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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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Journal ArticleDOI
TL;DR: In this article, the authors compared the asymptotic solutions based on lubrication theory in the gap with the macroscopic flow outside of the gap between the cylinders in a Bingham fluid, and showed that the external flow can have a large effect on the pressure profile within the gap and the resulting lubrication force on the cylinders.
Abstract: Direct numerical simulations of closely interacting infinite circular cylinders in a Bingham fluid are presented, and results compared to asymptotic solutions based on lubrication theory in the gap Unlike for a Newtonian fluid, the macroscopic flow outside of the gap between the cylinders is shown to have a large effect on the pressure profile within the gap and the resulting lubrication force on the cylinders The presented results indicate that the asymptotic lubrication solution can be used to predict the lubrication pressure only if the surrounding viscoplastic matrix is yielded by a macroscopic flow This has implications for the use of sub-grid-scale lubrication models in simulations of non-colloidal particulate suspensions in viscoplastic fluids

15 citations

Journal ArticleDOI
TL;DR: In this paper, the authors extended the lubrication theory for the flow of viscoelastic fluids of the Oldroyd-B type inside thin cavities, and applied it to transient free-surface-flow problems inside a thin (two-dimensional) channel.
Abstract: The lubrication theory is extended for the flow of viscoelastic fluids of the Oldroyd-B type inside thin cavities. The formulation accounts for nonlinearities stemming from inertia effects in the momentum conservation equation, and the upper-convected terms in the constitutive equation. The theory is applied to transient free-surface-flow problems inside a thin (two-dimensional) channel. The influence of fluid elasticity (Deborah number) and retardation on the shape and evolution of the front is examined. It is found that the mean position of the front is dictated by a nonlinear equation of second order. The multiple-scale method is applied to obtain an approximate solution at small Deborah number. Given the existence of a singularity in the limit De → 0, regular perturbation theory cannot be applied. Comparison with exact (numerical) solution indicates a wide range of validity for the multiple-scale results, which is not necessarily restricted to weakly elastic flows.

15 citations

Journal ArticleDOI
TL;DR: In this paper, the authors apply lubrication theory to advance fundamental understanding of the important limiting case of spreading of a planar droplet on a linear viscoelastic solid, and derive nonlinear evolution equations describing how the liquid-air and liquid-solid interfaces evolve in space and time.
Abstract: The spreading of droplets on soft solid substrates is relevant to applications such as tumor biophysics and controlled droplet condensation and evaporation. In this paper, we apply lubrication theory to advance fundamental understanding of the important limiting case of spreading of a planar droplet on a linear viscoelastic solid. The contact-line region is described by a disjoining-pressure/precursor-film approach, and nonlinear evolution equations describing how the liquid-air and liquid-solid interfaces evolve in space and time are derived and solved numerically. Parametric studies are conducted to investigate the effects of solid thickness, viscosity, shear modulus, and wettability on droplet spreading. Softer substrates are found to speed up spreading for perfectly wetting droplets but slow down spreading for partially wetting droplets. For perfectly wetting droplets, faster spreading is a result of more liquid being pumped toward the contact line due to a larger liquid-film thickness there arising from the repulsive component of the disjoining pressure. In contrast, slower spreading of partially wetting droplets is a result of less liquid being pumped toward the contact line due to a smaller liquid-film thickness there arising from the attractive component of the disjoining pressure. The model predictions for partially wetting droplets are qualitatively consistent with experimental observations, and allow us to disentangle the effects of substrate deformability and wettability on droplet spreading. Due to its systematic formulation, our model can readily be extended to more complex situations involving multiple droplets, substrate inclination, and droplet phase changes.

15 citations

Journal ArticleDOI
TL;DR: In this paper, the effect of wall slip on the squeeze flow of a power-law fluid between two rigid spherical particles has been examined based on the Reynolds lubrication theory, and it is shown that the viscous force arising from the squeezing flow with wall slip may be resolved to the noslip solution by introducing a slip correction coefficient.
Abstract: The effect of wall slip on the squeeze flow of a power-law fluid between two rigid spherical particles has been examined based on the Reynolds lubrication theory. It is shown that the viscous force arising from the squeeze flow with wall slip may be resolved to the noslip solution by introducing a slip correction coefficient. An expression for the slip correction coefficient of force is derived which is related to the slip parameter, the flow index and the upper limit of integration. Generally, wall slip results in a reduction in the viscous force. The reduction in the viscous force increases as the flow index increases, suggesting that wall slip has a more profound effect on shear thickening material. However, such reduction decreases as the upper limit of integration increases from finite liquid bridges to fully immersed systems. The reduction in the viscous force also increases as the slip parameter increases, which is the expected behaviour.

15 citations

Journal ArticleDOI
TL;DR: In this article, the hydrodynamics of a contact line, no matter whether advancing or receding, can formally reduce to that of a receding one with small interfacial slopes.
Abstract: When a contact line moves with a sufficiently large speed, liquid or gas films can be entrained on a solid depending on the direction of contact-line movement. In this work, the contact-line dynamics in the situation of a generic two-fluid system is investigated. We demonstrate that the hydrodynamics of a contact line, no matter whether advancing or receding, can formally reduce to that of a receding one with small interfacial slopes. Since the latter can be well treated under the classical lubrication approximation, this analogy allows us to derive an asymptotic solution of the interfacial profiles for arbitrary values of contact angle and viscosity ratio. For the dip-coating geometry, we obtain, with no adjustable parameters, an analytical formula for the critical speed of wetting transition, which in particular predicts the onset of both liquid and gas entrainment. Moreover, the present analysis also builds a novel connection between the Cox–Voinov law and classical lubrication theory for moving contact lines.

15 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202325
202265
202155
202062
201970
201864