A dynamic mathematical model has been developed to describe microbial desulfurization of coal by Thiobacillus ferrooxidans. The model considers adsorption and desorption of cells on coal particles and microbial oxidation of pyritic sulfur on particle surfaces. The influence of certain parameters, such as microbial growth rate constants, adsorption-description constants, pulp density, coal particle size, initial cell and solid phase substrate concentration on the maximum rate of pyritic sulfur removal, have been elucidated. The maximum rate of pyritic sulfur removal was strongly dependent upon the number of attached cells per coal particle. At sufficiently high initial cell concentrations, the surfaces of coal particles are nearly saturated by the cells and the maximum leaching rate is limited either by total external surface area of coal particles or by the concentration of pyritic sulfur in the coal phase. The maximum volumetric rate of pyritic sulfur removal (mg S/h cm(3) mixture) increases with the pulp density of coal and reaches a saturation level at high pulp densities (e.g. 45%). The maximum rate also increases with decreasing particle diameter in a hyperbolic form. Increases in adsorption coefficient or decreases in the desorption coefficient also result in considerable improvements in this rate. The model can be applied to other systems consisting of suspended solid substrate particles in liquid medium with microbial oxidation occurring on the particle surfaces (e.g., bacterial ore leaching). The results obtained from this model are in good agreement with published experimental data on microbial desulfurization of coal and bacterial ore leaching.