Prilling is the industrial process in which thin jets of a molten substance break up into drops and the subsequent solidification of the droplets into solids due to cooling when they fall down in the prilling tower. Prilling is widely used for efficient production of a variety of materials such as, e.g., fertilizer grains, laundry detergent, and substances for drugs and foods.
While in most prilling applications the jet can be considered as a pure liquid, in some cases the molten substance may contain suspended particles. The present study is motivated by prilling of fertilizers composed of Urea or Ammonium Nitrate (AN) containing polyhalite particles. To date, the effects of suspended particles on jet breakup, drop formation and crystallization are not well-understood. In the first part of this report a literature review is given on prilling and the current understanding of the effect of suspended particles on this. It has been found in literature that a large concentration of suspended particles will increase the viscosity of the suspension but also promote breakup of the jet. Besides, the size of the particles also influences the viscosity and jet breakup, resulting in a decrease in the amount of smaller formed secondary droplets at larger suspended particle sizes, hence increasing monodispersity. The objectives of this MSc research project are to assess under what conditions high-quality fertilizer grains can be optimally prilled from polyhalite suspensions in molten urea or ammonium nitrate. An experimental setup was designed to assess how molten liquid jets of Urea or AN with suspended polyhalite particles can be optimally prilled for producing high-quality fertilizer grains. This design consists of melting and mixing the batch of materials, from where it will pump the particulate suspension through a vertical tube with a screw pump to a nozzle. Here, a jet will be formed. This will breakup into droplets, which will fall in an oil batch to increase cooling and hence fasten the solidification process. Unfortunately, the current design was always dripping and not able to form a jet due clogging and the formation of hard lumps, which decreased the flow rate. The droplets were however collected and analyzed. It was found in this thesis that a larger concentration of P4 particles in urea will increase the viscosity. When the particles are grinded more, the viscosity increased as well, however a direct relationship between particle size and viscosity has yet to be determined. The particles were also unequally distributed over the prills, because P4 tends to stick together. To obtain the best quality prills, it is recommended to use relatively large P4 particles in combination with larger nozzles of >1mm to decrease the desired prilling force and prevent clogging. Also melting

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.