Breaking up of a drop of viscous liquid immersed in another viscous fluid which is extending at a uniform rate

Abstract

1—In a previous papers the present writer has discussed the instability of a long cylindrical column of an incompressible viscous liquid surrounded by another viscous fluid under the action of both surface tension and viscous forces. In this work the fluids were at rest except for the small disturbances which were assumed to develop slowly. It was shown that if the ratio of viscosities of the two fluids is neither zero nor infinity the maximum instability always occurs at a certain definite value of the wavelength of the assumed initial varicosity so that the formation of drops of definite size would be expected. A comparison of the theory with observation has also been made and satisfactorily good agreement between them was found. Now, in his experimental studies on the mode of formation of a cylindrical thread from a drop of a viscous liquid by the disruptive effect of the viscous drags of a surrounding liquid, professor G. I. Taylor observed that when a drop of black lubricating oil was surrounded by syrup, the thread formed by pulling out the drop did not at once break up into small drops but remained cylindrical for some time and finally broke up into small drops, the diameters of which were about 1/10th of the diameter of the original drop. On the other band, if as soon as the cylindrical thread was formed the apparatus was stopped the thread immediately began to break up in the manner described above. Thus, if the apparatus were kept going very much smaller drops were formed than if it were stopped as soon as the initial drop bad been pulled out into a cylindrical thread.