On the nature of instabilities in externally perturbed liquid sheets
Sandip Dighe, Hrishikesh Gadgil
Abstract
The evolution of the interfacial instabilities on a smooth and laminar liquid sheet formed by the oblique impingement of two liquid jets is investigated in the presence of external acoustic forcing. The forced liquid sheet exhibits different instability patterns, such as flapping flag, sinuous breakup and vibrating membrane structure, depending on the forcing frequency. The transition frequencies, where the instability pattern changes, are obtained using the linear theory of sheet instability and are shown to be increasing functions of the jet Weber number. These different instability patterns show distinct growth rate behaviours, which cannot be predicted using a unique theory such as the conventional linear theory of sheet breakup. The dynamics of liquid sheet breakup in the presence of forcing is further assessed with the help of established instability theories. Our measurements show that the sheet thickness distribution plays a major role in dictating the relative influence of different mechanisms on the instability characteristics. All the results are finally consolidated to arrive at the instability regime map on the Weber number versus frequency ( $We$ – $\tilde {\omega }$ ) space to serve as a guideline for adopting a suitable modelling approach.