Diffusive dissolution of a drop in a capillary

Dissolution of a drop in a cylindrical long capillary filled with a solvent is considered and a one-dimensional analytical solution of the problem is presented. Both the drop and the solvent do not flow. The rate of the drop dissolution, the time of the complete dissolution of the drop, the rate of the concentration front advances and the distance of the concentration front from the drop are calculated as functions of the main physico-chemical parameters: solubility of the drop in the solvent, diffusion coefficient, drop density, etc. The model is used for calculation of the dissolution rate of two typical organic pollutants, n-decane and benzene, which relatively slow dissolve in water. The suggested solution allows calculating the area penetrated by the dissolved organic phase and predicting extends of soil contamination by organic pollutants.