Control of jet breakup by a superposition of two Rayleigh–Plateau-unstable modes

Abstract

We experimentally, numerically and theoretically demonstrate a novel method of producing a stream of widely spaced high-velocity droplets by imposing a superposition of two Rayleigh-Plateau-unstable modes on a liquid jet. The wavelengths of the two modes are chosen close to the wavelength of the most unstable mode. The interference pattern of the two superimposed modes causes local asymmetries in the capillary tension. The velocity of the initial droplets depends on these local asymmetries. Due to their different velocities, the droplets coalesce to produce a stream of larger droplets spaced at a much larger distance than the initial droplets. We analytically derive the perturbations that robustly induce this process and investigate the influence of the nonlinear interactions of the two Rayleigh-Plateau-unstable modes on the coalescence process. Experiments and numerical simulations demonstrate that the jet breakup and the subsequent droplet merging are fully governed by the selected modes.

Fragmentation versus Cohesion

“…Duchemin et al (2015)) and travel long distances when their wavelength is smaller than the ligament (mean) radius because they are stable, with a non-zero group velocity (see § A.4). These waves possibly overlap with other preexisting waves (Driessen et al 2014;Doméjean, Bibette & Bremond 2016), thus altering dynamically the corrugations landscape of the ligament, and broadening its spectrum (Stone & Leal 1989), a phenomenon also known for gravity waves (Falcon, Laroche & Fauve 2007;Redor et al 2019). Corrugations may also be due to internal motions within the ligament, as these remnant from the liquid bulk from which the ligament has been stripped off either because the bulk is already turbulent (Goodridge, Tao Shi & Lathrop 1996), or as a result of the instability causing the stripping, as a shear for instance.…”

Effect of Superimposed Vibrations on Droplet Oscillation Modes in Prilling Process

“…Thus, the axes of the elliptical meridional cross-section of the jet are changed alternately under the action of capillary forces [19,20]. The amplitude of these oscillations gradually decreases, and the jet surface loses stability due to the unstable waves [21], surface tension-induced global instability [22], occurance of the Rayleigh-Plateau unstable modes [23], free-surface shear layer instabilities [24], and gas velocity oscillations [25], which ultimately leads to the decay of the liquid jet into droplets.…”

Frequency selection in a gravitationally stretched capillary jet in the jetting regime

“…On a different note, if the final aim is to eliminate the presence of satellite drops, the forcing should be modified such that it leads to the selective production of equi-sized drops. In this direction the work of Chaudhary & Redekopp (1980), who controlled satellite drops by forcing the jet with a suitable harmonic added to the fundamental, and Driessen et al (2014), who controlled the size of the droplet breaking off from a parallel jet by imposing a superposition of two Rayleigh-Plateau-unstable modes on the jet, could serve as the basis for formulating a theory for spatially varying gravity jets. A.2.…”

“…In the absence of white noise, a similar rationale should not be applied when evaluating the effect of a given pair of forcing frequencies. Indeed, their collective effect on the breakup characteristics could be different from their individual responses, as was demonstrated in the case of parallel jets (Driessen et al 2014).…”