Abstract
An extended lubrication model is proposed by taking into account a larger surface-to-surface distance than that for the Reynolds lubrication theory, and the wall-normal variation of the pressure is related to the longitudinal derivative of the local velocity of the Couette-Poiseuille flow.
Highlights
Dense particulate flows containing large numbers of solid particles [1,2,3,4,5] are common in industrial applications and biological environments, and lubrication plays a crucial role in the interparticle region for determining the global behavior and dissipation of the particulate flows, including jamming transition via a lubrication breakdown [6,7,8,9,10,11]
In our previous work [24], the Reynolds lubrication equation was incorporated into a particulate flow solver for correcting the flow in the interparticle region, and the numerical solution was confirmed to be in good agreement with the results of the analytical and independently conducted numerical studies for eccentric-bearing film flow and fluid-particle interaction problems in a low Reynolds number range with less computational time
In a feasible extended lubrication model for the non-Reynolds regime, pRe is obtained from the Reynolds lubrication equation, and with padj(x, y) determined by Eq (17), the pressure is eventually given by p(x, y) = pRe(x) + padj(x, y)
Summary
Dense particulate flows containing large numbers of solid particles [1,2,3,4,5] are common in industrial applications and biological environments, and lubrication plays a crucial role in the interparticle region for determining the global behavior and dissipation of the particulate flows, including jamming transition via a lubrication breakdown [6,7,8,9,10,11]. In our previous work [24], the Reynolds lubrication equation was incorporated into a particulate flow solver for correcting the flow in the interparticle region, and the numerical solution was confirmed to be in good agreement with the results of the analytical and independently conducted numerical studies (by direct numerical simulation) for eccentric-bearing film flow and fluid-particle interaction problems in a low Reynolds number range with less computational time. Our previous study revealed the limited applicability of the Reynolds lubrication equation to model particle-induced flows due to the strong constraints of ε 1 and ε2Re 1; only a limited configuration satisfies this condition, and in other cases, the variation in the wall-normal direction is non-negligible. The pressure gradient in the surface-normal direction may be non-negligible, and the Reynolds lubrication equation does not describe the correct film flow. To assess the validity of the extended lubrication model, the pressure fields obtained by the present model are compared with analytical and direct-numerical solutions for lubrication flows between moving and stationary walls
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