  We have developed a theory of air leakage at interfaces between two elastic
solids with application to suction cups in contact with randomly rough
surfaces. We present an equation for the airflow in narrow constrictions which
interpolate between the diffusive and ballistic (Knudsen) air-flow limits. To
test the theory we performed experiments using two different suction cups, made
from soft polyvinylchloride (PVC), in contact with sandblasted
polymethylmethacrylate (PMMA) plates. We found that the measured time to
detatch (lifetime) of suction cups were in good agreement with theory, except
for 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 caused
blockage of critical constrictions. Suction cup volume, stiffness and elastic
modulus have a huge influence on the air leakage and hence the failure time of
the cups. Based on our research we propose an improved biomimetic design of
suction cups, that could show improved failure times in varying degree of
roughness under dry and wet environments.
