Investigation of the onset of dislodgment of a nonpermeating oil droplet at a membrane surface: Standard models and a new force balance model

Abstract

The need to determine the onset of dislodgment of an oil droplet pinning over a membrane surface is important in order to determine the critical conditions at which oil droplets detach. Although, previous studies considered this case in relation to an oil droplet pinning over a single pore, in reality, relatively larger size droplets pin over multitude of pore openings. In other words, droplets contact the surface over an area large enough to render the torque balance, which was devised previously to determine critical velocity, inaccurate. Another framework based on force balance is developed in this study from which critical velocity for the dislodgment of pinned droplet may be estimated. A friction force is assumed to balance the drag force due to crossflow field. The friction force is proportional to the resultant normal force that applies on pinned droplet. The proportionality factor is a friction coefficient that is determined as the ratio of the drag force due to crossflow and the resultant normal force. In this work, we determine these forces in addition to the crossflow velocity required to dislodge pinned droplet through computational fluid dynamic study (CFD). This analysis may be applicable to systems in which the deformation of the droplet is not large enough. In this case the resultant component of surface forces along the surface may be considered small. In this study a rectangular domain is considered with a 9 × 9 vertical tubes representing a pattern of pore openings. An oil droplet is released closer to the surface, where the permeation flux carries the droplet to reside on the membrane surface. The pressure inside the domain is adjusted such that it is less than the critical entry pressure and therefore, the droplet will not permeate. We seek to determine the velocity at the top surface that is barely enough to dislodge the droplet. This velocity, in addition to permeation flux, is used to determine the different hydrodynamic forces required to determine the friction force. In this study a number of droplets of different diameters are considered, namely 8, 10 and 12 microns. A base scenario is considered to determine the friction factor when no pores exist. A formula is suggested to estimate the friction factor for the more complex multipored system using that obtained when no pores exist. The numerical work is validated against the data exist in literature and excellent qualitative and quantitative match are obtained, which builds confidence in the numerical approach.