Free surface effects in squeeze flow of Bingham plastics

New results for the squeeze flow of Bingham plastics show the shape of the free surface in quasi-steady-state simulations, and its effect on the yielded/unyielded regions and the squeeze force. The present simulation results are obtained for both planar and axisymmetric geometries as in our previous paper A. Matsoukas, E. Mitsoulis, Geometry effects in squeeze flow of Bingham plastics, J. Non-Newtonian Fluid Mech. 109 (2003) 231–240] and for aspect ratios ranging from 0.01 to 1. Bigger aspect ratios produce more free surface movement relative to the disk radius or plate length, but less movement relative to the gap. Planar geometries give more free surface movement than axisymmetric ones. Viscoplasticity serves to reduce the free surface movement and its deformation. In some cases of planar geometries and big aspect ratios, unyielded regions appear at the free surface, while the small unyielded regions near the center of the disks or plates are not affected. Including the free surface in the calculations of the squeeze force adds a small percentage to the values depending on aspect ratio and Bingham number. The previously fitted easy-to-use equations are corrected to account for that effect.