Multi-particle collision dynamics modeling of viscoelastic fluids

TL;DR

This paper develops a mesoscopic MPC model for viscoelastic fluids using harmonic dumbbells, enabling efficient simulation of rheological properties and flow behaviors under shear conditions.

Contribution

It introduces a novel MPC algorithm for harmonic dumbbells that allows efficient simulation of viscoelastic fluids with boundary effects and oscillatory shear, matching theoretical predictions.

Findings

Boundary layer thickness proportional to dumbbell size

Zero-shear viscosity depends on spring constant and mean free path

Viscoelastic properties align with Maxwell fluid behavior

Abstract

In order to investigate the rheological properties of viscoelastic fluids by mesoscopic hydrodynamics methods, we develop a multi-particle collision dynamics (MPC) model for a fluid of harmonic dumbbells. The algorithm consists of alternating streaming and collision steps. The advantage of the harmonic interactions is that the integration of the equations of motion in the streaming step can be performed analytically. Therefore, the algorithm is computationally as efficient as the original MPC algorithm for Newtonian fluids. The collision step is the same as in the original MPC method. All particles are confined between two solid walls moving oppositely, so that both steady and oscillatory shear flows can be investigated. Attractive wall potentials are applied to obtain a nearly uniform density everywhere in the simulation box. We find that both in steady and oscillatory shear flow, a boundary layer develops near the wall, with a higher velocity gradient than in the bulk. The thickness of this layer is proportional to the average dumbbell size. We determine the zero-shear viscosities as a function of the spring constant of the dumbbells and the mean free path. For very high shear rates, a very weak ``shear thickening'' behavior is observed. Moreover, storage and loss moduli are calculated in oscillatory shear, which show that the viscoelastic properties at low and moderate frequencies are consistent with a Maxwell fluid behavior. We compare our results with a kinetic theory of dumbbells in solution, and generally find good agreement.