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.

Dynamic spreading of droplets containing nanoparticles.

Abstract: Recent experiments and models for the spreading of liquids laden with nanoparticles have demonstrated particle layering at the three-phase contact line; this is associated with the structural component of the disjoining pressure. Effects driven by structural disjoining pressures occur on scales longer than the diameter of a particle, below which other disjoining pressure components such as van der Waals and electrostatic forces are dominant. Motivated by these experimental observations, we investigate the dynamic spreading of a droplet laden with nanoparticles in the presence of structural disjoining pressure effects. We use lubrication theory to derive evolution equations for the interfacial location and the concentration of particles. These equations account for the presence of the structural component of the disjoining pressure for film thicknesses exceeding the diameter of a nanoparticle; below such thicknesses, van der Waals forces are assumed to be operative. The resulting evolution equations, for the particle motion and free surface position, are solved allowing for the viscosity to vary as a function of nanoparticle concentration. The results of our numerical simulations demonstrate qualitative agreement with experimental observations of a "step" emerging from the contact line. The results are also relevant to a wide range of other phenomena involving layering, or terraced spreading of nanodroplets, or stepwise thinning of micellar thin films.

Three-Dimensional Chemical Mechanical Planarization Slurry Flow Model Based on Lubrication Theory

Abstract: A three-dimensional chemical mechanical planarization slurry flow model based upon lubrication theory is developed, utilizing a generalized Reynolds equation that includes pad porosity and bending. The model is used to calculate slurry film thickness and slurry velocity distributions between the wafer and pad, with the minimum slurry film thickness determining the degree of contact between the wafer and pad. The dependence of the removal rate of copper films as a function of applied pressure and velocity agrees well with model predictions. The minimum slurry film thickness is examined over a range of input variables, namely, applied pressure, wafer-pad velocity, wafer radius and curvature, slurry viscosity, and pad porosity and compressibility.

Hydraulic fracturing: Computational modelling

Abstract: This paper presents an efficient algorithm for modelling hydraulic fracturing based on the finite element method. The algorithm is employed for modelling the different coupled non-linear processes that are involved in the problem of hydraulic fracturing. The fluid flow in the fracture is modelled by lubrication theory and the algorithm may allow for a dry zone to form near the fracture tip. Rock deformation can be modelled by plasticity theory for an elastoplastic and dilatant material. A cohesive model based on the softening behaviour of rocks is employed as the propagation criterion. The above processes are linked in a special continuation method based on the volume of injected fluid in the fracture for direct coupling of the fluid-flow with rock deformation and for driving the solution during propagation. Sample results are provided for the problem of hydraulic fracturing during propagation and closure to demonstrate the efficiency of the proposed algorithm.

An elastohydrodynamic theory for the rheology of concentrated suspensions of deformable particles

Abstract: The equations which govern thin films of a Newtonian liquid confined between deformable solid surfaces are applied to the regions of near contact in a concentrated suspension of deformable particles. For the case of slightly deformable elastic particles, one obtains the socalled “elastohydrodynamic” equations of lubrication theory. The appropriate asymptotic solution of these equations yields estimates for the viscosity, of a form proposed earlier by Frankel and Acrivos [1] for rigid particles, as well as a relaxation time for a suspension of near spheres. The present method, which goes beyond the dissipation calculation of Frankel and Acrivos to a derivation of the full stress tensor, yields the same form of dependence of viscosity on particle concentration. However, there is an as yet unexplained difference between the methods in the value of a numerical coefficient determined by the assumed packing of the spheres. While further work is needed on the kinetic theory for fluid suspensions, the methods employed here for the derivation of the stress tensor should have direct utility for certain solid dispersions, where it is possible to specify a priori the particle-packing in the system.

Thermocapillary migration of long bubbles in cylindrical capillary tubes

Abstract: We consider the problem of the migration of a long bubble in a tube with a prescribed axial temperature gradient. The resulting thermocapillary stress moves the bubble toward hotter regions and we are interested in determining the speed of the bubble. Assuming small Peclet, Reynolds, Bond, and capillary numbers, Ca allows the uncoupling of the temperature field from the flow field, the use of creeping flow and lubrication theory, the assumption of axisymmetry, and the use of matched expansions in Ca, respectively. The structure of the solution is that of a constant thickness film bounded by constant curvature cap regions, with transition layers in between. A modified Landau–Levich equation governing the film profile in the transition regions is solved numerically, establishing the relationship between the unknown film thickness and the unknown bubble speed. A global mass conservation relation is then used to complete the solution and relate the bubble speed to the thermophysical properties. The solution i...