Cavitation in lubrication. Part 1. On boundary conditions and cavity—fluid interfaces

Abstract

The flow of viscous lubricant in narrow gaps is considered for those geometries in which cavitation arises. A detailed review is presented of those boundary conditions which have been proposed for terminating the lubrication regime (i.e. those valid where the cavity forms). Finally it is shown that a uniform cavity-fluid interface remains stable to small disturbances provided that \[ \frac{d}{dx}\left(P+\frac{T}{r}\right) < 0, \] in which T and r represent the surface tension of the fluid and the radius of curvature of the interface respectively whilst dP/dx is the gradient of fluid pressure immediately upstream of the interface.

Use of a finite‐element method to interpret rheological effects in blade coating

“…Boundary conditions at the ends of the blade are not at all obvious and have been the subject of debate for a number of similar converging-diverging flow problems involving free surfaces (Coyne and Elrod, 1970;Birkoff and Hayes, 1963;Savage, 1977;Taylor, 1974). In our previous lubrication analysis (Sullivan and Middleman, 1986), we specified ambient pressure at both ends of the blade.…”

The screen printing of a power-law fluid

“…In the immediate vicinity of the meniscus, the flow is essentially two-dimensional and the Stokes equations must be solved. In light of this problem, Coyne and Elrod [27] attempted an approximate solution near the meniscus, and a review of their work and a number of other proposed boundary conditions for the meniscus is given by Savage [28].…”

Effects of shear thinning on forward roll coating

“…Importantly for forward mode roll coating where meniscus stability can be an issue the stability of the coating bead is analysed by examining the restoring forces resulting from a perturbation in meniscus location [25].…”

“…The small disturbance stability of the downstream meniscus was analysed using the stability criteria of Pitts & Greiller [19] and Savage [25]. The analysis examines the forces acting on the meniscus when subjected to a small perturbation.…”