Binary drop collisions

G. Brenn, V. Kolobaiic SatelUte droplet formation by unstable binary drop collisions, Phys. Fluids 18, paper 087101 (2006). 

Initiated by meteorological investigations on formation of rain drops, as well as spray combustion, binary drop collision has been investigated for more than half a century [3-5]. The outcomes of binary droplet collisions are typically summarized in collision maps as shown in Fig. 6.1. The Weber-number measures the ratio of the inertial force to the surface tension force. We = pu d/a, where p is the density, u is the collision velocity, d is the drop diameter, and a is the surface tension. The impact parameter B is a measure of the geometry of drop collisions as illustrated in Fig. 6.1. 

Fig. 6.14 Left. Sketch of the HiDrip droplet generator nozzle head (a) servomotor drive, (b) adjusting thread for sealing between (c) and (d), (c) multiple-hole cutter disc, and (d) single-hole nozzle plate. Right. Sketch of the experimental setup for binary drop collision. The colUsion velocities are varied by adjusting the angle between the two streams of drops...

Abstract We put together the state of knowledge on binary colUsional interactions of droplets in a gaseous environment. Phenomena observed experimentally after drop collisions, such as coalescence, bouncing, reflexive separation and stretching separation, are discussed. Collisions of drops of the same liquid and of different -miscible or immiscible - liquids, as well as collisions of drops of equal and different size are addressed. Collisions of drops of immiscible liquids may lead to an unstable interaction which is not observed with drops of equal or miscible liquids. Regimes characterized by the various phenomena are depicted in nomograms of the Weber number and the non-dimensional impact parameter. The state-of-the-art in the simulation of binary droplet collisions is reviewed. Overall three different methods are represented in the literature on these simulations. We discuss models derived from numerical simulations and from experiments, which are presently in use for simulations of spray flows to account for the influence of coUisional interactions of the spray droplets on the drop size spectrum of the spray. 

Keywords Binary drop colUsions Bouncing Coalescence Collision model Crossing separation Gaseous environment Immiscible liquids Lattice-Boltzmann simulation Miscible liquids Navier-Stokes simulation Reflexive separation Satellite droplets Spray flow simulation SPH simulation Stretching separation... 

Fig. 7.1 Experimental setup for drop collision studies [26] (Reprinted from Colloids and Surfaces A - Physicochemical and Engineering Aspects, doi 10.1016/j.colsurfa.2009.12.011 (2009), Plan-chette, Lorenceau, Brenn, Liquid encapsulation by binary collisions of immiscible liquid drops, Copyright 2009, with permission from Elsevier)...

Modeling of the complicated phenomena in binary droplet collisions occurring in spray flows is difficult due to the variety of potential outcomes from a collision [69-71]. The first necessity is to predict the stability against stretching or reflexive separation. Then, for unstable drop collisions, the resulting drop sizes need to be predicted. All predictions should follow from algebraic models without the need to solve additional transport equations in the spray flow code to account for the collisions. Needless to say that it is impossible to simulate the full detail of the processes in droplet collisions, as done in the simulations discussed in section Simulations of Droplet Collisions, in the course of a spray flow simulation [72-82]. 

An important phenomenon, particularly in the dense region of the spray, is the collision of drops. A canonical example is the head-on collision of binary drops. 

PLA 12] Planchette C., Laueenceau E., BRENN G., The onset of fragmentation in binary liquid drop collisions . Journal of Fluid Mechanics, vol. 702, pp. 7-25, 2012. 

Fig. 6.16 Typical scenarios of binary droplet collisions of viscous liquids with a shear viscosity from 116 mPa s to 729 mPa s. (a) coalescence, (b) stretching, and (c) separation. Because of the limited field of view the final spherical shape of the drop in (b) and the final separation of the drop in (c) could not he visualized...

Pan and Suga [171], for example, performed 3D dynamic simulations of binary droplets collisions for cases of different Weber numbers and impact parameters. The systems used are water drops in air and tetradecane drops in nitrogen at atmospheric conditions. The bulk fluids are considered incompressible. The simulations cover the four major regimes of binary collision bouncing, coalescence, reflexive separation. 

Newton s law-conversion factor Shear rate Effective shear rate Fictitious transfer coefficient Collision frequency between drops of sizes a and a for a binary collision process based on number concentration... 

During the expansion, the random translational kinetic energy and any internally stored energy (rotations and vibrations) is converted into mass flow through binary collisions. The effective rotational and vibrational temperature drops, the velocity distribution narrows and moves out along the flow velocity axis. Since local thermodynamic equilibrium was assumed to exist at all times in the derivation of Equations 79 that describe this process, we can calculate the flow velocity as a function of gas temperature, giving... 

C. Planchette, E. Lorencean, G. Brenn Liquid encapsulation by binary collisions of immiscible liquid drops. Colloids Surf. A Physicochem. Eng. Aspects 365, 89-94 (2010). 

Ashgriz, N. and Y. Poo. Coalescence and Separation in Binary Collisions of Liquid Drops. J. Fluid Mech. 221 183-204 (1990). 

Ashgriz, N., Poo, J. Y. (1990). Coalescence and separation in binary collisions of liquid drops. Journal of Fluid Mechanics, 221, 183-204. 

Roisman, I. V., Planchette, C., Loienceau, E., Brenn, G. (2012). Binary collisions of drops of immiscible liquids. Journal of Fluid Mechanics, 690, 512-535. 

Ashgriz N, Poo JY Coalescence and separation in binary collisions ofhquid drops, J Fluid Mech 221 183-204, 1990. 

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