Squeeze-film flow between a curved impermeable bearing and a flat porous bed

Axisymmetric squeeze-film flow in the thin gap between a stationary flat thin porous bed and a curved impermeable bearing moving under a prescribed constant load is analysed. The unsteady Reynolds equation is formulated and solved for the fluid pressure. This solution is used to obtain the time for the minimum fluid layer thickness to reduce to a given value, and, in particular, the finite time for the bearing and the bed to come into contact. The effect of varying the shape of the bearing and the permeability of the layer is investigated, and, in particular, it is found that both the contact time and the fluid pressure behave qualitatively differently for beds with small and large permeabilities. In addition, the paths of fluid particles initially situated in both the fluid layer and the porous bed are calculated. In particular, it is shown that, unlike in the case of a flat bearing, for a curved bearing there are fluid particles, initially situated in the fluid layer, that flow from the fluid layer into the porous bed and then re-emerge into the fluid layer, and the region in which these fluid particles are initially situated is determined.