Rise regimes of freely rising droplets with a moderate viscosity ratio

arXiv:2606.08575v1 Announce Type: new Abstract: The dynamics of buoyant droplets rising freely in a large body of an immiscible liquid is investigated numerically for a moderate drop-to-fluid viscosity ratio $\mu^\ast$. We focus on toluene droplets rising in clean water, for which $\mu^\ast=0.62$, and vary the radius over $0.5\,\text{mm}\leq R\leq3.0\,\text{mm}$. Direct numerical simulations are performed in imposed axisymmetric and fully three-dimensional configurations. As $R$ increases, the system displays a rich sequence of rise regimes. Starting from steady vertical rise with an axisymmetric disturbance flow, it first undergoes an internal flow instability associated with an azimuthal mode $m=2$, leading to a biplanar-symmetric wake and reduced terminal speed. This state is followed by a steady oblique regime, in which the $m=1$ mode also becomes unstable and coexists with the $m=2$ mode. At larger radii, the path becomes nearly vertical again before the flow enters an $m=2$ rotating-wave regime, where the wake drifts azimuthally at an approximately constant angular velocity. For still larger droplets, persistent shape oscillations and vortex shedding lead to fully three-dimensional chaotic paths. Simulations initialised from finite-amplitude asymmetric states further reveal several multistable size ranges, in which distinct terminal states coexist depending on the initial condition. Taken together, these findings show that the path instability of moderate-viscosity-ratio droplets differs fundamentally from that of bubbles and solid particles: in most regimes encountered here, axisymmetry breaking is initiated within the droplet, highlighting the central role of the internal flow instability in shaping the subsequent wake structure, rise speed and droplet dynamics.