Thermodynamics of capillary adhesion between rough surfaces

A computational stochastic multiscale methodology for MEMS structures involving adhesive contact

“…inside the range h C the pressure is constant and equal to the Laplace pressure, while outside this range the pressure vanishes. That model is consistent with the assumption of constant pressure [10]. The calculated Laplace pressures and condensing water heights for contact angles ρ 1 = ρ 2 = 0 are illustrated in Fig.…”

“…4(a). In terms of physics, during the separation process, the meniscus geometry varies depending on the competition between evaporation and condensation of water [10]. On the one hand, when the separation is rapid, the volume of meniscus is constant.…”

“…On the other hand, if the separation is slow the radius of meniscus and its water pressure are constant. Between the two extreme cases, the adhesion energy of the latter is reduced by a factor of 2 [10]. In this paper, the assumption that the water pressure and the meniscus radius are constant is applied.…”

“…That assumption respects the condition of the experiments reported in [5,9] which will be used for the experimental comparison in Section 5. With the constant pressure assumption, the pressure inside the meniscus is equal to the Laplace pressure, which is evaluated at a given relative humidity level RH as [10,46] …”

“…In the present work, a stochastic multiscale model is developed to quantify the uncertainty of MEMS stiction. The model is developed with three assumptions: (i) the considered source of the scatter in stiction is the randomness of contacting surfaces; (ii) the contacting surfaces are nominally flat with nanometers roughness; (iii) to model the capillary forces, the constant pressure assumption is applied [10].…”