On the squeeze flow of a power-law fluid between rigid spheres

The lubrication solution for the squeeze flow of a power-law fluid between two rigid spherical particles has been investigated. It is shown that the radial pressure distribution converges to zero within the gap between the particles for any value of the flow index, n, provided that the gap separation distance is sufficiently small. However, in the case of the viscous force, it is useful to consider that there are two contributions. The first is developed in the inner region of the gap and corresponds to the lubrication limit. The second is due to an integration of the pressure in the adjacent outer region of the gap. The relative contribution to the force in this outer region increases as n decreases and the separation distance increases. In particular, for flow indices in the range n > 1/3, the contribution in the outer region is negligible if the separation distance is sufficiently small. For n less than or equal to 1/3, this is the dominant term and an accurate prediction of the viscous force is possible only for discrete liquid bridges. Based on "zero" pressure and lubrication criteria for the upper limits of integration, two closed-form solutions have been derived for the viscous force. Both are accurate for n > 0.5 and are in close agreement with a previously published asymptotic solution in the range n > 0.6. For smaller values of n, the asymptotic solution over-estimates the viscous force and predicts a singularity when n approaches 1/3. The two closed-form solutions show continuous and monotonic behaviour for all values of n. Moreover, the solution satisfying the lubrication limit is valid in the range n < 1/3 provided that it is restricted to liquid bridges. (C) 2001 Elsevier Science B.V. All rights reserved.