Drop oscillations in liquid-liquid systems

When the ratio of the drop radius to the distance separating any two drops and the relative importance of gravitational to surface forces are both small, the small amplitude oscillations of a drop of one viscous fluid immersed in another fluid are governed by the nonlinear dispersion relation derived by Miller and Scriven (1968). The dispersion relation has been solved numerically to determine the character of oscillations for arbitrary values of drop size, physical properties of the two fluids, and interfacial tension. The new theoretical results determine the range of validity of the low‐viscosity approximation of Miller and Scriven, and are also shown to be essential for proper interpretation of many previously reported experimental results. New experimental measurements of natural frequencies of oscillation of water drops falling in 2‐ethyl‐1‐hexanol, a system having properties characteristic of many others in solvent extraction, agree well with the theoretical predictions when drop radius is smaller than a critical size. The frequencies of oscillations of larger drops are better described by the dispersion relation due to Subramanyam (1969), which accounts for the relative motion of the two phases.