Session E33: Drops V: Buoyancy-Driven Motion

Sedimentation and deformation of an aqueous sodium hydroxide drop in vegetable oil

The addition of water droplets in fuels is known to provide benefits such as decreased Nitrous Oxide $NOx$ emissions. Unfortunately the shelf life of a water-fuel emulsion is limited by the sedimentation rate of the water droplets. It is well known that adding surfactants can significantly slow the sedimentation rate due to the introduction of Marangoni stresses. In the case of a vegetable oil fuel, adding sodium hydroxide ($NaOH$) to the water droplets will produce surfactants through saponification in the form of sodium-carboxylate salts. Pendant drops of aqueous $NaOH$ solutions with pH between 11 and 13 will be suspended in several oils such as corn, olive, canola and soybean oil in order to measure the interfacial tension. The change in interfacial tension with time will be used to estimate the surfactant concentration and the saponification rate. Then individual drops will be placed in the oils to observe the settling velocity and drop deformation.   

Steady, axisymmetric, buoyancy-driven motion of a drop rising through a less viscous liquid

We report finite-element computations of steady, axisymmetric motion of a drop rising through a much less viscous liquid. The results focus on drops of liquid CO$_{2}$ rising through water, under conditions where the hydrostatic pressure variation is small enough for the density and viscosity variation in the drop to be neglected. A range of novel drop shapes is reported, with a recirculating flow region sometimes developing near the front or near the centerline of the drop. We also compute and discuss several measures of the velocity and drop shape relevant to transport of a passive scalar from the drop to the suspending liquid, or vice versa.   

Gravitational Interactions of Two Small Evaporating Drops

Relative trajectories are calculated for two sedimenting spherical drops with exact methods for determining the hydrodynamic forces at finite Stokes number and low Reynolds number. The drops are losing mass by isothermal evaporation controlled by diffusion, and bispherical coordinates are used to solve for the vapor concentration between the two liquid spheres. When the Reynolds number is small, fluid inertia is negligible, and the hydrodynamic forces are linear functions of the translational velocities of the drops. However, at nonzero Stokes numbers, drop inertia must be taken into account, and the hydrodynamic forces do not balance the applied forces. For drops in close approach, lubrication forces and attractive molecular forces are considered. The effect of evaporation is studied by comparison with trajectories for two drops of constant mass. The effect of the second drop on mass loss is analyzed by comparing trajectory results with those for two interacting drops, each evaporating at the isolated drop rate. An important application is to raindrop growth. For water droplets in the atmosphere, at drop radii between 10 and 30 $\mu$m, drop inertia is important while the Reynolds based on the surrounding air is still small.   

Ascending dynamics of a swarm of drops in a stratified fluids

The motion of drops and bubbles in stratified fluids has several natural and industrial applications such as bubbles rising across pycnoclines in marine and aquatic environments, oil spills, ocean sequestration of CO2, and bubble mixers used for lake/reservoir destratification and aeration. Even though the motion of bubbles and drops in a homogenous fluid has been extensively studied, their motion in a stratified fluid has not been explored. We perform direct numerical simulation of three-dimensional motion of a swarm of drops rising in a linearly stratified fluid. The pair correlation function is calculated to characterize the microstructure formation. The results show stronger tendency to form horizontal clusters of drops in a stratified fluid compared to a homogenous fluid. The mean rise velocity of the swarm of drops is reduced compared to the one in a homogenous fluid.   

Low Temperature Distillation for Desalination

We examine a unique configuration that combines the evaporator and condenser in a low temperature distillation process. The low temperature (pressure) container is designed to use waste heat from a power plant as the hot source and a water reservoir as the cold source. Fresh and saline streams of droplets in close proximity create interesting hydrodynamic challenges for the directional stability of the droplets.