Patterned membrane surfaces offer a hydrodynamic approach to mitigating concentration polarization and subsequent surface fouling. However, when subjected to steady crossflow conditions, surface patterns promote particle accumulation in the recirculation zones of cavity-like spaces. In order to resolve this issue, we numerically subject a two-dimensional, patterned membrane surface to a rapidly pulsed crossflow. When combined with cavity-like spaces, such as the valleys of membrane surface patterns, a rapidly pulsed flow generates mixing mechanisms (i.e., the deep sweep and the vortex ejection) and disrupts recirculation zones. In only four pulses, we demonstrate the ability of these mechanisms to remove over half of the particles trapped in recirculation zones via massless particle tracking studies (i.e., numerical integration of the simulated velocity field). 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 that require operational downtime and often involve the use of abrasive chemical agents.