The Langmuir, steric hindrance, and spreading equations were evaluated separately in a mathematical model of protein purification using ion-exchange membranes. The spreading equation provided the best fit to experimental breakthrough curves (BTCs) for a-lactalbumin (ALA) and thyroglobulin (THY), followed by the steric hindrance equation, and finally the Langmuir equation. The intrinsic rate of protein adsorption to the membrane was found to be rate-limiting, whereas effects of liquid-phase mass transfer and flow nonidealities were negligible. An adsorption rate constant that decreased with increasing surface coverage was required to fit BTCs that were sharp initially and then broadened dramatically as the membrane approached saturation. Predictions using the spreading equation agreed with literature reports on the spreading of blood proteins such as fibrinogen on polymer surfaces.