Multi-Scale Modeling of Tubular Cross-Flow Microfiltration of Metalworking Fluids

Metalworking fluids are a vital part of modern machining processes but have significant negative economic, health, and environmental impacts. In-process purification of these fluids by microfiltration has been shown to reduce these impacts. This research uses a two-stage computational modeling methodology to investigate how particles within the membrane are transported from the turbulent flow within the center of the tubular membrane to the laminar sub-layer near the membrane wall and finally into the membrane pores. A macro-model of the complete flow within the tubular membrane is used to determine the steady-state flow profile within 25 microns of the membrane surface. This flow profile is then used to develop a micro-model of the flow at the membrane wall using a flat-plate assumption. The micro-model includes individual pores randomly located and sized based on statistical analysis of alumina membrane surfaces. A 2³ full factorial design of experiments was used with variables of cross-flow velocity, transmembrane pressure, and membrane resistance. The responses of effective filtration region and total mass flowing through the pores were analyzed. Based on the simulation results, recommendations are made for future membrane design to provide the most efficient transport of particles from the bulk into the pores.