A computational fluid dynamics (CFD) model was used to simulate unsteady fluid flow with mass transfer in two-dimensional narrow channels containing zigzag spacers. A solute with a Schmidt number of 600 dissolving from the wall and channel Reynolds numbers up to 1683 were considered. Time averaging and Fourier analysis were performed to gain insight into the dynamics of the different flow regimes encountered, ranging from steady flow to vortex shedding behind the spacer filaments. The relationship between vortex shedding, pressure drop, and mass-transfer enhancement was explored. It was found that, at a Reynolds number between 526 and 841, the flow becomes unsteady. As the Reynolds number increases, the region of maximum mass transfer moves upstream from the wall opposite the downstream spacer to the region between spacers. The regions of high mass transfer are correlated not only to those of high shear rate but also to those where the fluid flow is toward the wall. Two main causes for mass-transfer enhancement were found: increased wall shear and an inflow of lower concentration fluid into the boundary layer, with the latter dominating unsteady mass-transfer enhancement for membrane filtration of sodium chloride.