Abstract
Surface tension makes the shape of a fluid cylinder unstable with respect to periodic corrugations of wavelength greater than the cylinder circumference, and the thread eventually breaks up into a series of droplets separated by the wavelength of the fastest growing instability. We derive in this paper the relation between the wavelength and the growth rate of the sausage instability of a thread embedded in a matrix, in the limit of vanishing Reynolds number and for incompressible fluids. The theory applies to general viscoelastic fluids, and takes into account the dynamic properties of the interfacial tension due to adsorbed contaminants or interfacial agents, as well as the capability of the interface to resist a shear deformation. It includes the special cases treated by Tomotika and by Chin and Han, and provides a valuable tool for measuring the static and dynamic properties of the interfacial tension.
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