Reaction-limited sintering in nearly saturated environments

TL;DR

This paper investigates the shape evolution and growth rates of sintered sphere necks under reaction-limited conditions, identifying critical shapes and confirming scaling laws relevant to geological processes.

Contribution

It provides a detailed analysis of neck shape dynamics in reaction-limited sintering, including critical shape determination and validation of a scaling conjecture.

Findings

Identified the critical neck shape separating sintering and dissolution regimes.

Confirmed the scaling conjecture for asymptotic neck shapes.

Analyzed the relevance to sedimentary rock diagenesis.

Abstract

We study the shape and growth rate of necks between sintered spheres with dissolution-precipitation dynamics in the reaction-limited regime. We determine the critical shape that separates those initial neck shapes that can sinter from those that necessarily dissolve, as well as the asymptotic evolving shape of sinters far from the critical shape. We compare our results with past results for the asymptotic neck shape in closely related but more complicated models of surface dynamics; in particular we confirm a scaling conjecture, originally due to Kuczinsky. Finally, we consider the relevance of this problem to the diagenesis of sedimentary rocks and other applications.