Fluid Stiction With Mechanical Contact: A Theoretical Model

Published theoretical work about fluid stiction between two separating plates was so far limited to a finite initial gap. It was shown that pressure and force evolution are well described by fluid film lubrication equations if cavitation is taken into account. The practically important case that plate separation starts from a mechanical contact condition was only studied by experiments. They showed that quite substantial negative pressures can occur in the gap for a very short time and that the peak forces are varying strongly even between consecutive experiments with equal test conditions. In this paper two models are presented which complement the Reynolds equations with dynamical bubble evolution equations. Initial gap height, bubble number density, and initial bubble radius are the three unknown parameters of these models. Initial gap height accounts for surface roughness, the two other parameters refer to the bubble nucleation of the fluid in the small roughness indentations of the gap. A first model employs the Rayleigh-Plesset bubble dynamic model. It requires that the bubbles stay small compared to the gap. Results show that its stiction force dynamics is two orders of magnitude faster than experimentally observed and that the bubble size condition is violated. The second model assumes that bubbles span over the whole gap height and that the flow of the liquid between the bubbles is guided by the Reynolds equation. This model can be brought into reasonable agreement with the experiments. Force variation from experiment to experiment can at least in part be reproduced by a random variation of the initial bubble sizes. The model exhibits a kind of boundary layer behavior close to the outer boundary. This layer represents the interaction zone between bubble growth dynamics, pressure distribution due to viscous flow, and the pressure boundary condition.