Reverse osmosis (RO) is by far the most widely used membrane desalination process worldwide. The RO process depends on the properties of semi-permeable membranes which allow the separation of water from a salt solution by applying external pressure higher than the osmotic pressure on the seawater. The main problem in membrane separation process is the fouling of the membrane walls, which decreases the permeate flux. Having spacer filaments in the feed channel has been proven to dynamically change the concentration boundary layer and preventing fouling. In this study, computational fluid dynamics (CFD) techniques were used to study the hydrodynamics of feed channels of a desalination membrane filled with spacers in zigzag arrangements and transverse in relation to the flow. Numerical solutions were obtained with FLUENT software for laminar flows. A fully developed laminar flow, quasi-periodically repeating in successive inter-filament regions, was used. Four types of settings were tested with different inter-filament distances in the range of Reynolds numbers between 10 and 300. The results show the effect of the distance between elliptical filaments in the velocity field, streamlines, local and average friction factors, pressure drop and on the shear stress developed in the membrane walls. Further, the decrease in distance between filaments may lead to more active recirculation patterns that may promote mass transfer on the membrane surfaces, despite the decrease in their usable area.