A free boundary problem in hydrodynamic lubrication including surface tension

The aim of this paper is to study hydrodynamic partial lubrication in a journal bearing where the surface tension on the cavity-fluid interface is taken into account. For solving this problem we present two methods. When the surface tension σ is equal to zero we formulate the problem as a variational inequality of elliptic type which can be solved numerically by standard methods. For σ ≽ 0 we formulate the problem as a problem of optimum design. For some values of σ we observe the so called fingering phenomenon which is typical for partial lubrication in a journal bearing and of great engineering interest.