Mathematical modeling of vibratory shear-enhanced nanofiltration in the preconcentration of coffee extracts for soluble coffee manufacturing

A semi-empirical model was applied to evaluate the performance of a vibratory nanofiltration (NF) system, using 150-Da TS80 NF membrane, for the preconcentration of coffee extracts in soluble coffee processing. The effects of transmembrane pressure (TMP), feed concentration, and module vibration on flux enhancement were correlated with membrane surface concentrations and fouling resistances under steady state operation. Vibratory shear thinned the boundary layer and increased the mass transfer coefficient of the solvent (water) by a factor of 3.5. Membrane surface concentrations and fouling resistances reduced by 60% compared with crossflow (CF) NF operation. These reductions enhanced permeate fluxes by about 2–3 times that of CF operation, with low flux decline. Feed concentration and TMP promoted polarization more than the negative effect of vibration. Osmotic pressure resistances were dominant under low feed concentrations and TMP. However, concentration polarization resistances exceeded osmotic pressure resistances as TMP and feed concentrations were increased. Real rejections relative to membrane surface chemical oxygen demand (COD) were above 0.99, indicating the potential of the operation to recover permeate that is reusable for ancillary plant operations. Overall, the experimental and theoretical permeate fluxes and CODs were in reasonable agreement, indicating the reliability of the model. Practical Applications: Vibratory membrane processes alleviate the issues on membrane fouling that is advantageous when integrated into food and beverage processes. Its application as a coffee extract preconcentration alternative to thermal evaporation opens opportunities for sustainable soluble coffee production that can be adapted in other food and beverage industries. However, the unique dynamic nature of the vibratory membrane system challenges conventional approaches for understanding and predicting the mechanisms of the process. This gap limits the overall transferability of the technology to broader industry sectors. The semi-empirical resistance-in-series model developed in this study correlates the important factors with the vibratory NF performance based on fundamental concepts: concentration polarization, osmotic pressure effects, and fouling resistance. The model is not only useful in managing membrane fouling in vibratory systems, but also in optimizing and developing alternative approaches on similar lines and their scale-up to promote other industrial applications.