Membrane liquid desiccant dehumidification is deemed as an advanced alternative to air dehumidification, as its operation can be sustained using low-grade waste heat. Many of the existing studies focused on the development and investigation of the dehumidifiers with different flow patterns and geometries, however, the key factors that dominate the dehumidification process are not clear. Therefore, in this paper, an in-depth scaling and dimensional analysis is carried out to investigate the basic physical process in the membrane liquid desiccant dehumidifier. A cross-flow flat-plate membrane liquid desiccant dehumidifier has been developed and tested. Concurrently, a 2-D computational fluid dynamics (CFD) model has been proposed. The model was converted into a dimensionless form so that the governing dimensionless numbers/groups were identified. The relative importance of these dimensionless numbers was determined. A key finding emerged from this study revealed that the relevant dimensionless numbers that dictate performance in the dehumidifier are Re-a, Re-l, H/L, delta/H, D-vm/D-va and beta. In addition, the heat and mass transfer process is controlled by heat and mass convection, as well as transverse heat conduction and mass diffusion. Finally, a correlation has been judiciously formulated for the dehumidified air temperature and humidity which demonstrated good predictive accuracy within +/- 3.5% and can potentially evolve to become an invaluable tool to predict and optimize the dehumidifier's performance.