The traditional approach to modeling solid-solid separations is based on solving differential equations for particle concentration profiles. This approach is difficult to generalize when the particle properties, such as size and charge, are random variables. If we view particle trajectories as the ultimate differentiating factor, and the nonsharpness of separation as a result of the existence of various random variables such as the random particle properties, and random velocities caused by such phenomena as hydrodynamic interactions, then the recovery can be modeled as a joint probability of particles reaching a certain separation boundary. It is shown that the probabilistic model is a unified approach for various trajectory-based particle separations including sink-float, froth flotation, and electrostatic separation. We transform the recovery models, which have various forms, to the single-form partition curve model that can simplify the design. The design procedure is reduced to optimally setting two model parameters by adjusting the design and operating variables. (c) 2005 American Institute of Chemical Engineers.