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: This work calculates the shape of the rim as well as the speed of the front using lubrication theory and employs asymptotic matching between the contact line region, the rim, and the film.
Abstract: Consider a film of viscous liquid covering a solid surface, which it does not wet. If there is an initial hole in the film, the film will retract further, forming a rim of fluid at the receding front. We calculate the shape of the rim as well as the speed of the front using lubrication theory. We employ asymptotic matching between the contact line region, the rim, and the film. Our results are consistent with simple ideas involving dynamic contact angles and permit us to calculate all free parameters of this description, previously unknown
61 citations
TL;DR: In this article, the effect of non-Newtonian viscosity is explored by adopting a purely viscous power-law model, and the lubrication equations are solved by the method of Horowitz and Steidler [1], and predict an increase in coating thickness relative to the Newtonian case.
Abstract: Coating of viscous and viscoelastic liquids is examined both theoretically and experimentally. A rigid blade, accurately positioned over a rotating roll, provides an experimental system in which coating thickness is measured as a function of geometric parameters. A perturbation solution to the Navier—Stokes equations yields a lubrication theory which shows agreement with the data to an extent depending on the specific geometry. The effect of a non-Newtonian viscosity is explored by adopting a purely viscous power-law model. The lubrication equations are solved by the method of Horowitz and Steidler [1], and predict an increase in coating thickness relative to the Newtonian case. Data for viscoelastic fluids show both an increase and a decrease in coating thickness compared with Newtonian liquids depending on the relative magnitude of shear thinning and elastic effects.
61 citations
TL;DR: In this article, the hydrodynamics of the filling of a rectangular mold cavity by a molten polymer is considered in terms of lubrication theory and the relationship of the velocity field to the cavity geometry and temperature dependence of the rheological properties is predicted.
Abstract: The hydrodynamics of the filling of a rectangular mold cavity by a molten polymer is considered in terms of lubrication theory. Both isothermal and nonisothermal mold filling are analyzed. The relationship of the velocity field to the cavity geometry and temperature dependence of the rheological properties is predicted. Increasing the activation energy of viscous flow increases the tendency for channeling of melt through the center of the cavity. The results are compared to the experimental observations of our previous studies.
60 citations
TL;DR: The evaporation of sessile multi-component droplets is modeled with an axisymmetic finite element method and results are compared with corresponding results of aubrication theory model, showing that the application of lubrication theory can cause considerable errors.
60 citations
TL;DR: In this article, a more general class of similarity solutions is considered, and a transformation is identified reducing the governing partial differential equations to a set of nonlinear ordinary differential equations, the solutions of which correspond to integral curves in a two-dimensional phase plane.
Abstract: Consider a dilute, insoluble surfactant monolayer on the free surface of a thin viscous film. A gradient in surfactant concentration generates a gradient in surface tension, driving a flow that redistributes the surfactant so that these gradients decay. The nonlinear evolution equations governing such flows, derived using lubrication theory, have previously been shown to admit a set of simple similarity solutions representing the spreading of a monolayer over an uncontaminated interface. Here, a much more general class of similarity solutions is considered, and a transformation is identified reducing the governing partial differential equations to a set of nonlinear ordinary differential equations, the solutions of which correspond to integral curves in a two‐dimensional phase plane. This allows the construction of solutions to a wide range of problems. Many new solutions are revealed, including one that cannot be determined by simpler techniques, namely the closing of an axisymmetric hole in a monolayer,...
60 citations