Random walks and moving boundaries: Estimating the penetration of diffusants into dense rubbers

TL;DR

This paper introduces a random walk algorithm for accurately simulating the penetration of diffusants into dense rubbers, effectively capturing the moving boundary behavior and estimating material service life.

Contribution

It proposes a novel decoupled random walk scheme for solving moving boundary problems in rubber diffusion, validated against finite element methods and experimental data.

Findings

The algorithm accurately estimates penetration depth in dense rubbers.

Numerical results match experimental measurements.

The method demonstrates controlled convergence and efficiency.

Abstract

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.