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Numerical solutions of the Navier-Stokes equations of motion and the equations of mass transfer have been obtained for the unsteady state transfer into a spherical drop moving in an unbounded fluid medium of different viscosity. The effect of the viscosity ratio, k, between the dispersed phase and the continuous phase, on the mass transfer into a spherical drop, is investigated for different ranges of viscosity (0 < k < 10), Reynolds number (0 < Re < 100) and Peclet number (04). [ABSTRACT FROM AUTHOR]

In this work, we solve numerically the unsteady conduction-convection equation including heat generation inside a fluid sphere. The results of a numerical study in which the Nusselt numbers from a spherical fluid volume were computed for different ranges of Reynolds number (0 < Re < 100), Peclet number (0 < Pe < 10000) and viscosity ratio (0 < κ < 10), are presented. For a circulating drop with Re→0, steady creeping flow is assumed around and inside the sphere. In this case, the average temperatures computed from our numerical analysis are compared with those from literature and a very good agreement is found. For higher Reynolds number (0 < Re < 100), the Navier-Stokes equations are solved inside and outside the fluid sphere as well as the unsteady conduction-convection equation including heat generation inside the fluid sphere. It is proved that the viscosity ratio κ (κ = = μd/μc) influences significantly the heat transfer from the sphere. The average Nusselt number decreases with increasing κ for a fixed Peclet number and a given Reynolds number. It is also observed that the average Nusselt number is increasing as Peclet number increases for a fixed Re and a fixed κ. [ABSTRACT FROM AUTHOR]

The unsteady mass transfer from a contaminated fluid sphere moving in an unbounded fluid is examined numerically for unsteady-state transfer. The effect of the interface contamination and the flow regime on the concentration profiles, inside and outside a fluid sphere, is investigated for different ranges of Reynolds number (0 < Re < 200) and Peclet number (0 < Pe < 10), viscosity ratio between the dispersed phase and the continuous phase (0 < κ < 10), and the stagnant-cap angle (0° < θ < 180°). It was found that the stagnant-cap angle significantly influences the mass transfer from the sphere to a surrounding medium. For all Peclet and Reynolds numbers and κ, the contamination reduces the mass transfer flux. The average Sherwood number increases with an increase of stagnant-cap angle and reaches a maximum equal to the average one for a clean fluid sphere at low viscosity ratio and large Peclet numbers. A predictive equation for the Sherwood number is derived from these numerical results. © 2010 American Institute of Chemical Engineers AIChE J, 2011 [ABSTRACT FROM AUTHOR]