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.

In this paper, the stability of falling films with different flow conditions at the inlet is studied. This is done with an algorithm for the numerical investigation of stability of steady-state solutions to dynamical systems, which is based on an Arnoldi-type iteration. It is shown how this algorithm can be applied to free boundary problems in hydrodynamics. A volume-of-fluid solver is employed to predict the time evolution of perturbations to the steady state. The method is validated by comparison to data from temporal and spatial stability theory, and to experimental results. The algorithm is used to analyse the flow fields of falling films with inlet and outlet, taking the inhomogeneity caused by different inlet conditions into account. In particular, steady states with a curved interface are analysed. A variety of reasonable inlet conditions is investigated. The instability of the film is convective and perturbations at the inlet could be of importance since they are exponentially amplified as they are transported downstream. However, the employed algorithm shows that there is no significant effect of the inlet condition. It is concluded that the flow characteristics of falling films are stable with respect to the considered time-independent inlet conditions.

This contribution is concerned with interfacial mass transfer into falling films, for which detailed insight is achieved by means of Direct Numerical Simulation employing the Volume-of-Fluid method. As for the numerical model for mass transfer across the fluid interface of falling films, we employ the two-scalar approach.We examine the influence of wave regimes and flow patterns on local Sherwood numbers and identify distinct mass transfer enhancement mechanisms taking effect in specific wave regimes. (C) 2013 Elsevier Ltd. All rights reserved.

Three surface tension models are investigated within the Volume-of-Fluid code Free Surface 3D: unbalanced Continuum Surface Force, Continuum Surface Stress, and balanced Continuum Surface Force with height functions, where the latter was adapted to the simulation of laminar falling films. Unbalanced Continuum Surface Force exhibits large distortions when the grid is refined and is discarded for producing unphysical results. The remaining two models are thoroughly evaluated by comparison to recent experimental data of Dietze, and to an analytical solution for an oscillating free surface. Furthermore, grid dependence is examined. The most apparent hydrodynamical difference between Continuum Surface Stress and balanced Continuum Surface Force is the number of vortices inside the solitary wave in the reference frame of the moving wave. The first model shows three vortices, whereas the latter model displays only one vortex. It is demonstrated that Continuum Surface Stress gives inadequate results, whereas balanced Continuum Surface Force yields a considerable improvement. Thus it is shown that the choice of the surface tension model and its discretization heavily influence the resulting hydrodynamics in simulations of falling films. Although all models work in three dimensions, the numerical experiments are performed in 2D. (C) 2012 Elsevier Ltd. All rights reserved.