Computational model of interacting suspensions at low Reynolds number in the presence of external fields

This dissertation concentrates on developing and implementing models to predict the motion of rigid suspensions immersed in a viscous fluid. The spheres are subjected to prescribed forces, torques or an imposed linear shear flow. Hydrodynamic as well as electrostatic interactions between the suspensions is investigated. Analytical models are developed for binary interactions in an N-body simulation. Green's functions of Stokes equation, integrated over the surface of the spheres and the boundary patches are utilized to derive these binary interactions. The method accurately accounts for both near-field lubrication and multi-body interactions. A method of boundary effects in sheared concentrated suspensions is implemented to simulate the suspension of spheres confined between two plane walls that translate relative to one another. Periodic boundary conditions are imposed in the stream-wise direction to simulate an infinite suspension. Using linear superposition of forces, it is then possible to derive the net force acting on each particle due to its interaction with all other particles in the suspension via hydrodynamic forces propagated through the fluid medium, and the interaction with the boundaries.; The electrostatic effects are added to the hydrodynamic effects to produce a more faithful simulation of electro-rheological effects. In order to consider multipole and multi-body effects of electro-rheological interactions, a method is implemented that relates the charge and dipole moments of the particles to their potentials and the applied electric field. This method includes both the multi-body far-field and near-field particle interactions and properly accounts for the long-range interactions. Coupled with multi-body hydrodynamics interactions of the particles, the dynamics of the microstructure and its rheological properties can be determined. A series of simulations are conducted to understand the effect of water, concentration of suspensions, electric field frequency on the overall behavior of the fluids. Predictions for computer simulation are qualitatively compared with experimental results featuring both microstructural details and rheological properties of the mixture.