Control of capillary break-up in spiralling liquid jets

Abstract

A cylindrical column of fluid breaks into drops under the action of surface tension when other forces are relatively small. This phenomenon is called the capillary break-up. Since the introduction of the seminal theory of inertial-capillary jet instability by Rayleigh in the late 19th century, this phenomenon has seen a rich influx of academic research and industrial interests over the past few decades. The theory suggests that out of all the unstable wavelengths only the most unstable wavelength determines the drop size. But in reality, random background perturbations and non-linear pinch-off dynamics result in bi-modal drop size distribution. The two peaks in the bi-modal distribution correspond to the formation of main drops and satellite drops. The main drops are the desired product of the industry and the satellite drops are relatively smaller in size and are discarded by post-production processes like sieving. To reduce post-production processes and ensure repeatability, the industrial demand is to have a "narrow uni-modal" drop size distribution. Meaning, elimination of satellite drops and having uniform-sized main drops. Narrow distribution is achieved by employing finite-amplitude perturbation on the jet. This way the jet is not affected by the random background perturbation as the finite-amplitude perturbation dominates the break-up process. But this does not ensure satellite drop elimination. Uni-modality is achieved when the satellite drops merge with the main drops. Merging happens when the satellite and the main drop have different velocities and follow the same trajectory. The amplitude of the sinusoidal perturbation can be tuned to have this merging condition. The externally perturbed jet finds its application in a plethora of industrial processes such as powder production, combustion, micro-encapsulation, extreme ultraviolet rays (EUV) and, laser-plasma production (LPP), ink-jet printing, etc. The focus of this thesis is the production of crystalline fertilizer pellets from the capillary break-up of a spiralling jet of molten fertilizer. This process is called rotary prilling. Experimental studies in spiraling jets without external perturbation also shows bi-modal distribution of drops. The fine satellite drops produced in prilling process are a potential safety hazard as they can cause dust explosions which can be detrimental to air quality. Expensive filters and wet scrubbers are placed inside the prilling tower to remove the fine satellite drops. Hence uni-modal drop size distribution in prilling is highly beneficial for both economic and environmental reasons. As perturbed spiralling jets are not studied in detail in the existing literature, this thesis employs sinusoidal perturbations on spiraling water jets and aims to achieve uni-modal drop size distribution. While the straight jets have a nearly constant base flow, the spiraling jets have a base flow that accelerates due to the centrifugal and Coriolis forces in the downstream direction. As a result of mass conservation the accelerating base flow results in jet stretching in the downstream direction. The evolution of perturbations on such a stretched jet not only depends on surface tension and inertial forces of the local jet radius, but also on the wavelength that is excited initially. Hence the evolution of perturbations on straight jets with constant base flow is an eigen-value problem whereas, on a stretched jet it is an initial value problem. When the stretching rate is faster than the capillary growth rate damping of the surface perturbations will occur. For the process parameters investigated in this thesis, the capillary growth rate is faster resulting in negligible damping. The other effect of jet stretching is that the wavelengths are also stretched, that is the wavelength that is excited initially becomes longer in the downstream direction, thus the wavenumber decreases. The linear spatial instability theory for spiraling jets is experimentally validated in this thesis. For the set of non-dimensional numbers chosen in this thesis, uni-modal distribution of drops is achieved by tuning the frequency and amplitude of the sinusoidal perturbation. Uni-modality is observed when the non-dimensional wavenumber near break-up is approximately 0.7 and the amplitude is tuned accordingly. As the wavenumber decreases in downstream direction the wavenumber excited at the nozzle should be greater than 0.7.