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Membrane filtration is used in a variety of industries, including water treatment and the food industry. Membrane systems include microfiltration and reverse osmosis processes. Membranes used in reverse osmosis are nonporous or pores at 0.2-2 A. This work will focus on mechanical microfiltration. These filtration systems suffer from an accumulation of the rejected material near the membrane surface. This causes additional resistance to the flow through the membrane (flux), resulting in a decline in the performance of the system. Sparging gas bubbles into the mixture has been shown to improve performance. The flow field promotes the transport of material away from the membrane surface and into the bulk. The goal is to predict the sparging that will achieve the maximum flux. Existing flux prediction models often assume steady shear at the membrane surface but in bubbling regimes the shear stresses are unsteady. In this thesis a model is developed to calculate the flux based not solely on shear but on the behaviour and resistance of suspended particles in a gas-liquid flow field. The bubble shape and flow field is calculated using computation fluid dynamics (CFD). The flow around a bubble in gap between two parallel flat sheet membranes is investigated. The calculated bubble shape correlates well with the results seen in experiments. The bubble rise velocity with respect to gap width is shown to transition between that expected in the literature for extended flow for large gap widths and that for a two dimensional case for smaller gap widths. The transitional region however, does not behave as may be expected. The rise velocity does not monotonically decrease as the gap width is reduced. The particle concentration is found by the solution of the convection-diffusion equation, where the convection velocity terms are given by the results of the CFD calculation. The permeate flux is then calculated using a resistance model giving the enhancement due to the bubble. The model is also applied to single phase crossflow. As the shear stresses are steady in this single-phase flow regime, established membrane shear linked mass-transfer coefficient methods can be employed. Good agreement is found between the model and theory. The flux results obtained when the model is applied to the flow around the bubble show a peak in performance with respect to the gap between the membranes for a given bubble volume. The optimal flux enhancement is found to correlate well with the bubble size compared to the flow area. The results show a bubble width of around 60% of the flow width provides the best flux performance.