Dynamic behaviour of buoyant high viscosity droplets rising in a quiescent liquid

Abstract

The present paper initiates a systematic computational analysis of the rise dynamics of high viscosity droplets in a viscous ambient liquid. This represents a relevant intermediate case between free rigid particles and bubbles since their shape adjusts to outer forces while almost no inner circulation is present. As a prototype system, we study corn oil droplets rising in pure water with diameters ranging from 0.5 to 16 mm. Since we are interested in the droplet dynamics from the viewpoint of a bifurcation scenario with increasingly complex droplet behaviour, we perform fully three-dimensional numerical simulations, employing the in-house volume-of-fluid (VOF)-code FS3D. The smallest droplets (0.5–2 mm) rise in steady vertical paths, where for the smallest droplet (0.5 mm) the flow field, as well as the terminal velocity, can be described by the Taylor and Acrivos approximate solution, despite the Reynolds number being well above one. Larger droplets (3.2 mm) rise in an oblique path and display a bifid wake, and those with diameters in the range (3.7–8 mm) rise in intermittently oblique paths, showing an intermittent bifid wake of alternating vorticity. The droplets’ shapes in this range change from spherical into oblate ellipsoids of increasing eccentricity, followed by bi-ellipsoidal shapes with higher curvature on the downstream side. Even larger droplets (10–16 mm) rise in oscillatory, essentially vertical paths with drastically different wake structures, including deadzones and aperiodic or periodic vortex shedding. The largest considered droplets (diameter of 14 and 16 mm) display significant shape oscillations and vortex shedding is accompanied by a complex evolution of coherent vortex structures. Their rise paths are best described as zigzagging, but the bifurcation scenario seems to be substantially different from that leading to the zigzagging of air bubbles. In contrast to the rise behaviour of bubbles, helical paths are not observed in the present study.