Analysis of lubricated squeezing flow
Abstract
A thin film of lowviscosity lubricating liquid between a solid wall and a viscous material reduces shear stress on the latter and tends to make it flow as though it were slipping along the wall. The result when the lubricated material is being squeezed out of the gap between approaching parallel plates is flow more nearly irrotational, or extensional, the more effective the lubricating film on the plates. Two Newtonian analyses of this flow situation are reported. One is an approximate, asymptotic analytical solution for Newtonian lubricating flow in the films and combined mixed flow, shear and extension, in the viscous layer. The second is a full twodimensional axisymmetric solution of the momentum and continuity equations along with the kinematic condition which governs the motion of the interface. Both analyses indicate that there are two limiting flow regimes, depending on the ratio of the thickness of each of the two phases to radius and on the viscosity ratio of the two liquids. In one limit the flow is parallel squeezing and the lubricant layer slowly thins and persists a long time. In the other the lubricant is expelled preferentially. Implications of the results are discussed for rheological characterization of viscoelastic liquids and for prediction of lubricated for autolubricated flows in processing situations.
 Publication:

International Journal for Numerical Methods in Fluids
 Pub Date:
 November 1986
 DOI:
 10.1002/fld.1650061105
 Bibcode:
 1986IJNMF...6..819P
 Keywords:

 LiquidSolid Interfaces;
 Lubrication;
 Solid Surfaces;
 Squeeze Films;
 Asymptotic Methods;
 Isoparametric Finite Elements;
 Newtonian Fluids;
 Rheology;
 Shear Stress;
 Thin Films;
 Viscoelasticity;
 Fluid Mechanics and Heat Transfer