Polygon model for solution of non-linear velocity gradient of interface and asymmetric break-up of droplet

Abstract

In this study, a novel model is proposed to accurately depict the changes in the droplet-matrix interface as a function of the velocity gradient at different times. Using the iteration method and drawing the droplet shape, the interface velocity gradient-matrix shear rate non-linear equation is simultaneously solved. The initial droplet shape is assumed to be a polygon, with each side independently undergoing modifications under stress. By sequentially adjusting each side at different time points, the overall shape of the droplet is reconstructed. The experimental section examines droplets consisting of alcohols (polyvinyl alcohol and polyethylene glycol) in water-soluble form with different concentrations and glycerol. The matrix material used is poly dimethyl siloxane. The viscosity ratio between the droplet and matrix falls within the range of 0.18–3.08. The experimental findings show two types of droplet breakup: a single-end bulb and two non-uniform end bulbs of different sizes. The simulation results from the model align well with the experimental observations, accurately capturing the dimensions and volume of the droplets and the aspect ratio of the bulbs. The model also predicts the aspect ratio, lateral area, and rotation of the droplets before breakup with minimal deviation from the experimental data.