For a given type of rock, the effectiveness of oil recovery through wettability alteration is highly dependent upon the nature of the water-soluble surfactant used. Different mechanisms have been proposed by others to explain wettability alteration by surfactants, and understanding the process is crucial to improve recovery performance. Known mechanisms include (1) surfactant adsorption onto the oil-wet solid surface (coating mechanism) and (2) surfactant molecules complexing with contaminant molecules from the crude oil which are adsorbed on the rock surface so as to strip them off (cleaning mechanism). With the second mechanism, the wettability is reatored by lifting the contaminant layer away, exposing the rock surface which was originally water-wet We previously focused on the numerical modeling of the surfactant coating mechanism (Hammond and Unsal Langmuir 2009, 25, 12591; 2010, 26, 6206.), and we now present a numerical study for the cleaning process. Our new model shows that when a wettability altering surfactant solution is allowed to imbibe spontaneously and acts by the cleaning process, the meniscus advances more rapidly than when there was wettability alteration by coating alone. In our previous model there was a concentration threshold below which imbibition was not possible. That threshold arose because a finite amount of surfactant needs to be adsorbed onto the oil-wet surface to change the contact angle to a water-wet value, but the maximum amount that can be absorbed is limited by the requirement that it be in equilibrium with the surfactant concentration near the meniscus. In the new model, with the cleaning mechanism there is no such threshold, since the cleaning process is driven by the surfactant flux into the vicinity of the advancing meniscus rather than the surfactant concentration there. As long as there are surfactant molecules present in the aqueous solution, the flux is nonzero and molecule pairs can form and alter the wettability by removing the contaminant from the oil-wet surface. However, under very low surfactant concentrations, the process is extremely slow compared to at higher concentrations.