A three-dimensional fluid dynamic model is developed to predict flux decline due to membrane fouling during the microfiltration of semisynthetic metalworking fluids. The model includes surface forces as well as hydrodynamic effects. Two pore model geometries are developed based on sintered aluminum oxide membranes. Simulations conducted using a single-pathway pore geometry illustrate the ability of the three-dimensional model to represent how flow continues through a partially blocked pore and how partial blocking reduces effective cross-sectional area. A four-disk pore geometry is used to compare flux decline behavior for different pore size distributions representing a new membrane and a membrane that had become partially blocked. Flux decline results are found to be consistent with published experimental results for similar membranes. An example shows how the three-dimensional fluid dynamic model may be used to determine the best membrane pore size distribution for a given situation and therefore demonstrates its overall utility as a design tool.

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