Squeeze film between two spheres in a power-law fluid

An asymptotic solution for the squeezing motion of two nearly touching rigid spheres imbedded in a power-law fluid is presented. It is shown that the resistance to the motion is dominated by the flow in the gap only if m greater than or equal to 1/3, where m is the exponent that relates the shear stress tau and the corresponding strain rate gamma, tau proportional to gamma(m). For m < 1/3, the resistance depends upon details of the flow in the outer region. Also, in this case, the resistance is reduced to such a level that the gap can be closed in a finite time. A connection between the asymptotic solution for two spheres and the asymptotic solution for two nearly touching circular plates is discussed. Also the force-velocity relationships are given for the parallel problems for long cylinders and rectangular plates.