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Showing papers on "Lubrication theory published in 1988"



Journal ArticleDOI
TL;DR: In this paper, the axial variations of the free surface on the coating layers of a rotating cylinder were investigated and it was shown that they are dominated by the same type of balance between capillarity and centripetal acceleration which determines the shape of rotating drops and bubbles in the absence of gravity.
Abstract: A layer of liquid can be supported on the inside or outside of a horizontal rotating cylinder if the viscous forces pulling the liquid around with the cylinder are large enough to overcome the force of gravity. If there are places on the cylinder where the thickness of the layer is larger than a critical value, the excess fluid will run off. For a given maximum thickness the critical condition may be expressed as the minimum speed at which the given layer can be maintained. An approximation of the critical condition using lubrication theory was given by Wallis (1969) and by Deiber & Cerro (1976) for rimming flow and by Moffatt (1977) for coating and rimming flow. Here we address the question of the axial variations of the free surface on the coating layers, and show that they are dominated by the same type of balance between capillarity and centripetal acceleration which determines the shape of rotating drops and bubbles in the absence of gravity. The main results of this paper are the experiments which establish the validity of approximations used to describe the underlying fluid mechanics involved in rimming and coating flows.

70 citations


Journal ArticleDOI
TL;DR: In this paper, an analysis of calendering of inelastic (power-law) and viscoelastic sheets of finite initial thickness has been carried out using a perturbation method based on lubrication theory; an approximate treatment including normal stress effects; and a full numerical analysis using boundary element method.
Abstract: An analysis of calendering of inelastic (power-law) and viscoelastic sheets of finite initial thickness has been carried out using (i) a perturbation method based on lubrication theory; (ii) an approximate treatment including normal stress effects; (ii) a full numerical analysis using the boundary element method. The Phan-Thien-Tanner (PTT) fluid model was used in the viscoelastic analyses. Attention is focused on the separation criterion at the roll exit plane. While it is usual to assume in the inelastic case that separation occurs when the pressure and pressure gradient vanish simultaneously, it is not clear that this is appropriate in the viscoelastic model. The main new results are (a) a method of determining the separation point numerically using the criterion of zero tangential traction; (b) a computation of welling (∼ 5%) after the sheet leaves the nip; (c) a demonstration that the roll force first decreases as Weissenberg number (roll speed) rises, and then increases.

36 citations


01 Jan 1988

19 citations


Journal ArticleDOI
TL;DR: In this paper, a new method of direct numerical calculation for the fluid film lubrication problem is presented by applying the boundary fitted coordinates system to the divergence formulation (DF) method, which makes it possible to deal with an arbitrary configuration of a lubricated surface.
Abstract: A new method of direct numerical calculation for the fluid film lubrication problem is presented in this paper. The present method is derived by applying the boundary fitted coordinates system to the divergence formulation (DF) method. The present method makes it possible to deal with an arbitrary configuration of a lubricated surface, so the disadvantage of the DF method compared with the finite element method is solved. The present method has the following advantages : (1) An arbitrary configuration of a lubricated surface can be calculated. (2) Computer programing is easy. (3) The scale of computer program and cpu time are small, so calculation by a personal computer is possible.

14 citations


Journal ArticleDOI
TL;DR: In this article, the Galerkin finite element method is used to study the steady two-dimensional flow of a Newtonian liquid in the bank of liquid that accumulates on the upstream side of the nip in a forward roll coater.

6 citations


Journal ArticleDOI
TL;DR: In this paper, a modified Reynolds equation for nonlinear viscoelastic fluids based on a nonlinear four-element model was derived, and the effects of visco-elastic behavior on the performance of parallel circular squeeze bearings oscillated sinusoidally was clarified by comparing the theoretical results with the experimental ones.
Abstract: A modified Reynolds equation for nonlinear viscoelastic fluids based on a nonlinear four-element model was derived, and the effects of viscoelastic behavior on the performance of parallel circular squeeze bearings oscillated sinusoidally was clarified by comparing the theoretical results with the experimental ones, in the previous paper. This paper presents two applications of the modified Reynolds equation to fluid film lubrication problems. Firstly, by applying the modified Reynolds equation to a finite-width journal bearing which is oscillated sinusoidally, the analytical procedure for viscoelastic lubrication problems under three-dimensional flows of lubricants is clarified, and good agreement is shown between the experimental results and the theoretical predictions based on the four-element model. Secondly, to clarify the effects of viscoelastic behavior on the performance of parallel circular bearings under irregular squeeze motion, theoretical and experimental studies of parallel circular plates in normal approach are shown.