TY - JOUR

T1 - On the stability of the plane flow of viscoelastic polymer liquid

AU - Semenko, R. E.

AU - Shukurov, G. N.

PY - 2025

Y1 - 2025

N2 - We have studied the spectral problem for plane Poiseuille-type flow of viscoelastic polymer liquid. The flow was modeled with the equations of rheological Vinogradov–Pokrovskii model. The numerical spectral procedure was used to calculate eigenvalues of the problem and to determine the critical values of parameters where the instability of the flow occurs. It was shown that the critical Reynolds number goes to well-known value of approximately 5772 (that is the critical value for the viscous fluid) while the relaxation time goes to zero. The slight increase of elastic properties of the fluid (or Weissenberg number) leads to rapid increase of critical Reynolds number, while further increase of Weissenberg number destabilizes the flow by pushing the critical Reynolds number to zero. Similar to a number of other rheological models, the Vinogradov–Porkovskii model demonstrates the elastic instability effect, that is the spectral problem has unstable modes that are not a continuation of unstable modes of the viscous newtonean flow.

AB - We have studied the spectral problem for plane Poiseuille-type flow of viscoelastic polymer liquid. The flow was modeled with the equations of rheological Vinogradov–Pokrovskii model. The numerical spectral procedure was used to calculate eigenvalues of the problem and to determine the critical values of parameters where the instability of the flow occurs. It was shown that the critical Reynolds number goes to well-known value of approximately 5772 (that is the critical value for the viscous fluid) while the relaxation time goes to zero. The slight increase of elastic properties of the fluid (or Weissenberg number) leads to rapid increase of critical Reynolds number, while further increase of Weissenberg number destabilizes the flow by pushing the critical Reynolds number to zero. Similar to a number of other rheological models, the Vinogradov–Porkovskii model demonstrates the elastic instability effect, that is the spectral problem has unstable modes that are not a continuation of unstable modes of the viscous newtonean flow.

KW - Poiseuille flow

KW - Vinogradov–Pokrovskii rheological model

KW - spectral problem

UR - https://www.scopus.com/pages/publications/105030085253

UR - https://www.mendeley.com/catalogue/ecc3f046-d344-3771-943d-c083527359b4/

U2 - 10.33048/semi.2025.22.108

DO - 10.33048/semi.2025.22.108

M3 - Article

VL - 22

SP - 1756

EP - 1775

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 2

ER -