Our research derives from the study of a novel principle of mechanical energy loss, called surface dissipation, induced by the dynamic contact angle hysteresis which occurs when a lyophobic liquid is forced to penetrate and then naturally exudes from a mesoporous matrix. Here, the mesoporous matrix is from silica gel modified by linear chains of alkyldimethylchlorosilanes and water is the associated liquid. This new kind of dissipation could be attractive for many applications, e.g., oil-free and environment-friendly absorbers, but the subject remains almost unexplored in the scientific literature. Though the energy loss can be explained by the contact angle hysteresis, its mechanism is not fully understood; it seems to be mainly induced by the surface roughness and its chemical heterogeneity. In this work, silica gel micro-grains are supposed to be obtained by the aggregation of nano-grains, which produces rough mesopores of variable radius. Considering the amorphous silica gel as a distorted crystal of β-tridymite, the minimum diameter of the nano-grains reaches about 1nm. At the boundary of two silica gel nano-grains the maximum angular coating range is determined by the steric hindrance that occurs when the upper parts of the bonded molecules come into contact. Modification of the contact angle and surface energy during the water adsorption/desorption in/from the hydrophobized mesoporous silica gel matrix is evaluated in the nanometer range by employing a generalized Wenzel-Cassie model. Since the contact angle hysteresis has a dissipative effect, the energy loss occurs as the difference of the surface energy in advancing and receding motion of the interface. One finds the optimum diameter of the nano-particles which maximizes the dissipated energy. Such results are useful for the appropriate design of ultrahydrophobic surfaces in general, and for the optimal design of silica gel grains with mesoporous architecture destined to environment-friendly dampers.

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1. Experimental investigation of the dynamic contact angle hysteresis past a solid surface from hydrophobized silica gel