On the breakup of a permeating oil droplet in crossflow filtration: Effects of viscosity contrast

Abstract

The critical velocity of dislodgment of a permeating oil droplet in crossflow filtration is an important parameter in the analysis of the filtration of produced water systems using membrane technology. In this work, the effects of the viscosity contrast between the droplet and the surrounding fluid on the critical velocity of dislodgment are investigated. In the limit when the viscosity of the droplet approaches infinity, the gripping of the crossflow field on the droplet is maximum. When the viscosity contrast is finite, the smaller the viscosity contrast is, the smaller the gripping becomes. In order to highlight this effect, a comprehensive computational fluid dynamics study is conducted. A permeating droplet in the crossflow field is considered with the viscosity contrast ranging within two orders of magnitude. For each scenario, the critical velocity of dislodgment is determined by increasing the velocity incrementally until breakup occurs for every viscosity contrast. It is found that an increase in the viscosity contrast results in a decrease in the critical velocity of dislodgment. This represents a direct manifestation of the effect of the gripping of the droplet by the crossflow field, which increases as the viscosity contrast increases. Modification of the critical velocity of dislodgment, therefore, needs to be considered to account for this effect of viscosity contrast. The formula that was developed to estimate the critical velocity of dislodgment has been modified, and comparison with simulation gives a very good match.