Scaling theory of pore growth in a reactive solid

Abstract

Pores in a reactive solid are modeled as a randomly selected fraction p of the bonds of a lattice. Solid bonds adjacent to the open porosity are consumed, leading to the opening of previously closed pores. Just above the pore percolation threshold $p_c$, exact analysis of the Bethe lattice indicates that the solid is consumed in a time $t_0$∼ln[ln(1/ε)], where ε=p-$p_c$. A scaling argument, supported by computational results, gives $t_0$∼ln(1/ε) for finite-dimensional lattices. Aspects of the time-varying morphology of the solid are examined analytically and computationally.