Passage and deformation of oil drops through non-converging and converging micro-sized slotted pore membranes

The model presented in the paper is the continuation of the previous work where a mathematical model was developed for the passage and deformation of micro-sized oil drops through a 4 μm converging slotted pore membrane. In the previous work, it was assumed that drops deform from a spherical shape to a prolate spheroid when pass through a converging slot. In the present study, it has been assumed that drops deform into an oblate spheroid while passing through a non-converging slot and a mathematical model is developed for the deformation of drops through non-converging slots. After extending the idea of static and drag forces, it is readily seen that the magnitude of static force (Fcx) for the non-converging slotted pore membrane is higher than the static force for the converging slotted pore membranes. This is because of drops deform suddenly in the non-converging slots, while, in case of converging slots, the drops deform gradually. Micro-sized oil drops of two systems with different interfacial tensions (4 and 9 mN/m) have been used in the study and it is observed that a higher interfacial tension leads to a higher rejection rate for both converging and non-converging slotted pore membranes at various in-pore filtration velocities.