Effect of interfacial air entrapment on the adhesion of bio-inspired mushroom-shaped micro-pillars

Recent theoretical and experimental studies have shown that mushroom shaped micro-pillars exhibit strongly enhanced adhesive performance in comparison to other pillar shapes. However, in the presence of interfacial impurities (e. g. solid particles or air bubbles) the adhesive strength could drastically drop. In this paper we theoretically investigate the effect of the entrapment of micro-bubbles of air at the interface between the mushroom shaped micro-pillar and a rigid substrate on the adhesive performance. We calculate the critical pull-off stress as a function of the initial volume of the entrapped air, and compare these results with those obtained when, instead of air, small external solid particles are entrapped at the interface. Our results show that the presence of entrapped air is more critical since it strongly reduces the suction effect. The critical stress, indeed, is about 35-40% smaller than the value observed in the case of solid particles, thus resulting in a considerable reduction of the adhesive performance of the mushroom shaped pillar.