Forced and Spontaneous Imbibition of Surfactant Solution into an Oil-Wet Capillary: The Effects of Surfactant Diffusion Ahead of the Advancing Meniscus

A previous paper (Hammond, P.; Unsal, E. Langmuir 2009, 25, 12591-12603) reported a simplified model for the flow of a surfactant solution into an oil-wet capillary. Results were computed by neglecting the spreading of surfactant molecules ahead of the moving oil/water meniscus onto the It surface. We now present a more thorough version of the theory where such spreading is considered. Both spontaneous and forced imbibitions are studied. As the differential pressure across the capillary increases, a slow increase in the meniscus velocity is observed until the capillary threshold pressure is reached. At this point, the pattern changes and the velocity increases dramatically. The surfactant concentration did not have a significant effect on the speed under differential pressures greater than the capillary threshold. For lower pressures, there is a critical surfactant concentration below which the interface was not able to advance into the capillary even under positive differential pressure.