Reduced description of mixed lubrication

Modelling friction and wear between rough and lubricated surfaces is an important problem of modern technologies. The complexity of the problem is in the necessity of simultaneously solving for elastic deformations of contacting bodies and fluid flow between the bodies. We show that the problem can be considerably reduced in the case when the lubrication layer is so thin that the main contribution to the contact interaction comes from a small part of microcontacts with a distance much smaller than the average distance between the bodies. In this case, it is possible to model the dynamics of lubrication by non-conservative forces between surface elements depending on both the distance and the relative velocity. The possibility of further reduction in the problem by using a one-dimensional system is discussed.