction ratio of the channel width ). We find that the constricted part of the wall is depleted of polymer, when the polymer diffusion length-scale, expressed by the ratio of / , increases. The migration is more pronounced for macromolecules characterized by longer relaxation times, and takes place towards the expanding part of the channel or towards the centerplane. Migration is also enhanced by the width variability of the channel: the more corrugated the channel, the stronger the transfer of polymer to the centerplane. This increases the spatial extent of polymer depletion near the wall or induces a zone of sharp variation in polymer stress and concentration, which moves away from the channel wall, especially in lower polymer concentration. The development of a polymer-depleted layer smooths out the boundary layer which is known to arise with Boger fluids at the walls of such corrugated channels or tubes and gives rise to an “apparent” slip in the constricted section of the wall and to a very low value of the drag force on the wall. When and where boundary layers arise, they scale as (1/De) for the stresses and as (De⁄Pe)^(1⁄3) for the concentration. -- 2015-09-18T11:04:11Z 2015-09-18T11:04:11Z 2015-06-08 Thesis http://hdl.handle.net/10889/8829 en 0 application/pdf |
institution |
UPatras |
collection |
Nemertes |
language |
English |
topic |
Polymers Fluid mechanics Computational FEM Viscoelastic Rheology Πολυμερή Ρευστομηχανική Υπολογιστική Πεπερασμένα στοιχεία Ιξωδοελαστικό Ρεολογία 532.51 |
spellingShingle |
Polymers Fluid mechanics Computational FEM Viscoelastic Rheology Πολυμερή Ρευστομηχανική Υπολογιστική Πεπερασμένα στοιχεία Ιξωδοελαστικό Ρεολογία 532.51 Τσούκα, Σοφία Stress-gradient induced migration of polymers in complex geometries |
description |
We study the flow of a dilute polymer solution in a wavy channel under steady-state flow conditions by employing the non-equilibrium thermodynamics two-fluid model (Mavrantzas-Beris, 1992), allowing for the coupling between polymer concentration and polymer stresses. The resulting highly complex system of partial differential equations describing inhomogeneous transport phenomena in the fluid are solved with an efficient implementation of the mixed finite-element method. We present numerical results for polymer concentration, stress, velocity and fluxes of polymer as a function of the non-dimensional parameters of the problem (the Deborah number , the Peclet number , the Reynolds number , the ratio of the solvent viscosity to the total fluid viscosity , and the constriction ratio of the channel width ). We find that the constricted part of the wall is depleted of polymer, when the polymer diffusion length-scale, expressed by the ratio of / , increases. The migration is more pronounced for macromolecules characterized by longer relaxation times, and takes place towards the expanding part of the channel or towards the centerplane. Migration is also enhanced by the width variability of the channel: the more corrugated the channel, the stronger the transfer of polymer to the centerplane. This increases the spatial extent of polymer depletion near the wall or induces a zone of sharp variation in polymer stress and concentration, which moves away from the channel wall, especially in lower polymer concentration. The development of a polymer-depleted layer smooths out the boundary layer which is known to arise with Boger fluids at the walls of such corrugated channels or tubes and gives rise to an “apparent” slip in the constricted section of the wall and to a very low value of the drag force on the wall. When and where boundary layers arise, they scale as (1/De) for the stresses and as (De⁄Pe)^(1⁄3) for the concentration. |
author2 |
Τσαμόπουλος, Ιωάννης |
author_facet |
Τσαμόπουλος, Ιωάννης Τσούκα, Σοφία |
format |
Thesis |
author |
Τσούκα, Σοφία |
author_sort |
Τσούκα, Σοφία |
title |
Stress-gradient induced migration of polymers in complex geometries |
title_short |
Stress-gradient induced migration of polymers in complex geometries |
title_full |
Stress-gradient induced migration of polymers in complex geometries |
title_fullStr |
Stress-gradient induced migration of polymers in complex geometries |
title_full_unstemmed |
Stress-gradient induced migration of polymers in complex geometries |
title_sort |
stress-gradient induced migration of polymers in complex geometries |
publishDate |
2015 |
url |
http://hdl.handle.net/10889/8829 |
work_keys_str_mv |
AT tsoukasophia stressgradientinducedmigrationofpolymersincomplexgeometries AT tsoukasophia metanasteusēpolymerouspouprokaleitaiapotēbathmidatōntaseōnsesynthetesgeōmetries |
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1771297264805871616 |