TY - JOUR

T1 - Unsteady Flows of Viscoelastic Fluids in the Johnson–Segalman Model with Multiple Relaxation Times

AU - Karmushin, S. R.

N1 - Karmushin, S.R. Unsteady Flows of Viscoelastic Fluids in the Johnson–Segalman Model with Multiple Relaxation Times. J Appl Mech Tech Phy 67, 234–247 (2026). https://doi.org/10.1134/S0021894426700239 This work was supported by the Russian Science Foundation (project no. 25-21-00216).

PY - 2026/8/10

Y1 - 2026/8/10

N2 - One-dimensional unsteady flows of an incompressible non-Newtonian viscoelastic fluid between parallel plates are considered using the Johnson–Segalman model with multiple relaxation times. A distinctive feature of the model under consideration is its hyperbolicity over a wide range of flow parameters. A general model of this type with relaxation times (modes) is obtained, and a change of variables is made, allowing the model equations to be written in a conservative (divergent) form. A series of calculations of unsteady flows in various regimes is performed, showing the occurrence of the shear banding effect as the mean flow velocity increases. The wall shear stress versus shear rate relation and the flow rate versus pressure gradient relation were obtained for steady plane Couette and Poiseuille flows, respectively. The resulting curves were validated by comparison with several sets of experimental data. The structure of steady solutions exhibiting shear banding, obtained as a numerical limit of unsteady solutions, is investigated. A selection rule is formulated for steady-state solutions that are asymptotically attained in unsteady numerical simulations. The hysteresis phenomenon under cyclic changes in flow velocity is analyzed.

AB - One-dimensional unsteady flows of an incompressible non-Newtonian viscoelastic fluid between parallel plates are considered using the Johnson–Segalman model with multiple relaxation times. A distinctive feature of the model under consideration is its hyperbolicity over a wide range of flow parameters. A general model of this type with relaxation times (modes) is obtained, and a change of variables is made, allowing the model equations to be written in a conservative (divergent) form. A series of calculations of unsteady flows in various regimes is performed, showing the occurrence of the shear banding effect as the mean flow velocity increases. The wall shear stress versus shear rate relation and the flow rate versus pressure gradient relation were obtained for steady plane Couette and Poiseuille flows, respectively. The resulting curves were validated by comparison with several sets of experimental data. The structure of steady solutions exhibiting shear banding, obtained as a numerical limit of unsteady solutions, is investigated. A selection rule is formulated for steady-state solutions that are asymptotically attained in unsteady numerical simulations. The hysteresis phenomenon under cyclic changes in flow velocity is analyzed.

KW - hysteresis

KW - instability

KW - non-Newtonian viscoelastic fluid

KW - nonlinear hyperbolic model

KW - one-dimensional shear flows

KW - relaxation time

KW - rheology

KW - shear banding

KW - неньютоновская вязкоупругая жидкость

KW - реология

KW - нелинейная гиперболическая модель

KW - одномерные сдвиговые течения

KW - неустойчивость

KW - образование полос сдвига

KW - время релаксации

KW - гистерезис

UR - https://www.mendeley.com/catalogue/734b88c5-1cae-3b16-a141-2d26f1f883ec/

UR - https://www.scopus.com/pages/publications/105046944183

U2 - 10.1134/S0021894426700239

DO - 10.1134/S0021894426700239

M3 - Article

VL - 67

SP - 234

EP - 247

JO - Journal of Applied Mechanics and Technical Physics

JF - Journal of Applied Mechanics and Technical Physics

SN - 0021-8944

IS - 2

ER -