On modeling flow between adjacent surfaces where the fluid is governed by implicit algebraic constitutive relations

Andreas Almqvist; Evgeniya Burtseva; Kumbakonam R. Rajagopal; Peter Wall

Applications of Mathematics (2024)

  • Volume: 69, Issue: 6, page 725-746
  • ISSN: 0862-7940

Abstract

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We consider pressure-driven flow between adjacent surfaces, where the fluid is assumed to have constant density. The main novelty lies in using implicit algebraic constitutive relations to describe the fluid's response to external stimuli, enabling the modeling of fluids whose responses cannot be accurately captured by conventional methods. When the implicit algebraic constitutive relations cannot be solved for the Cauchy stress in terms of the symmetric part of the velocity gradient, the traditional approach of inserting the expression for the Cauchy stress into the equation for the balance of linear momentum to derive the governing equation for the velocity becomes inapplicable. Instead, a non-standard system of first-order equations governs the flow. This system is highly complex, making it important to develop simplified models. Our primary contribution is the development of a framework for achieving this. Additionally, we apply our findings to a fluid that exhibits an S-shaped curve in the shear stress versus shear rate plot, as observed in some colloidal solutions.

How to cite

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Almqvist, Andreas, et al. "On modeling flow between adjacent surfaces where the fluid is governed by implicit algebraic constitutive relations." Applications of Mathematics 69.6 (2024): 725-746. <http://eudml.org/doc/299606>.

@article{Almqvist2024,
abstract = {We consider pressure-driven flow between adjacent surfaces, where the fluid is assumed to have constant density. The main novelty lies in using implicit algebraic constitutive relations to describe the fluid's response to external stimuli, enabling the modeling of fluids whose responses cannot be accurately captured by conventional methods. When the implicit algebraic constitutive relations cannot be solved for the Cauchy stress in terms of the symmetric part of the velocity gradient, the traditional approach of inserting the expression for the Cauchy stress into the equation for the balance of linear momentum to derive the governing equation for the velocity becomes inapplicable. Instead, a non-standard system of first-order equations governs the flow. This system is highly complex, making it important to develop simplified models. Our primary contribution is the development of a framework for achieving this. Additionally, we apply our findings to a fluid that exhibits an S-shaped curve in the shear stress versus shear rate plot, as observed in some colloidal solutions.},
author = {Almqvist, Andreas, Burtseva, Evgeniya, Rajagopal, Kumbakonam R., Wall, Peter},
journal = {Applications of Mathematics},
keywords = {implicit algebraic constitutive relation; flow between adjacent surfaces},
language = {eng},
number = {6},
pages = {725-746},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On modeling flow between adjacent surfaces where the fluid is governed by implicit algebraic constitutive relations},
url = {http://eudml.org/doc/299606},
volume = {69},
year = {2024},
}

TY - JOUR
AU - Almqvist, Andreas
AU - Burtseva, Evgeniya
AU - Rajagopal, Kumbakonam R.
AU - Wall, Peter
TI - On modeling flow between adjacent surfaces where the fluid is governed by implicit algebraic constitutive relations
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 6
SP - 725
EP - 746
AB - We consider pressure-driven flow between adjacent surfaces, where the fluid is assumed to have constant density. The main novelty lies in using implicit algebraic constitutive relations to describe the fluid's response to external stimuli, enabling the modeling of fluids whose responses cannot be accurately captured by conventional methods. When the implicit algebraic constitutive relations cannot be solved for the Cauchy stress in terms of the symmetric part of the velocity gradient, the traditional approach of inserting the expression for the Cauchy stress into the equation for the balance of linear momentum to derive the governing equation for the velocity becomes inapplicable. Instead, a non-standard system of first-order equations governs the flow. This system is highly complex, making it important to develop simplified models. Our primary contribution is the development of a framework for achieving this. Additionally, we apply our findings to a fluid that exhibits an S-shaped curve in the shear stress versus shear rate plot, as observed in some colloidal solutions.
LA - eng
KW - implicit algebraic constitutive relation; flow between adjacent surfaces
UR - http://eudml.org/doc/299606
ER -

References

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