Direct numerical simulation of two-dimensional channel flows of electro-rheological fluids

Direct numerical simulation (DNS) of electro-rheological (ER) fluid flows in two-dimensional (2D) electrode channel has been performed by adopting a combined finite element method (FEM). Hydrodynamic interactions between the particles and the fluid are described by the Navier-Stokes equations for the fluid in combination with the equations of motion for the particles, while the multi-body electrostatic interaction is represented by the point-dipole model. ER effects on the plane channel flow for a given pressure gradient have been studied by varying the Mason number and volume fraction of the particles, and interrogating the motion of the particles in views of the formation of ER chain structures, the fluid velocity profile in the channel, and the shear stress versus the shear rate. As the Mason number decreases and volume fraction increases, the tendency that particles align to form chain structures becomes stronger. The yield stress of the ER fluid increases with the electric field intensity and the particle concentration. The quadratic correlation between the yield stress and the electric field intensity has been extracted from the present direct numerical simulation. Lastly, it has been shown that the yield stress linearly increases with the volume fraction in the intermediate range.