Spinning disk atomization: Theory of the ligament regime

Abstract

A method of the mathematical modeling of the spinning disk atomization process as a whole, from the film flow on a rotating disk to the drop formation and detachment from the ends of the ligaments spiralling out of the disk's rim, is formulated and the key results illustrating its implementation are described. Being one of the most efficient nozzle-free atomization techniques, spinning disk atomization is used in many applications, ranging from metallurgy to pharmaceutical industry, but until now its design and optimization remain empirical which is time consuming and costly. In the present work, the entire spinning disk atomization process is, for the first time, modelled mathematically by (a) utilizing all known analytic results regarding its elements, notably the film flow on the disk and the dynamics of outgoing spiral jets, where the flow description can be simplified asymptotically and (b) using the full-scale numerical simulation of the three-dimensional unsteady free-boundary flow in the transition zone near the disk's rim which brings these elements together. The results illustrating the developed modeling approach reveal some previously unreported qualitative features of the spinning disk atomization process, such as the drift of the outgoing ligaments with respect to the disk, and elucidate the influence of physical factors on the size distribution of the drops and, where this is the case, satellite droplets. The comparison of the obtained results with available experimental data confirms the validity of the assumptions used in the modeling.

On the breakup of spiralling liquid jets

“…As the results of the numerical simulations in the present study show, the linear analysis is inadequate for describing the nonlinear stage of the wave propagation as well as the drop formation, and, as for the satellite droplets, they result from the pinch-off of a long thin ligament connecting the main drops, not from short waves, which may be considered in the linear stage of the wave propagation. This is what can be seen in the experimental photographs of Wallwork et al (2002) as well as in numerous experimental studies of particular atomization systems (see Li et al (2018) for a recent overview of the most nontrivial one).…”

“…The results presented here, which come from the combination of the linear analysis and numerical simulations of the nonlinear regime, where the location of the linear-nonlinear interface is varied, show that for waves with the initial amplitude (in terms of the jet's radius variation) of 0.01 or larger, the initially fastest spatially growing wave approach can be relied upon. Interestingly, this approach appears to be working even when applied to the spinning disc atomization process (Li et al 2018), where, pictorially, there is no well-defined 'starting point of the jet' as it has to be determined from the dynamic properties of the gradually forming jet.…”

“…This technique routinely used to manufacture polymer and glass fibers (Pearson 1985) has been extended recently to produce nanofibers (Mellado et al 2011). In the second group of applications, the liquid jets spiralling out of a rotating container, as, for example, in the prilling process (Saleh et al 2015), or driven from the edge of a spinning disc (Li et al 2018), as in the spinning disc atomization (Senuma et al 2000), are used as a source of droplets which on solidification become pellets or powder particles. In both types of application, it is important to understand the dynamics of rotating jets, their instability mechanisms and, for atomization techniques, the process of formation of drops, satellite droplets and the factors that control the distribution of their sizes.…”

Controlling the breakup of spiralling jets: results from experiments, nonlinear simulations and linear stability analysis

“…2016) and homogenization (Singh et al. 2019), spinning disc atomization (Li, Sisoev & Shikhmurzaev 2018; Keshavarz et al. 2020) and prilling (Decent, King & Wallwork 2002; Saleh et al.…”

Dynamics of Drop Release from the Edge of a Spinning Disc

“…At moderate flow rates, the liquid emerges as ligaments attached to the disc edge. The ligaments are of nearly fixed shape and orientation. − They release drops from the free end by the Rayleigh–Plateau instability. The drop formation in jetting mode from a capillary (away from the capillary tip by jet instability) is analogous.…”