Analysis of contact mixing with boundary and hydrodynamic fluid films considering boundary slippage

An analysis is presented for a micro-contact where boundary and hydrodynamic fluid films simultaneously occur considering boundary slippage appearance at the upper contact surface in the boundary film area. The contact is one-dimensional, composed of two parallel plane surfaces, which are respectively rough rigid with rectangular projection in profile and ideally smooth rigid. In the outlet zone of the contact a boundary film occurs, and in the inlet zone of the contact a conventional hydrodynamic fluid film emerges. In the boundary film area, the film slips at the upper contact surface due to the limited shear stress capacity of the film-contact interface, while the film does not slip at the lower contact surface due to the shear stress capacity of the film-contact interface, which is large enough. In the boundary film area, the viscosity and density of the film are varied across the film thickness due to the film-contact interactions, and their effective values are used in modelling which depends on the boundary film thickness. In the fluid film area, the film does not slip at either of the contact surfaces.