TY - JOUR

T1 - Hyperbolic models of unsteady flows of viscoelastic fluilds

AU - Liapidevskii, V. Yu

AU - Neverov, V. V.

AU - Karmushin, S. R.

N1 - Liapidevskii, V. Yu. Hyperbolic models of unsteady flows of viscoelastic fluids / V. Yu. Liapidevskii, V. V. Neverov, S. R. Karmushin // Journal of Applied Mechanics and Technical Physics. – 2024. – Vol. 65, No. 5. – P. 895-906. – DOI 10.1134/S0021894424050110.

PY - 2025/4/8

Y1 - 2025/4/8

N2 - ABSTRACT: Unsteady one-dimensional shear flows of a viscoelastic fluid are considered. A general approach is formulated for fluids with several relaxation times, which allows the known models of viscoelastic flows to be presented as evolutionary systems of first-order equations. Conditions of hyperbolicity of flow classes considered are found for the Johnson–Segalman, Giesekus, and Rolie-Poly models. The equations of motion of the viscoelastic fluid are presented in the form of a full nonlinear system of conservation laws. A method of calculating unsteady discontinuous flows within the framework of the models under consideration is proposed. The class of unsteady Couette flows in the gap between the cylinders used in rheological tests is studied numerically. The process of shear banding and its influence on the structure of steady flows are investigated. The numerical results obtained are compared with experimental data.

AB - ABSTRACT: Unsteady one-dimensional shear flows of a viscoelastic fluid are considered. A general approach is formulated for fluids with several relaxation times, which allows the known models of viscoelastic flows to be presented as evolutionary systems of first-order equations. Conditions of hyperbolicity of flow classes considered are found for the Johnson–Segalman, Giesekus, and Rolie-Poly models. The equations of motion of the viscoelastic fluid are presented in the form of a full nonlinear system of conservation laws. A method of calculating unsteady discontinuous flows within the framework of the models under consideration is proposed. The class of unsteady Couette flows in the gap between the cylinders used in rheological tests is studied numerically. The process of shear banding and its influence on the structure of steady flows are investigated. The numerical results obtained are compared with experimental data.

KW - hyperbolic models

KW - rheology

KW - unsteady shear flows

KW - viscoelasticity

UR - https://www.mendeley.com/catalogue/f6f407a4-06ea-30a3-b8d9-efd3754804af/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-105002910476&origin=inward&txGid=10678353cb2cd5adbc8cf4518a494916

UR - https://elibrary.ru/item.asp?id=80616327

U2 - 10.1134/S0021894424050110

DO - 10.1134/S0021894424050110

M3 - Article

VL - 65

SP - 895

EP - 906

JO - Journal of Applied Mechanics and Technical Physics

JF - Journal of Applied Mechanics and Technical Physics

SN - 0021-8944

IS - 5

ER -