Dynamics of the conformation tensor in viscoelastic FENE polymer models

A. P. Chupakhin^ab, E. S. Stetsyak^abc, D. S. Chutkov<sup>b

a</sup> Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk, Russia
^b Novosibirsk National Research State University, Novosibirsk, Russia
^c Skolkovo Institute of Science and Technology, Moscow, Russia

Abstract: In this work, the equations for the dynamics of the invariants of the conformational tensor for FENE polymer solution models are derived and integrated. Explicit formulas for the invariants as functions of the time parameter along the trajectory of fluid particles are obtained. The invariants are represented as functions of the Lambert function. A description of the qualitative behavior of the invariants under different regimes is given.

Keywords: FENE polymer equations, Lie derivative, invariants of the conformational tensor, integration of equations.

UDC: 514.8 + 532.5.01

DOI: 10.22363/2413-3639-2025-71-4-686-700