Concentration fields in drying droplets

This paper presents an analytical solution of the diffusion equation on a spherical domain with its surface shrinking linearly with time. The solution is given as a series expansion in confluent hypergeometric functions and is valid for arbitrary ratios of the rate of shrinkage of the surface of the sphere to the diffusion coefficient in the liquid phase. ne description derived allows for a prediction of the morphology of the dried particles, i.e., whether hollow or solid spheres of the dried substance result from the drying process. The field of application of the results is spray drying of solutions of solid substances with very low vapor pressure, e.g., salt solutions. The mathematical functions found may be used as a benchmark for numerical computations.