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.