The U.S. Bureau of Mines is optimizing the design of an air-sparged hydrocyclone. This report summarizes the initial stage of the project--the prediction of collision efficiencies for use in a comprehensive air-sparged hydrocyclone model. The equations of motion are presented in nondimensional form and solved numerically for a small spherical particle passing around a larger bubble in an infinite fluid under the influence of a strong force field. Collision efficiencies are determined from the calculated particle trajectories for values of stokes' number, k, between 0.01 and 100 and for values of the nondimensional force, w, between 0.0 and 100. These large values of k and w are needed to model high-performance flotation devices like the air-sparged hydrocyclone; solutions for the required k and w values have not appeared in the literature prior to this study. Effects of changes in particle-to-bubble radius ratio are considered for both viscous and potential flows. The results help predict the improved recovery of fine particles when flotation is performed in a strong force field.