Numerical investigation of shear-thinning and viscoelastic binary droplet collision

Abstract

In this work we present a 2D numerical study of the binary collision of viscoelastic drops under surface tension effects. The governing equations for incompressible fluids with free surface are completed with constitutive equations that represent three models for non-Newtonian fluids. We analyze a viscous shear-thinning Carreau–Yasuda (CY) equation and the viscoelastic constitutive models of Oldroyd-B and Phan–Thien–Tanner (PTT). From a computational point of view, the 2D free surface dynamic is handled using the Front-Tracking representation with marker particles, combined with the Marker-And-Cell (MAC) method. In order to discretize the equations, we employ a finite differences scheme. We provide maps of outcomes associated with the categories of Bouncing, Coalescence, and Separation as functions of the dimensionless numbers that govern the problem. In addition to the traditional space defined by the Weber and the impact factor, associated with the collision angle, commonly adopted in Newtonian studies, we explore the power-law index of the CY model, the Weissenberg number in the viscoelastic models, and the extensibility parameter in the PTT model. The transient interface dynamics of the problem is illustrated in a variety of cases. For non-bouncing scenarios, the results show that surface tension and elasticity act to maintain the integrity of the merged drop and avoid Separation. On the other hand, shear-thinning effects induce the Separation outcome. Hence, in the PTT model there are opposite trends associated with elasticity and shear-thinning, what can lead to non-monotonic responses.