The phenomenon of interfacial motion between two immiscible viscous fluids in the narrow gap between two parallel plates (Hele-Shaw cell) is considered. This flow is currently of interest because of its relation to pattern selection mechanisms and the formation of fractal, structures in a number of physical applications. Attention is concentrated on the fingers that result from the instability when a less-viscous fluid drives a more-viscous one. The status of the problem is reviewed and progress with the thirty-year-old problem of explaining the shape and stability of the fingers is described. The paradoxes and controversies are both mathematical and physical. Theoretical results on the structure and stability of steady shapes are presented for a particular formulation of the boundary conditions at the interface and compared with the experimental phenomenon. Alternative boundary conditions and future approaches are discussed.

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Viscous fingering in Hele-Shaw cells

Study of coating flow by the finite element method

Even though the list of references associated with this review is rather extensive, in no way does it exhaust the vast literature dedicated to the study of cavitation. The intent was to summarize (i) advances in analytical and numerical modelling, (ii) draw attention to the thermodynamic aspects of cavitation, and (iii) do so while reflecting on physical or experimental observations.

Cavitation formation and modelling for fluid film bearings: A review

A model based on the lubrication approximation is put forward for the general case of asymmetric forward roll coating of Newtonian liquids. Two more-rigorous theories are developed, one based on asymptotic expansions for small ratios of gap-to-roll diameter (H0/R), the second on Galerkin/finite-element solutions of the full Navier–Stokes equations over the relevant flow domain. The lubrication model is useful only as an approximation at high capillary numbers . The asymptotic analysis is accurate when H0/R 0.1. The ratio of the film thicknesses on the two rolls is predicted to equal the speed ratio to the 0.65 power, which is confirmed experimentally. The Galerkin/finite-element solutions give full details of the steady two-dimensional free-surface flows including complex recirculation patterns in the film-splitting region, and show how the film-splitting stagnation line becomes a static contact line in the limit as one roll surface becomes stationary.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112086001416

Film-splitting flows in forward roll coating

This Paper presents a survey of important papers pertaining to thermal effects in journal bearings. It includes discussions on theoretical, computation, and experimental works pertaining to heat effects in journal bearings published in various technical journals. Presented at the 4191 Annual Meeting in Toronto, Ontario, Canada May 12–15, 1986

A Review of Thermal Effects in Hydrodynamic Bearings. Part II: Journal Bearings

Conditions for the Rupture of a Lubricating Film. Part I: Theoretical Model

The pressure and flow conditions upstream of the rupture point of a lubricating film are analyzed with the theoretical model derived in Part I. The boundary conditions on the pressure and pressure gradient for use with Reynolds’ equation are developed as functions of a dimensionless parameter involving viscosity, speed, and surface tension. The load-carrying capacity which results from the use of these new boundary conditions does not differ appreciably from that of other boundary conditions in current use, except when the bearing load is extremely light, or when surface tension is large compared with the product of speed and viscosity. A simple experiment was conducted using a cylindrical lens bearing on a rotating oil-lubricated glass plate. Measurements of the bearing load and the location of the film attachment to the lens were in good agreement with the theory.

J. C. Coyne

Papers

Conditions for the Rupture of a Lubricating Film. Part I: Theoretical Model

Conditions for the Rupture of a Lubricating Film—Part II: New Boundary Conditions for Reynolds Equation

An Exact Asymptotic Solution for a Separating Film