No abstract

Droplet grouping is important in technical applications and in nature where more than one droplet is seen. Despite its relevance for such problems, the fundamentals of the grouping processes are not yet fully understood. Initial conditions that expedite or impede the formation of droplet groups have been studied, but a thorough investigation of the temporal and spatial evolution of the forces at play has not been conducted. In this work, the grouping process in monodisperse droplet streams is examined in detail by Direct Numerical Simulation (DNS), for the first time, using the multiphase code Free Surface 3D. The code is based on the Volume-of-Fluid (VOF) method and uses the piecewise linear interface calculation (PLIC) method to reconstruct the interface. A method is established to quantify the development and evolving differences of pressure and shear drag forces on each droplet in the stream using the available DNS data. The results show a linear increase in the difference between the forces, where the drag force on the leading droplet is always larger than that on the trailing droplet. A comprehensive parametric study reveals that large initial inter-droplet separation and small group distances increase grouping time due to reduced difference in the drag coefficients. Higher initial Reynolds numbers and larger irregularities in the geometrical arrangement promote droplet grouping. The flow field shows stable wake structures at initial Reynolds numbers of 300 and the onset of vortex shedding at Reynolds numbers of 500 affecting the next pair of droplets, even for larger separation distances.

The condition for the formation of droplet groups in liquid sprays is poorly understood. This study looks at a simplified model system consisting of two iso-propanol droplets of equal diameter, Dd0, in tandem, separated initially by a center-to-center distance, a20, and moving in the direction of gravity with an initial velocity, Vd0>Vt, where Vt is the terminal velocity of an isolated droplet from Stokes flow analysis. A theoretical analysis based on Stokes flow around this double-droplet system is presented, including an inertial correction factor in terms of drag coefficient to account for large Reynolds numbers (≫1). From this analysis, it is observed that the drag force experienced by the leading droplet is higher than that experienced by the trailing droplet. The temporal evolutions of the velocity, Vd(t), of the droplets, as well as their separation distance, a2(t), are presented, and the time to at which the droplets come in contact with each other and their approach velocity at this time, ΔVd0, are calculated. The effects of the droplet diameter, Dd0, the initial droplet velocity, Vd0, and the initial separation, a20 on to and ΔVd0 are reported. The agreement between the theoretical predictions and experimental data in the literature is good.

In monodisperse droplet streams, the inter-droplet distances can change in a manner that brings pairs or triplets of droplets closer to one another, a process known as grouping. In the advanced stages of this process, droplet pairs can coalesce to form larger droplets. The grouping mechanisms in these droplet streams are not yet fully understood. Potentially, such a process can be controlled by an acoustic field. In the present study, computational fluid dynamics (CFD) simulations of isopropanol droplet streams in air are performed in ANSYS Fluent using the Eulerian-Lagrangian approach to analyze this process and to provide insight into grouping mechanisms. User-defined functions (UDFs) are used to tailor the code to the problems addressed here. Three scenarios are investigated. For the case of a single stream of droplet pairs, the mechanism of drag coefficient differences between the leading and trailing droplets enables reproduction of the results of longitudinal grouping experiments. For the case of two parallel streams, the lift force enables reproduction of lateral grouping trends, which are observed in experiments. Finally, for a single droplet stream in an acoustic standing wave, the experimentally observed sequence of single droplets and droplet pairs, induced by the acoustic wave, is reproduced computationally. It is found that the acoustic field significantly affects both grouping behavior and the droplet distribution in the computational domain, thereby either enhancing or delaying grouping tendencies. These results strongly indicate the potential that lies in employing an acoustic field to exercise control over how, where, and if droplet grouping occurs.

No abstract