Direct simulation of electrorheological suspensions subjected to spatially nonuniform electric field

A numerical method based on the distributed Lagrange Multiplier method (DLM) [2,8] is developed for direct simulations of electrorheological (ER) liquids subjected to spatially varying electric fields. The flow inside particle boundaries is constrained to be rigid body motion by the distributed Lagrange multiplier method. The point-dipole approximation [6] is used to model the electrostatic forces acting on the polarized particles. The code is verified by performing a convergence study that shows that the results are independent of mesh and time step sizes. In a spatially nonuniform electric field the particles move to the regions where the magnitude of electric field is locally maximum when the particle permittivity is greater than that of the liquid. On the other hand, when the particle permittivity is smaller than that of the liquid the particles move to the regions of local minimum of electric field.