A Novel Brownian Dynamics Simulation Algorithm to Study the Rheological Properties of a Dilute Suspension of Elastic Prolate Spheroidal Particles

Rheological properties are calculated for a dilute suspension of elastic prolate spheroidal particles utilizing a novel Brownian dynamics simulation algorithm to account for the effects of particle elasticity on both the suspension dynamics and stress. From force and torque balances on the system, diffusion equations are derived for the configurational distribution functions for both the internal configurations and orientations of the particles in the suspension. These equations are in the form of Fokker-Planck equations and can be interpreted as stochastic differential equations, which are then integrated forward in time using an Euler integration scheme. The particle elasticity can be modeled in various ways, including: (1.) adding springs along each principal axis of a particle or (2.) specifying a form of the stress tensor for the stress inside of a particle. It is assumed that a particle remains spheroidal in shape and that the stress inside of a particle is uniform for the duration of a simulation. Simulation results are compared to numerical results presented by H. Brenner (1974) for rigid prolate spheroidal particles. Extension of the algorithm to elastic triaxial ellipsoidal particles is also discussed.