The effect of mass transfer on steady two-dimensional rimming flow

Motivated by applications in rapidly rotating machinery, the standard lubrication model of two-dimensional thin-film flow on the inside of a rotating circular cylinder is adapted in a simple manner to incorporate the effect of mass flux into the free surface of the film. A numerical attack, validated against published results for the zero-mass-flux case, is used to study the case of constant mass fraction with non-zero injection into and extraction from the film, this representing the steady-state operating condition in an aero-engine. It is found that increasing mass flux inhibits the formation of the steep fronts on the film surface, thus reducing the chances of droplets being stripped away from the film when there is a core flow present, and that recirculation zones may be suppressed by an increase in the Bond number, thus reducing the chances of oil degradation in rapidly rotating machinery.