Lateral flow membrane microdevices are widely used for chromatographic separation processes and diagnostics. The separation performance of microfluidic lateral membrane devices is determined by mass transfer limitations in the membrane, and in the liquid phase, mass transfer resistance is dependent on the channel dimensions and transport properties of the species separated by the membrane. We present a novel approach based on an active bulk acoustic wave (BAW) mixing method to enhance lateral transport in micromachined silicon devices. BAWs have been previously applied in channels for mixing and trapping cells and particles in single channels, but this is, to the best of our knowledge, the first instance of their application in membrane devices. Our findings demonstrate that optimal resonance is achieved with minimal influence of the pore configuration on the average lateral flow. This has practical implications for the design of microfluidic devices, as the channels connected through porous walls under the acoustic streaming act as 760 µm-wide channels rather than two 375 µm-wide channels in the context of matching the standing pressure wave criteria of the piezoelectric transducer. However, the roughness of the microchannel walls does seem to play a significant role in mixing. A roughened (black silicon) wall results in a threefold increase in average streaming flow in BAW mode, suggesting potential avenues for further optimization.