A continuum model for non-dense growth

Abstract

We present a continuum model for diffusion-limited non-dense growth. Our approach leads to a set of two coupled partial differential equations which describe the time evolution of the (spherically) averaged aggregation density and concentration of growth units in the liquid phase. For time-independent parameters the solution of the equations yields a constant (non-fractal) aggregation density. The model gives a phenomenological description of non-fractal unstable growth, e.g. non-fractal spherulitic growth, on a macroscopic scale in terms of a minimal number of parameters and can be used in combination with experimental data, such as the front velocity and the width of the growth front, for both a qualitative and quantitative interpretation of the growth process. The analytical solution of the equations in the diffusion-limited regime leads to simple relations involving the aggregation density and the velocity and width of the growth front. This allows for an easy quantitative analysis of experimental data.