Abstract: The present invention is a method for optimizing operating conditions for yield, purity, or selectivity of target species, and/or processing time for crossflow membrane filtration of target species in feed suspensions. This involves providing as input parameters: size distribution and concentration of particles and solutes in the suspension; suspension pH and temperature; physical and operating properties of membranes, and number and volume of reservoirs. The method also involves determining effective membrane pore size distribution; suspension viscosity, hydrodynamics, and electrostatics; pressure-independent permeation flux of the suspension and cake composition; pressure-independent permeation flux for each particle and overall observed sieving coefficient of each target species through cake deposit and pores; solving mass balance equations for all solutes; and iterating the mass balance equation for each solute at all possible permeation fluxes, thereby optimizing operating conditions.