Abstract: 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.

Cite: Karmushin S.R.
Unsteady Flows of Viscoelastic Fluids in the Johnson–Segalman Model with Multiple Relaxation Times
Journal of Applied Mechanics and Technical Physics. 2026. V.67. N2. P.60–75. DOI: 10.1134/S0021894426700239 WOS Scopus OpenAlex

Original: Karmushin S.R.
Нестационарные течения вязкоупругой жидкости в модели Джонсона–Сигалмана с несколькими временами релаксации
Journal of Applied Mechanics and Technical Physics. 2026. Т.67. №2. С.234-247. DOI: 10.15372/PMTF202515638

Dates:

Submitted:	Mar 20, 2025
Accepted:	Apr 28, 2025
Published print:	Aug 10, 2026

Identifiers:

≡ Web of science:	WOS:001845946800005
≡ Scopus:	2-s2.0-105046944183
≡ OpenAlex:	W7202136534

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