Convective and diffusional mass transport to an isolated crystal growing from solution., with slow linear interface kinetics, is considered analytically as a generic scaling model. We focus on the interface kinetics which is slow as compared to the diffusion mass transport which is typical of protein crystal growth, Independently, full-scale numerical solutions of transport equations around a cylindrical crystal, at the center of the bottom of a cylindrical cell filled with the solution, are found. The two approaches give results that agree over a wide range of parameters, providing dimensionless relationships that allow predictions of the contribution of convection and diffusion to mass transport. Requirements for microgravity level in Space experiments to achieve diffusional mass transport are estimated on the basis of these relationships. Coefficients of impurity distribution between a growing crystal and its solution, under the influences of convection and diffusion around the crystal, were numerically evaluated as functions of time. The results provide further support for the hypothesis concerning the role of the impurity depletion zone in the purification of a growing crystal. They also reveal that in general, the impurity distribution within the crystal is not homogeneous due to convection. The effects of various factors on growth kinetics and crystal purity are considered. (C) 2002 Published by Elsevier Science B.V.