Onset of folding in plane liquid films

The onset of the folding effect characteristic of highly viscous liquid films (plane jets) slowly impinging on a wall is studied. Nonlinear quasi-one-dimensional equations are derived to describe the flow. In the linear approximation they reduce to the eigenvalue problem, whose solution predicts that instability (the onset of folding) sets in when the length of the film exceeds a critical value. The critical folding heights and the oscillation frequencies at the onset of instability are predicted as a function of flow parameters. Theoretical results are compared with Cruickshank's (1988) experimental data. Agreement is quite good only in the range of parameters where the quasi-one-dimensional approximation is applicable (thin films at the onset of folding).