Active control of jet breakup and droplet formation using temperature modulation

Abstract

Using a slender-jet approach, we numerically investigate the control of jet breakup using temperature modulation at the nozzle with a specified frequency and amplitude. Our results show that temperature modulation does lead to instability through capillary and Marangoni stresses, providing control of the droplet formation in terms of intact length and resultant drop size distribution, which is otherwise irregular due to inevitable presence of background noise. For understanding the mechanisms underpinning the breakup of a thermally modulated jet in the presence of noise, it is useful to decompose the surface tension forces into a contribution from curvature-gradient forces and a contribution from surface tension-gradient forces, associated with axial variations in the jet curvature and the temperature-dependent surface tension coefficient, respectively. We show that in the limit of slow axial heat diffusion and slow cooling to the ambient, as considered here, the breakup of a thermally modulated jet is governed by the ratio of the surface tension-gradient force to the imposed random perturbation force at nozzle exit. This so-called “thermal modulation strength number” depends on the amplitude and frequency of the thermal modulation, the sensitivity of the surface tension coefficient to variations in temperature, the Weber number, and the strength of the Gaussian white noise added to the nozzle exit velocity. We show that the thermal modulation strength number governs the shift in breakup characteristics from forward to rear pinchoff for increasing modulation strength as well as the nature of the instability. When thermal modulation is weak, the surface tension-gradient forces act only as a trigger, and curvature-gradient forces soon take over and grow exponentially downstream from the jet due to inertio-capillary growth. When thermal modulation is strong, the surface tension-gradient forces not only act as a trigger, but remain significant until breakup. The thermal modulation strength number is thus useful to the design of thermal modulation in practical applications as a possible alternative to often-used mechanical excitation mechanisms to control jet breakup.