Lubrication theory

About: Lubrication theory is a research topic. Over the lifetime, 1713 publications have been published within this topic receiving 50261 citations. The topic is also known as: Fluid bearing.

A numerical analysis of calendering

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.

The elastic Landau–Levich problem

Abstract: We study the classical Landau–Levich dip-coating problem in the case where the interface has significant elasticity. One aim of this work is to unravel the effect of surface-adsorbed hydrophobic particles on Landau–Levich flow. Motivated by recent findings (Vella, Aussillous & Mahadevan, Europhys. Lett., vol. 68, 2004, pp. 212–218) that a jammed monolayer of adsorbed particles on a fluid interface makes it respond akin to an elastic solid, we use the Helfrich elasticity model to study the effect of interfacial elasticity on Landau–Levich flow. We define an elasticity number, , which represents the relative strength of viscous forces to elasticity. The main assumptions of the theory are that be small, and that surface tension effects are negligible. The shape of the free surface is formulated as a nonlinear boundary value problem: we develop the solution as an asymptotic expansion in the small parameter and use the method of matched asymptotic expansions to determine the film thickness as a function of . The solution to the shape of the static meniscus is not as straightforward as in the classical Landau–Levich problem, as evaluation of higher-order effects is necessary in order to close the problem. A remarkable aspect of the problem is the occurrence of multiple solutions, and five of these are found numerically. In any event, the film thickness varies as in qualitative agreement with the experiments of Ouriemi & Homsy (Phys. Fluids, 2013, in press).

Motion of a circular cylinder in a viscous liquid between parallel plates

Abstract: The two-dimensional motion of a cylinder in a viscous fluid between two parallel walls of a vertical channel is studied. It is found that when the cylinder moves very closely along one of the channel walls, it always rotates in the direction opposite to that of contact rolling along the nearest wall. When the cylinder is away from the walls, its rotation depends on the Reynolds number of the flow. In this study two numerical methods were used. One is for the unsteady motion of a sedimenting cylinder initially released from a position close to one of the channel walls, where the Navier-Stokes equations are solved for the fluid and Newton's equations of motion are solved for the rigid cylinder. The other method is for the steady flow in which a cylinder is fixed in a uniform flow field where the channel walls are sliding past the cylinder at the speed of the approaching flow, or equivalently a cylinder is moving with a constant velocity in a quiescent fluid. The flow field, the drag, the side force (lift), and the torque experienced by the cylinder are studied in detail. The effects of the cylinder location in the channel, the size of the channel relative to the cylinder diameter, and the Reynolds number of the flow are examined. In the limit when the cylinder is translating very closely along one of the walls, the flow in the gap between the cylinder and the wall is solved analytically using lubrication theory, and the numerical solution in the other region is used to piece together the whole flow field.

Gravitational Drainage of a Tangentially-Immobile Thick Film.

Abstract: We use lubrication theory to derive an evolution equation for the free surface of a draining thick free film with a zero tangential velocity component along the free surface. The films are “thick” because effects that are important in very thin films, such as intermolecular forces, do not play a role in the situation of interest. The evolution equation results from the balance of surface tension, gravity, and dynamic viscosity. Subregions of the film appear and they involve balancing these effects pairwise. Computations are performed on the full evolution equation and for various boundary conditions corresponding to different parts of the film. Matched asymptotics are developed that predict the behavior as the film enters the bath and these agree very well with the computed results. Comparison with experiment is favorable for the rate of decrease of the film thickness.