Using Brownian Dynamics Simulations to Study Elastic Axisymmetric Particles

Brownian dynamics simulations are used to study the rheological properties of dilute suspensions of elastic, axisymmetric particles. During a simulation, a particle's orientation is calculated from a torque balance on the particle. In order to incorporate the effects of elasticity on particle shape and suspension rheology, a force balance on the particle is also calculated. The forces considered are the hydrodynamic force acting on the particle and the elastic force inside of the particle. A coordinate system, having its origin fixed at the center of the particle, is positioned such that the three semiaxes of the particle align with the positive x, y, and z coordinate axes. The normal components of the hydrodynamic force acting on each of the three halves of the particle, symmetric about the three positive coordinate directions, are balanced by the elastic forces inside of the particle acting in the same directions. This balance allows for the shape of the particle to be updated at each time step during a simulation. Also, Lagrange multiplier constraints are utilized in order to ensure that the particle remains axisymmetric and that the particle's volume is constant. Results are presented and compared with those for rigid particles.