Membrane filtration is a popular choice in the treatment of wastewater for reuse. However, when used to produce clean water, these devices are subject to concentration polarization and fouling, which inhibit their ability to operate efficiently and provide high-quality permeate streams. Patterned membrane surfaces offer a hydrodynamic approach to mitigating concentration polarization and the surface fouling that follows. However, when subject to a steady feed flow rate, surface patterns generally produce stagnant zones in cavity-like spaces where particulate from the bulk flow recirculates in stationary vortices. To prevent aggregation in these recirculation zones, and therefore the onset of surface fouling, we study a rapidly pulsed feed flow. When combined with cavity-like geometries, such as the valleys present in membrane surface patterns, a rapidly pulsed flow generates mixing mechanisms (i.e., the deep sweep and the vortex ejection) that disrupt otherwise stagnant regions. First, we confirm the existence of these mechanisms, which are typically induced in impermeable cavities at relatively low Reynolds numbers, for near transitional feed Reynolds numbers in permeable cavity spaces via numerical simulation of the flow field. Following this confirmation, we demonstrate the ability of these mechanisms to remove particles trapped in recirculation zones via massless particle tracking studies. The results of this work suggest that when combined with a rapidly pulsed inlet flow, patterned membrane surfaces can not only alleviate concentration polarization and the surface fouling that follows but also reduce the need for traditional cleaning methods, which require operational downtime and often involve the use of abrasive chemical agents.