Abstract: Permeable materials, such as perforated grapheme and other two-dimensional materials, can be used in filtration applications. However, there are presently no effective testing apparatuses or techniques to determine if a particular permeable material or other membrane is suitable for a given filtration process. Determining concentration polarization in a cross-flow filtration configuration can be especially difficult. Apparatuses disclosed herein for evaluating permeable materials, particularly perforated two-dimensional materials, in filtration membranes can include a flow channel, such as a lateral flow channel, in fluid communication with a membrane containing a permeable material, a porous substrate supporting the permeable material, and a plurality of fluid collection ports disposed laterally with respect to the flow channel. The fluid collection ports are disposed on the side of the permeable material that is opposite the flow channel. Other membranes can also be evaluated with the described apparatuses.