Shape evolution and scaling analysis of soluble cylinders in dissolutive flow

Abstract

The evolution of solid shapes in dissolutive flows is studied using molecular dynamics simulations. The final self-similar structures of the solid are distinct under the convection- and diffusion-dominated conditions. Introducing a dimensionless number, Ds, allows characterizing the relative influence of convection and diffusion on the final structure. When convection dominates, the convergent shape of the solid is approximately triangular, while the solid is more likely to be sculptured into a cylinder when diffusion dominates. There is a critical value of Ds that controls the transition between convection- and diffusion-dominated cases. However, the convergent shapes are insensitive to their initial states due to the solid assembly at the nanoscale. Furthermore, we discuss the influences of solid dissolution and assembly on the liquid density along different directions and provide fitting curves for the theoretical density distribution as explained from the Smoluchowski equation. Finally, the scaling laws are constructed to quantify the solid evolution, which can analytically forecast the shape evolution under different dominant factors. We believe that these findings provide theoretical support for structure optimization and industrial applications.