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.

Non-Newtonian fluid–structure interactions: Static response of a microchannel due to internal flow of a power-law fluid

Abstract: We study fluid–structure interactions (FSIs) in a long and shallow microchannel, conveying a non-Newtonian fluid, at steady state The microchannel has a linearly elastic and compliant top wall, while its three other walls are rigid The fluid flowing inside the microchannel has a shear-dependent viscosity described by the power-law rheological model We employ lubrication theory to solve for the flow problem inside the long and shallow microchannel For the structural problem, we employ two plate theories, namely Kirchhoff–Love theory of thin plates and Reissner–Mindlin first-order shear deformation theory The hydrodynamic pressure couples the flow and deformation problem by acting as a distributed load onto the soft top wall Within our perturbative (lubrication theory) approach, we determine the relationship between the flow rate and the pressure gradient, which is a nonlinear first-order ordinary differential equation for the pressure From the solution of this differential equation, all other quantities of interest in non-Newtonian microchannel FSIs follow Through illustrative examples, we show the effect of FSI coupling strength and the plate thickness on the pressure drop across the microchannel Through direct numerical simulation of non-Newtonian microchannel FSIs using commercial computational engineering tools, we benchmark the prediction from our mathematical theory for the flow rate–pressure drop relation and the structural deformation profile of the top wall In doing so, we also establish the limits of applicability of our perturbative theory

Fingering instabilities in driven thin nematic films

Abstract: Motivated by experimental work (Cazabet et al., unpublished), we consider the possibility of fingering instabilities in thin films of nematic liquid crystals. We use lubrication theory on the flow equations for nematic liquid crystals to derive a simple model describing the evolution of the film height. As far as we are aware, this is the first time such a systematically derived, time-dependent thin film model for nematics has been presented. Simple “leading-order” solutions (depending on only one spatial coordinate) are found for two different flow driving mechanisms: (i) gravity perpendicular to the film and (ii) gravity parallel to the film (capillarity is also included in both cases). The effect of imposing two-dimensional perturbations to these solutions is studied. We find that for case (i) instability is possible, depending on whether or not there is complete wetting (i.e., whether or not the equilibrium contact angle of the droplet with the substrate is zero). For case (ii) we always have instability, as we would expect from the analogous result for Newtonian fluids [Phys. Fluids 8, 460 (1996); Europhys. Lett. 10, 25 (1989)].

Surfactant spreading on a thin weakly viscoelastic film

Abstract: A mathematical model is presented for surfactant-driven thin weakly viscoelastic film flows on a flat, impermeable plane. The Oldroyd-B constitutive relation is used to model the viscoelastic fluid. Lubrication theory and a perturbation expansion in powers of the Weissenberg number (We) are employed, which give rise to non-linear coupled evolution equations governing the transport of insoluble surfactant and thin liquid film thickness. Spreading on a Newtonian film is recovered to leading order and corrections to viscoelasticity are obtained at order We. These equations are solved numerically over a wide range of viscosity ratio (ratio of solvent viscosity to the sum of solvent and polymeric viscosities), pre-existing surfactant level and Peclet number (Pe). The effect of viscoelasticity on surfactant transport and fluid flow is investigated and the mechanisms underlying this effect are explored. Shear stress, streamwise normal stress and the temporal rate of change of extra shear stress generated from gradients in surfactant concentration dominate thin viscoelastic film flows whereas only shear stresses play a role in Newtonian thin film flows. Our results also reveal that, for weak viscoelasticity, the influence of viscosity ratio on the evolution of surfactant concentration and film thickness can be significant and varies considerably, depending on the concentration of pre-existing surfactant and surfactant surface diffusivity.