Stability of a moving radial liquid sheet: experiments

Abstract

A recent theory [Tirumkudulu & Paramati, "Stability of a moving radial liquid sheet: Time dependent equations.", Phys. of Fluids, 102107, 25, 2013] for a radially expanding liquid sheet that accounts for liquid inertia, interfacial tension and thinning of the liquid sheet while ignoring inertia of surrounding gas and viscous effects shows that such a sheet is convectively unstable at all frequencies and Weber numbers (W e ≡ ρ l U 2 h/σ) to small sinuous disturbances. Here, ρ l and σ are the density and surface tension of the liquid, respectively, U is the speed of the liquid jet, and h is the local sheet thickness. In this study, we use a simple non-contact optical technique based on laser induced fluorescence to measure the instantaneous local sheet thickness and its displacement of a circular sheet produced by head on impingement of two laminar jets. When the impingement point is disturbed via acoustic forcing, sinuous waves produced close to the impingement point travel radially outward. The phase speed of the sinuous wave decreases while the amplitude grows as they propagate radially outwards. Our experimental technique was unable to detect thickness variations in the presence of forcing suggesting that the variations could be smaller than the resolution of our experimental technique. The measured phase speed of the sinuous wave envelope matches with predictions while there is a qualitative agreement in case of spatial growth. We show that there is a range of frequencies over which the sheet is unstable due to both aerodynamic interaction and thinning effects while outside this range, thinning effects dominate. These results imply that a full theory that describes the dynamics of a radially expanding liquid sheet should account for both effects.

On the nature of instabilities in externally perturbed liquid sheets

“…All these regime maps are shown in figure 10, which is qualitatively similar to figure 12 in Paramati et al. (2015). The methodology and procedure for obtaining these regime maps is provided in Appendix C.…”

“…It was shown that the growth rate of the sinuous waves is primarily dominated by the sheet thinning effect alone for the set of flow conditions chosen by them. Further, it was observed from their comparative study (Paramati et al 2015) that there exists a certain region of flow conditions where the thinning theory is better suited for predictions.…”

“…Recently, the role of the sheet thinning effect on the instability of the sheet has been studied theoretically and experimentally by Tirumkudulu & Paramati (2013) and Majumdar & Tirumkudulu (2018). Paramati, Tirumkudulu & Schmid (2015) used acoustic forcing at the point of impingement to compare the predictions using the conventional aerodynamic theory and their thinning theory. It was shown that the growth rate of the sinuous waves is primarily dominated by the sheet thinning effect alone for the set of flow conditions chosen by them.…”

“…The curve with circular markers separates the two regimes. (d) The cutoff frequencies using Squire's theory for a single jet impinging on a solid surface (h = d 2 0 /8x)(Bremond et al 2007) and the upper boundary of the envelope for a similar configuration(Paramati et al 2015).…”

Atomization of acoustically forced liquid sheets

“…However, the reason for this is not clearly understood. The stability of radially moving circular liquid sheets when only the impingement point is perturbed by the acoustics was assessed by Paramati, Tirumkudulu & Schmid (2015). The existence of a critical Weber number was reported, below which the sheet thinning effect dominates the breakup irrespective of the excitation frequency.…”