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.

Effect of small particles on the near-wall dynamics of a large particle in a highly bidisperse colloidal solution.

Abstract: We consider the hydrodynamic effect of small particles on the dynamics of a much larger particle moving normal to a planar wall in a highly bidisperse dilute colloidal suspension of spheres. The gap h0 between the large particle and the wall is assumed to be comparable to the diameter 2a of the smaller particles so there is a length-scale separation between the gap width h0 and the radius of the large particle b⪢h0. We use this length-scale separation to develop a new lubrication theory which takes into account the presence of the smaller particles in the space between the larger particle and the wall. The hydrodynamic effect of the small particles on the motion of the large particle is characterized by the short time (or high frequency) resistance coefficient. We find that for small particle-wall separations h0, the resistance coefficient tends to the asymptotic value corresponding to the large particle moving in a clear suspending fluid. For h0⪢a, the resistance coefficient approaches the lubrication va...

Propagation regimes of buoyancy-driven hydraulic fractures with solidification

Abstract: This study investigates the propagation of a semi-infinite buoyancy-driven hydraulic fracture in situations when the fluid is able to solidify along the crack walls. Such problems occur when hot magma ascends from a chamber due to buoyancy forces and solidifies by interacting with colder rock. In the model, the solidification rate is calculated assuming a one-dimensional heat transfer problem, in which case it becomes mathematically equivalent to Carter’s leak-off model, which is commonly used to describe the fluid leak-off from a hydraulic fracture into a porous rock formation. In order to construct a mathematical model for a buoyancy-driven hydraulic fracture with solidification, the aforementioned thermal problem is combined with (i) linear plane-strain elasticity to ensure equilibrium of the rock surrounding the fracture, (ii) linear elastic fracture mechanics to determine the fracture propagation, (iii) lubrication theory to capture the viscous fluid flow inside the crack and to account for the effect of buoyancy, and (iv) volume balance of the magma. To address the problem, the governing equations are first rewritten in terms of one integral equation with a non-singular kernel, which significantly simplifies the analysis and the procedure for obtaining a numerical solution. The latter solution is shown to obey a multiscale behaviour near the fracture tip that is fully resolved by the numerical scheme. In order to understand the structure of the solution and to quantify the regimes of propagation (and the associated transitions), a thorough analysis of the problem has been performed. Finally, the developments are applied to investigate the non-steady propagation of a buoyancy-driven fracture that is fed by a constant flux.

Interface morphologies in Liquid/liquid dewetting

Abstract: The dynamics and morphology of a liquid polystyrene (PS) film with a thickness on the scale of a hundred nanometer dewetting from a liquid polymethylmethacrylate (PMMA) film is investigated experimentally and theoretically. The polymers considered here are both below their entanglement lengths and have negligible elastic properties. A theoretical model based on viscous Newtonian flow for both polymers is set up from which a system of coupled lubrication equations is derived and solved numerically. A direct comparison of the numerical solution with the experimental findings for the characteristic signatures of the cross-sections of liquid/air and liquid/liquid phase boundaries of the dewetting rims as well as the dewetting rates is performed and discussed for various viscosity ratios of the PS and PMMA layers.

On the uniqueness of the solution of an evolution free boundary problem in theory of lubrication

Abstract: We study an evolution free boundary problem issued from hydrodynamic lubrication. The cavitation phenomenon takes place and is described by the Elrod-Adams model. This model is suggested in preference to the classical variational inequality due to its ability to describe input and output flow. The considered model is governed by the parabolic Reynolds equation and the unknows are the pressure of the lubricant contained in the narrow gap between two circular cylinders and its percentage in an elementary volume. The main result of this paper is the uniqueness of the solution for the parabolic free boundary problem. The proof of this result is based on a comparison principle permitting compare two solutions of the problem when their initial values and their values on the boundary can be compared. Previously, we state a continuity result and some monotonicity properties of the solution.