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 article, the stability of the interface between two thin leaky dielectric liquid layers bounded between two flat electrodes is considered and a coupled system of evolution equations is derived for the interfacial location and charge density using lubrication theory.
Abstract: The stability of the interface between two thin leaky dielectric liquid layers bounded between two flat electrodes is considered. A coupled system of evolution equations is derived for the interfacial location and charge density using lubrication theory. This system is parametrized by the dielectric constants of the two fluids in addition to ratios of their conductivities, viscosities, and thicknesses. A linear stability analysis is conducted and the behavior of the system in the nonlinear regime is also examined. The system is destabilized by electrical stresses that are resisted by capillarity and modified by viscous dissipation. Our results suggest that decreasing the thickness ratio is destabilizing, giving rise to periodic structures of decreasing wavelength. Decreasing the viscosity ratio was also found to lead to the formation of sharp-edged structures whose vertical extent is virtually equal to the gap width between the electrodes. Similar structures were also determined upon increasing the ratio of the dielectric constants and electric conductivities.
134 citations
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TL;DR: In this article, a model for spreading and sorption of a droplet on a thick porous substrate is derived in the frame of lubrication theory, assuming a discontinuous wetting front separating the saturated from the unsaturated regions.
132 citations
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TL;DR: In this article, the effects of the variation of chemical mechanical planarization (CMP) process parameters on slurry hydrodynamics and removal rate are studied using physically based models.
Abstract: The effects of the variation of chemical mechanical planarization (CMP) process parameters on slurry hydrodynamics and removal rate are studied using physically based models. The two models which are developed to describe and fundamentally understand the CMP process are (i) the lubrication model for slurry flow and ( ii) the mass transport model for material removal. The mass transport model is developed for copper CMP. Conditions for stable operation and reduced wafer scratching are identified from the lu brication model. The mass transport model takes into account the chemical reaction at the wafer surface, the slurry flow hydrodynam ics, and the presence of abrasive particles. The polish rates predicted by the model agree well with those measured experimental ly.
131 citations
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TL;DR: In this paper, an extension of the lattice-Boltzmann equation was proposed to model the forces on two moving solid particles, suspended in a fluid and almost in contact with each other, and the accuracy and robustness of this computational method were demonstrated with several test problems.
Abstract: Computational methods based on the solution of the lattice-Boltzmann equation have been demonstrated to be effective for modeling a variety of fluid flow systems including direct simulation of particles suspended in fluid. Applications to suspended particles, however, have been limited to cases where the gap width between solid particles is much larger than the size of the lattice unit. The present extension of the method removes this limitation and improves the accuracy of the results even when two solid surfaces are near contact. With this extension, the forces on two moving solid particles, suspended in a fluid and almost in contact with each other, are calculated. Results are compared with classical lubrication theory. The accuracy and robustness of this computational method are demonstrated with several test problems.
129 citations
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TL;DR: In this article, a theoretical model for ice growth due to droplets of supercooled fluid impacting on a subzero substrate is presented, which is valid for thin water layers and the Peclet number is small.
Abstract: A theoretical model for ice growth due to droplets of supercooled fluid impacting on a subzero substrate is presented. In cold conditions rime (dry) ice forms and the problem reduces to solving a simple mass balance. In milder conditions glaze (wet) ice forms. The problem is then governed by coupled mass and energy balances, which determine the ice height and water layer thickness. The model is valid for “thin” water layers, such that lubrication theory may be applied and the Peclet number is small; it is applicable to ice accretion on stationary and moving structures. A number of analytical solutions are presented. Two- and three-dimensional numerical schemes are also presented, to solve the water flow equation, these employ a flux-limiting scheme to accurately model the capillary ridge at the leading edge of the flow. The method is then extended to incorporate ice accretion. Numerical results are presented for ice growth and water flow driven by gravity, surface tension, and a constant air shear.
127 citations