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Two-fluid kinetic theory for dilute polymer solutions
Shiwani Singh1,2, Ganesh Subramanian2, Santosh Ansumali2
1Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom.
Abstract:
We provide a Boltzmann-type kinetic description for dilute polymer solutions based on two-fluid theory. This Boltzmann-type description uses a quasiequilibrium based relaxation mechanism to model collisions between a polymer dumbbell and a solvent molecule. The model reproduces the desired macroscopic equations for the polymer-solvent mixture. The proposed kinetic scheme leads to a numerical algorithm which is along the lines of the lattice Boltzmann method. Finally, the algorithm is applied to describe the evolution of a perturbed Kolmogorov flow profile, whereby we recover the major elastic effect exhibited by a polymer solution, specifically, the suppression of the original inertial instability.
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