The occurrence of mass transfer to and from droplets driven by buoyancy can be found in applications
Question:
The occurrence of mass transfer to and from droplets driven by buoyancy can be found in applications such as liquid-liquid extraction, and during environmental accidents such as deep water oil spills. (During the "Deepwater Horizon" accident in 2010 about 4.9 million barrels of oil was released into the Gulf of Mexico from a point of release located at a depth of around 1500 meters.) The oil droplets entering the oceanic environment during an accidental release are a mixture of many hydrocarbons. They can be treated as a pseudobinary mixture; the first component includes all the lighter hydrocarbons which are soluble in the surrounding water, and the second component represents all the heavier hydrocarbons practically insoluble in water.
When the droplets are released with an initial mixture density lower than that of the surrounding water, they rise due to buoyancy. However, as the droplet rises, the mass transfer of the lighter soluble components into the surrounding water causes the droplet density to increase gradually. As the density of the droplet approaches that of the water, the buoyancy effect disappears, and the droplet reaches a stationary stage. Further loss of the lighter components makes the density of the droplet higher than that of the water and the droplet starts to sink until it reaches the bottom of the ocean.
Rao et al. (2015) investigated this phenomenon experimentally as well as numerically. Their droplets were mixtures of acetonitrile (light, soluble component) and chlorobenzene (heavy, insoluble component). The droplets were released near the bottom of a glass tank filled with stagnant water. The motion of the droplets was captured using a high-speed camera. They measured the rate at which acetonitrile was transferred from the droplet (the dispersed phase) to the water (the continuous phase). They found that during both the ascent and descent stages, mass transfer is dominated by diffusion and forced convection. Their experimental data on the overall mass-transfer coefficient were well correlated by
Near the stationary stage, diffusion, forced convection, and natural convection are all important, and their correlation was
The fluid properties were evaluated at the bulk conditions of the continuous phase, virtually pure water at \(298 \mathrm{~K}\).
During Experiment \#4 of Rao et al. (2015), \(3.6 \mathrm{~s}\) after being released, a droplet ( \(27.5 \mathrm{wt} \%\) acetonitrile, \(72.5 \%\) chlorobenzene) had a diameter of \(4.8 \mathrm{~mm}\) and was rising in the water tank at a velocity of \(0.015 \mathrm{~m} / \mathrm{s}\). Estimate the value of the overall mass-transfer coefficient at that instant.
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