  For certain materials science scenarios arising in rubber technology,
one-dimensional moving boundary problems (MBPs) with kinetic boundary
conditions are capable of unveiling the large-time behavior of the diffusants
penetration front, giving a direct estimate on the service life of the
material. In this paper, we propose a random walk algorithm able to lead to
good numerical approximations of both the concentration profile and the
location of the sharp front. Essentially, the proposed scheme decouples the
target evolution system in two steps: (i) the ordinary differential equation
corresponding to the evaluation of the speed of the moving boundary is solved
via an explicit Euler method, and (ii) the associated diffusion problem is
solved by a random walk method. To verify the correctness of our random walk
algorithm we compare the resulting approximations to results based on a finite
element approach with a controlled convergence rate. Our numerical experiments
recover well penetration depth measurements of an experimental setup targeting
dense rubbers.
