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We have developed a theory of air leakage at interfaces between two elasticsolids with application to suction cups in contact with randomly roughsurfaces. We present an equation for the airflow in narrow constrictions whichinterpolate between the diffusive and ballistic (Knudsen) air-flow limits. Totest the theory we performed experiments using two different suction cups, madefrom soft polyvinylchloride (PVC), in contact with sandblastedpolymethylmethacrylate (PMMA) plates. We found that the measured time todetatch (lifetime) of suction cups were in good agreement with theory, exceptfor surfaces with the root-mean-square (rms) roughness below $\approx 1 \ {\rm\mu m}$, where diffusion of plasticizer from the PVC to the PMMA surface causedblockage of critical constrictions. Suction cup volume, stiffness and elasticmodulus have a huge influence on the air leakage and hence the failure time ofthe cups. Based on our research we propose an improved biomimetic design ofsuction cups, that could show improved failure times in varying degree ofroughness under dry and wet environments.

Theory for diffusive and ballistic air leakage and its application to suction cups