Direct numerical simulations of particles settling in stratified fluids*

Settling particles moving through sharp interfaces or continuously stratified layers are found in a variety of engineering and geophysical applications. Generally, engineering applications include settling particles in a column of immiscible fluids, where viscosity and surface tension play a key role in the settling dynamics. The non-dimensional parameterisation for a column of immiscible fluids consists of the Bond number, the Archimedes number, and the viscosity ratio. For geophysical applications, the fluid comprises sharp density layers due to temperature or salinity gradients, and the parameterisation consists of the non-dimensional Froude number as well as the particle Reynolds number. We perform three-dimensional direct numerical simulations to validate our numerical framework, which uses a hybrid front-tracking level-set interface capturing algorithm, with existing experimental and computational studies of settling particles in both immiscible and miscible fluid columns. The results show that stratification has an important effect on the particle settling velocities caused by the particle dragging a column of fluid with different physical parameters to the neighbouring fluid.