A new numerical approach of a lubrication free boundary problem

Alvarez, Sixto; Oujja, Rachid

doi:10.1016/s0096-3003(02)00856-1

Cited by 4 publications

(1 citation statement)

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“…Nevertheless, we will see that our results can be compared to their results. Also note that in [3] the authors compare their model to the Elrod-Adams one, which is the reference model in tribology, as cavitation phenomena occur [5,1]. Roughly speaking, the Elrod-Adams model is obtained when the ratio M (which is denoted ε in the reference [3]) tends to 0.…”

Section: Comparison With Previous Workmentioning

confidence: 99%

Steady state solutions for a lubrication multi-fluid flow

Chupin

Grec

2011

Eur. J. Appl. Math

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-In this paper, we describe possible solutions for a stationary flow of two superposed fluids between two close surfaces in relative motion. Physically, this study is within the lubrication framework, in which it is of interest to predict the relative positions of the lubricant and the air in the device. Mathematically, we observe that this problem corresponds to finding the interface between the two fluids, and we prove that it is equivalent to solve some polynomial equation.We solve this equation using an original method of polynomial resolution. First, we check that our results are consistent with previous work. Next, we use this solution to answer some physically relevant questions related to the lubrication setting. For instance, we obtain theoretical and numerical results enabling to predict the apparition of a full film with respect to physical parameters (fluxes, shear velocity, . . . ). In particular, we present a figure giving the number of stationary solutions depending on the physical parameters.Moreover, in the last part, we give some indications for a better understanding of the multi-fluid case.

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Section: Comparison With Previous Workmentioning

confidence: 99%