Directed random walk in adsorbed monolayer

We study the dynamics of a tracer particle, which performs a totally direct ed random walk in an adsorbed monolayer composed of mobile hard-core partic les undergoing continuous exchanges with a vapour phase. In terms of a mean -field-type approach, based on the decoupling of the tracer-particle-partic le correlation functions into the product of pairwise, tracer-particle corr elations, we determine the density profiles of the monolayer particles, as seen from the stationary moving tracer, and calculate its terminal velocity , V-tr. In the general case the latter is determined implicitly, as the sol ution of a certain transcendental equation. Tn two extreme limits of slow a nd fast monolayer particles diffusion,, we obtain explicit asymptotic forms of V-tr. We show next that the density profile in the monolayer is strongl y inhomogeneous: in front of the stationary moving tracer the local density is higher than the average value, rho(L), and approaches rho(L) as an expo nential function of the distance fi-om the tracer; past the tracer the loca l density is lower than rho(L), and the approach to rho(L). may proceed dif ferently depending on whether the particle number in the monolayer is expli citly conserved or not. In the former case the approach is described by an exponential dependence with a different characteristic length, compared wit h the behaviour in front of the tracer; in the latter case, the density ten ds to rho(L) algebraically. The characteristic lengths and the amplitudes o f the density relaxation functions are also determined explicitly. (C) 1999 Elsevier Science B.V. All rights reserved.