Summary
The extraction of a substance, dissolved in droplets of a fluid, when these are falling (or rising) in an other fluid under the influence of gravity, is investigated. The circulation currents which are caused in the droplets by the viscous forces between the two fluids modify the rate of extraction as compared with the case of droplets at rest. Under certain simplifying assumptions a differential equation governing the combined action of convection and diffusion is derived. The rate of extraction follows from the solution of an eigenvalue problem.
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References
Hadamard, J., C. R. Acad. Sci., Paris 152 (1911) 1735; see also H. Lamb, Hydrodynamics, 6th ed., p. 600; Cambridge, 1932.
Serret-Scheffers, Lehrbuch der Differential- und Integralrechnung, 4th and 5th ed., vol. 2, p. 78.
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Kamke, E., Differentialgleichungen, vol. 1, p. 220; Leipzig, 1942.
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Kronig, R., Brink, J.C. On the theory of extraction from falling droplets. Appl. sci. Res. 2, 142–154 (1951). https://doi.org/10.1007/BF00411978
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DOI: https://doi.org/10.1007/BF00411978