Squeeze-flow of a Herschel-Bulkley fluid

Squeeze-flow experiments of a Herschel-Bulkley material between two rigid plates, investigated both experimentally and computationally by Adams et al. (J. Non-Newtonian Fluid Mech. 71 (1997) 41) are compared against an approximate analysis for generalised Newtonian fluids presented by Sherwood and Durban (J. Non-Newtonian Fluid Mech. 62 (1996) 35), for the case in which the interface between the material and the plates is lubricated. The analysis presented here assumes a rigid-viscoplastic material, rather than the elastic-viscoplastic material of Adams et al., but the viscoplastic model for how is identical. However, the shear stress boundary condition at the plates differs from the Coulomb friction law of Adams et al.: the shear stress is here assumed to be a constant fraction of the effective stress land consequently turns out to be independent of position). A simple expression for the total force required to push the plates together is obtained for the case when friction at the plates is small. Agreement between this expression and the experimentally-measured force is good at high strain, though the elastic deformation observed prior to yield is not captured by the rigid-viscoplastic analysis. (C) 1998 Elsevier Science B.V. All rights reserved.