Material build-up on membrane surfaces is one of the vital challenges faced by Reverse Osmosis operations, leading to many operational and maintenance issues. To date, several modeling studies are dealt with flow behavior and concentration patterns for cross-flow membrane operations. However, the relative fouling propensities of top and bottom membrane surfaces are never addressed in any study for narrow channels filled with ladder-type spacers. In the present work, fluid flow patterns through different spacer configurations are visualized using ANSYS FLUENT by varying the dimensionless filament spacing, L (ratio of top or bottom filament spacing and channel height). Results clearly indicate that the average shear stress values at the top membrane surface are always higher (3-8 times) than that at the bottom membrane surface, but the mass transfer coefficient for the two walls yielded approximately similar average values having low to moderate filament spacings of L <= 3 (SP22 and SP33), indicating similar fouling propensities of membrane surfaces. Further increase in filament spacing with L >= 4 (SP44 and SP66), the average mass transfer coefficient for the top membrane indicated a sharp decline, suggesting high fouling propensity compared to bottom membrane which is not a desirable feature. Among the four spacer arrangements studied, SP44 (with L=4) was found to be the optimal arrangement, yielding moderate pressure drop with nearly equal/higher area weighted values of mass transfer coefficient for the two walls and would lead to lower and equal fouling tendencies for top and bottom membrane surfaces, respectively.