Anomalous surface diffusion: A numerical study

Abstract

We present a numerical study of bulk-mediated effective surface diffusion at liquid surfaces where surface-active molecules adsorb and desorb on experimental time scales. Adsorbed molecules execute Lévy walks on the interface, each step entailing desorption followed by bulk diffusion and readsorption elsewhere. Our results confirm the predicted anomalous scaling of surface displacement r at times before particles are finally lost to the bulk. Moments grow as 〈rq〉∼tζ(q), where ζ(q)=q for q<1, ζ(q)=(q+1)/2 for q≳1. We have also confirmed that the ‘‘speed’’ c which characterizes the q<1 behavior, r≊ct, is universally related to other observables: c=D/h where D and h are, respectively, the bulk diffusivity and the slope of the equilibrium adsorption isotherm.