Breakup of extending liquid threads

A theoretical and experimental study is made of the stability and breakup of an extending viscous liquid cylindrical thread suspended in an immiscible viscous liquid undergoing extensional flow.It is shown that disturbances initiated as the thread is formed will in general as time proceeds be damped, then amplified and finally damped again. By considering disturbances being continually given to the system it is thus found that a disturbance which dominates at one moment will be completely different from that at any other. Assuming that breakup occurs when the disturbance amplitude becomes equal to cylinder radius, results are obtained for the time to breakup and for the final drop size resulting from breakup in terms of fluid properties, extension rate and the amplitude of disturbance given to system.These results were confirmed by examining, with the aid of cinematography, the breakup of a liquid thread in hyperbolic flow.