Buckling of thin liquid jets

The present work deals with the buckling phenomenon characteristic of highly viscous liquid jets slowly impinging upon a plate. The quasi-one-dimensional equations of the dynamics of thin liquid jets are used as the basis for the theoretical analysis of buckling. With the problem linearized, the characteristic equation is obtained. Its solutions show that instability (buckling) sets in only in the presence of axial compression in the jet, and when the distance between the nozzle exit and the plate exceeds some critical value. The latter is calculated. It is shown that buckling instability corresponds to the rectilinear jet/folding jet bifurcation point. The value of the folding frequency is calculated at the onset of buckling. The theoretical results are compared with Cruickshank & Munson's (1981) and Cruickshank's (1988) experimental data and the agreement is fairly good.