Concentration boundary layer visualization in nanofiltration by holographic interferometry with light deflection correction

Abstract

Light deflection effects in thin concentration boundary layers adjacent to nanofiltration (NF) or reverse osmosis (RO) membranes are an important source of error associated to the measurement of concentration profiles by holographic interferometry (HI). In this work, a numerical method was developed that corrects the light deflection and minimizes this error. A classical HI setup was used to visualize the concentration boundary layer in a NF cell with a rectangular narrow channel (2 mm height and 15 mm width), in laminar flow using a He-Ne laser. Experiments were performed with binary aqueous solutions of K2SO4, glucose and sucrose, for two different concentrations (2 and 4 kg/L) and pressures (5 and 8 bar) and with average velocities ranging from 0.15 to 2.5 cm/s. A ray tracing numerical method was used to simulate the interferogram and the concentration profile was estimated by minimizing the difference between the predicted and experimental interferograms. The concentration profile estimated for each experimental condition was compared with the theoretical one obtained by computational fluid dynamics. The results indicate that light deflection can be neglected if the ratio of the difference of the refractive index between the membrane surface and the bulk of the aqueous solution, Δnbl, to the boundary layer thickness, δ is below 1 m−1. For Δnbl/δ>2 m−1, light deflection correction is required for quantification purposes. HI with light deflection correction can measure concentration profiles in 2D concentration boundary layers with a thickness of the order of 100 μm or higher.