Smoothed particle hydrodynamics simulation of shear-induced powder migration in injection moulding

We present the application of the smoothed particle hydrodynamics (SPH) discretization scheme to Phillips' model for shear-induced particle migration in concentrated suspensions. This model provides an evolution equation for the scalar mean volume fraction of idealized spherical solid particles of equal diameter which is discretized by the SPH formalism. In order to obtain a discrete evolution equation with exact conservation properties we treat in fact the occupied volume of the solid particles as the degree of freedom for the fluid particles. We present simulation results in two- and three-dimensional channel flow. The two-dimensional results serve as a verification by a comparison to analytic solutions. The three-dimensional results are used for a comparison with experimental measurements obtained from computer tomography of injection moulded ceramic microparts. We observe the best agreement of measurements with snapshots of the transient simulation for a ratio D(c)/D(η)=0.1 of the two model parameters.