On the Squeeze Flow of a Bingham Fluid Between Two Rigid Spheres

Abstract

Squeeze flow of a Bingham fluid between two rigid spheres was investigated based on Reynolds lubrication theory. This approach predicted that two regions are developed within the gap area—the yield region and the rigid region. Expressions for the thickness of the rigid layer—the pressure distribution, and the resulting squeeze force were derived. Several numerical results are presented that show that there is a small “hard core” of the rigid region at the centerline of the gap. In addition, surrounding this hard core, the yield layer immediately reaches a peak width that reduces gradually outward to a minimum value at the referenced boundary of the fluid domain. Meanwhile, the thickness of the rigid region increases as the yield layer becomes narrower. Comparison of velocity profiles indicates that the yield region results from the fluid shearing. Within the rigid region, the fluid behaves as a “rigid body” flows without shearing. The numerical results for pressure distribution show that it concentrates within a narrow central area, and the peak pressure is always located on the centerline and the main magnitude is concentrated within a narrow central area; therefore, the other area has little effect on the resulting squeeze flow. Finally, a numerical fitting expression with high precision (maximum deviation <6% and average deviation ∼3%) for the squeeze force was proposed in order to implement it into the code for simulation using the Discrete Element Method.