The passage of deforming drops through a slotted microfilter

In the flow of a deforming drop through a slotted pore, such as during the microfiltration of oil drops suspended in water, the mechanism for the convection of the oil drops is liquid drag caused by permeate flow through the filter. If the slot is designed to have a converging inlet section then it is possible to estimate the force on the drop from the liquid drag and determine where the drop comes to rest within the converging slot. This equilibrium position is established due to a balance of forces between the liquid drag and the force required to deform the drop to create a larger surface area as the drop becomes less spherical. Experimental measurements are presented for a bubble deforming within an aqueous flow field and a paraffin oil flow field, together with results for the motion of a paraffin oil drop within an aqueous flow field. The data is correlated using a ratio of drop to channel diameter (analogous to slot width) against superficial liquid velocity. Different curves are provided depending only on the physical properties of the fluids used. An analytical mathematical development predicts these curves to a good degree of reliability, which can then be used to predict the oil drop size that is 100% rejected during the filtration of oil drops on slotted microfiltration membranes. Experimental evidence is presented to support the prediction using the filtration of a crude oil on a slotted microfilter with a minimum pore width of 5 microns.