Collision Modes of Two Eccentric Compound Droplets

Khanh P Nguyen,Truong V Vu

doi:10.3390/pr8050602

Abstract

A compound droplet with its single inner droplet appears in a broad range of applications and has received much attention in recent years. However, the role of the inner droplet location on the dynamical behaviors of the compound droplet is still not completely understood. Accordingly, the present study numerically deals with the eccentricity of the compound droplet affecting its colliding behaviors with the other droplet in a simple shear flow. The solving method is a front-tracking technique that treats the droplet interface as connected elements moving on a rectangular fixed grid. Initially, two compound droplets assumed circular are placed at a distance symmetrically to the domain center and they come into contact, because of the shear flow, when time progresses. During the collision process, the inner droplet that is initially located at a distance to its outer droplet center circulates around this center. It is found that this rotation also contributes to the formation of the collision modes including the reversing, passing-over and merging ones. Starting from a passing-over mode, a transition to a reversing mode or a merging mode can appear when the inner droplets, in terms of their centroids, are closer than their outer droplets. However, the location of the inner droplet within the outer droplet only has an effect when the value of the Capillary number Ca is varied from 0.01 to 0.08. For Ca < 0.01 corresponding to the merging mode and Ca ≥ 0.16 corresponding to the passing-over mode, the inner droplet position has almost no impact on the collision behaviors of two compound droplets.

Highlights

Compound droplets exist in two types [1]
A compound droplet consists of an outer interface that completely encapsulates one or many inner droplets [3,4,5]
In these processes and applications, a compound droplet can collide with one or many other ones and the dynamical behaviors of collisions have been classified into three main modes—reversing, passing-over and merging [10,11]

Summary

Introduction

Compound droplets exist in two types [1]. The first type of compound droplets is available with the outer interface partially enclosing its inner droplets [2]. In a few other works, for example, References [18,19], the authors considered the role of the location of the inner droplet, that is, the eccentric compound droplet, in the dynamical behaviors of the droplet Once again, these works [18,19] have not extended to the cases of binary droplets collisions as done in our present study. The authors found that the compound droplet moves in a similar trajectory but deforms differently as compared with the single-phase droplet Revisiting this problem, our previous work [10] showed that, in addition to the passing-over and reversing modes, two compound droplets may become one as they are in contact with each other. Some animations of droplet collisions are provided in the Supplementary Materials

Numerical Problem and Method

Colliding

Effect of the Horizontal and Vertical Eccentricities

Conclusions