Topic
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.
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TL;DR: In this paper, the authors present both a theoretical model and Stokeslets-mesh-free computations to study the induced flow motions and transport in a 2D microchannel with moving multiple prescribed dynamic collapses (contractions) along the upper wall.
Abstract: We present both a theoretical model and Stokeslets-meshfree computations to study the induced flow motions and transport in a 2D microchannel with moving multiple prescribed dynamic collapses (contractions) along the upper wall. The channel is assumed to have a length that is much greater than its width, i.e., \({(\delta = W/L \ll1)}\) . The wall contractions are set to move with or without time (phase) lags with respect to each other. The theoretical analysis presented is based on the quasi-steady state approximations and the lubrication theory at the low Reynolds number flow regime. The meshfree numerical method is based on the method of fundamental solutions MFS, which uses a set of singularized force elements called Stokeslets to induce the flow motions. The flow field developments and structures induced by these wall contractions are given at various time snapshots during the collapsing cycle. The effect of the wall contractions amplitudes and the phase lags between individual contractions on the flow variables and on the time-averaged net flow over a complete cycle of contractions motions is studied. The present study is motivated by pumping mechanisms observed in insects, physiological systems that use multiple contractions to transport fluid, and the emerging novel microfluidic devices that mimic these systems.
21 citations
TL;DR: It is found that in the lubrication regime, the hydrodynamic resistance is dominated by the local behavior near the asperity, thus the apparent slip length can not always represent the surface roughness.
Abstract: We present a general solution of hydrodynamic resistance of close-approached slippery surfaces with a nanoasperity or a nanobubble as an idealized roughness effect. Based on Reynolds' lubrication theory and a simple slip boundary condition, the pressure distribution in the thin liquid film is predicted analytically and the total hydrodynamic resistance force at limiting cases are formulated in terms of correction functions to the Taylor's equation. Accessible parameters are included for the drainage experiment using atomic force microscope or surface force apparatus. We provide case studies to demonstrate the implication of roughness effect and the possible uncertainties involved in the dynamic force measurement. We found that in the lubrication regime, the hydrodynamic resistance is dominated by the local behavior near the asperity, thus the apparent slip length can not always represent the surface roughness.
21 citations
TL;DR: In this paper, the tangential viscous force models for a pendular liquid bridge used in Discrete Element Method (DEM) in literature are reviewed first, and then new models are proposed by modifying the Xu model (Xu et al., 2005) based on the numerical solution of the pressure equation derived from the lubrication theory.
21 citations
TL;DR: In this article, the steady axisymmetric flow of a thin fluid layer on a rotating disk is studied and it is shown that within the restrictions of lubrication theory the Coriolis force is of the same magnitude as inertia and therefore negligible at leading order.
Abstract: The steady axisymmetric flow of a thin fluid layer on a rotating disk is studied. It is shown that within the restrictions of lubrication theory the Coriolis force is of the same magnitude as inertia and therefore negligible at leading order. In this paper we extend the standard lubrication approximation to provide a correction to the classical relation between film height and flux. The correction terms, caused by the Coriolis force and inertia terms, lead to slightly higher predictions for the film height. This is in keeping with experimental results. It is also shown that recent work incorrectly concludes that the Coriolis force enters the leading order force balance.
21 citations
TL;DR: In this paper, the spreading of a thin, planar drop of fluid that completely wets a solid surface is described, from an initial state in which the drop has a compact shape through its final approach to an infinitesimally thin film extending to infinity.
Abstract: The spreading of a thin, planar drop of fluid that completely wets a solid surface is described, from an initial state in which the drop has a compact shape through its final approach to an infinitesimally thin film extending to infinity. Because the slope of the drop surface is everywhere small, the lubrication approximation can be used, and the effects of capillarity, viscosity, and intermolecular forces are all included. It is shown that a simple model for the intermolecular forces allows a mathematically acceptable solution to be found, without the need to invoke a large‐distance cutoff and without violating the small‐slope requirement of lubrication theory.
21 citations