Analysis of lubricated squeezing flow

Abstract

SUMMARYA thin film of low-viscosity 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 ofeach 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 or autolubricated flows in processing situations.

Squeeze flows of apparently lubricated thin films

“…The second of these assumes a correction to the second term of equation 21(c) in the original reference [10] which appears to have been misprinted without a power δ 0 −5 and with the wrong sign on the logarithmic term. As written in the original this is dimensionally inconsistent.…”

“…We can write the results of Papananstasiou et al [10] in terms of the dimensionless units used in the current work. They proposed two limiting results based on the dimensionless group F = ν/ (θ) 2 .…”

“…In a second paper [4] they extended their ideas to the oscillatory behaviour of visco-elastic materials under a constant load. [10] also carried out finite element solutions and then developed approximate analytical solutions based on the two limiting regimes that they observed. The analytical solutions were constructed by assuming velocity fields in both the sample and the lubricant layer to be of the general form of the Stefan solution (i.e.…”

Elongational viscosity by fiber spinning

“…These conditions, presently impossible to produce experimentally for liquids of not so high shear-viscosity, are those achieved in stretching highly viscous melts [24] or in lubricated flows under perfect slip [11,25]. The underlying idea of this work appears to be similar to the recent work by MacKay and Petrie [26], which was developed independently, on apparent elongational viscosity using the fiber-spinning and pure methods.…”

Squeeze flow of a nonconstant-viscosity fluid

“…Most experiments have employed either a constant squeeze velocity [9] or constant squeeze force [10][11][12][13]. Recently, a considerable amount of research has addressed the squeezing flow of materials that do not adhere to the walls (slip or partial-slip boundary conditions), whereupon the kinematics are primarily elongational in nature [14][15][16][17][18][19]. In this work we extend the classical lubrication results to include Newtonian fluids with axial and transverse viscosity distributions.…”