Determination of the orthokinetic coalescence efficiency of droplets in simple shear flow using mobile, partially mobile and immobile drainage models and trajectory analysis

The orthokinetic coalescence efficiency, of two Newtonian droplets submerged in a Newtonian fluid in simple shear flow, was theoretically investigated. The investigation considered three drainage models: immobile, partially mobile and mobile interfaces. The coalescence efficiency was also determined by solving the trajectory equations of the simple shear flow. The analysis showed that a critical approach angle, α_crit exists, below which the colliding droplets separate. Above this critical angle the collision leads to coalescence. The coalescence efficiency, ε, is related to α_crit by ε = cos(α_crit). Dimensional analysis showed that the coalescence efficiency depends on several dimensionless groups namely the flow number, the capillary number, the viscosity ratio and the radii ratio of the colliding droplets. The dependence of the coalescence efficiency on the flow number, the capillary number and the viscosity ratio was studied. It was found that the coalescence efficiency decreases as the capillary number and the flow number increase. For immobile interfaces the coalescence efficiency is independent of the capillary number until deformation sets in where it drops sharply. It was also found that the coalescence efficiency increases as the viscosity ratio increases. The coalescence efficiency calculated from the trajectory analysis decreases as the flow number increases. The dependence is strong for small values of the flow number and weak for large values. The relative position of one droplet with respect to the other in space strongly influences the coalescence efficiency. The maximum efficiency is achieved when the two droplets are in the same shear plane, i.e., when θ=90°. As the angle θ decreases the coalescence efficiency also decreases. Below a certain value of the angle θ the collision is inefficient and no coalescence takes place. The minimum distance between two colliding droplets as a function of θ was determined. The results revealed that the minimum distance is smallest when θ = 90°. An equation to calculate the average coalescence efficiency is presented.