The dynamics of head-on collision of unequal-size droplets were experimentally and theoretically investigated, with emphasis on identifying distinct collision outcomes and interpreting the size-ratio dependence. A unified regime diagram in terms of bouncing, permanent coalescence, and separation after coalescence was identified for hydrocarbon and water droplets in the parameter space of the size ratio and a collision Weber number. Experimental results show that the transition Weber number, Web-c, that separates the bouncing and permanent coalescence regimes, weakly depends on the size ratio, while the transition Weber number, Wec-s, that separates permanent coalescence and separation regimes, significantly increases with the size ratio. A theoretical model based on energy balance and scaling analysis was developed to explain the size-ratio dependence of Wec-s. The theoretical results show good agreement with the experimental data for tetradecane and decane droplets, with a moderate discrepancy for water ...

Bouncing, coalescence, and separation in head-on collision of unequal-size droplets

Three-dimensional binary droplet collisions are studied using a multiphase cascaded lattice Boltzmann method (LBM). With this model it is possible to simulate collisions with a Weber number of up to 100 and a Reynolds number of up to 1000, at a liquid to gas density ratio of over 100. This is made possible by improvements to the collision operator of the LBM. The cascaded LBM in three dimensions is introduced, in which additional relaxation rates for higher order moments, defined in a co-moving reference frame, are incorporated into the collision operator. It is shown that these relaxation rates can be tuned to reduce spurious velocities around curved phase boundaries, without compromising the accuracy of the simulation results. The range of attainable Reynolds numbers is therefore increased. Different outcomes from both head-on and off-centre collisions are simulated, for both equal and unequal size droplets, including coalescence, head-on separation, and off-centre separation. For head-on collisions the critical Weber number between coalescence and separation is shown to decrease with decreasing ambient gas pressure. The variation of critical Weber number with droplet size ratio is also studied. Comparisons are made with the theoretical predictions of Tang et al. [“Bouncing, coalescence, and separation in head-on collision of unequal-size droplets,” Phys. Fluids24, 022101 (2012)], and the effect of ambient gas pressure is again considered. For off-centre collisions, boundaries between different collision outcomes are accurately defined and quantitative comparisons are made with the theoretical predictions of Rabe et al. [“Experimental investigation of water droplet binary collisions and description of outcomes with a symmetric Weber number,” Phys. Fluids22, 047101 (2010)]. While general agreement between the simulated and theoretical boundaries is presented, deviations due to varying liquid viscosity are observed. Finally, the prediction of the independence of regime boundaries with varying droplet size ratio, when using the symmetric Weber number as defined by Rabe et al., is discussed. Simulation results showing qualitative agreement are presented, although some discrepancies are reported.

/pdf/binary-droplet-collision-simulations-by-a-multiphase-35j7ll6ljs.pdf

Binary droplet collision simulations by a multiphase cascaded lattice Boltzmann method

We experimentally examine the dynamics of droplet assembly and recombination processes in a two-dimensional pore-model system. Monodisperse trains of droplets are formed by focusing streams of immiscible fluids into a square microchannel that is connected to a diverging/converging slit microfluidic chamber. We focus on the limit of dilute emulsions and investigate the formation and stability of crystal-like structures when droplets are hydrodynamically coupled in the chamber. The minimal distance between droplets and the spread of droplet lattices are measured as a function of initial control parameters and the relationship between droplet velocity and trajectory is discussed. We demonstrate that the onset of coalescence depends on both the capillary number based on the viscosity of the external phase and the droplet concentration. The draining time of the thin film between droplets in apparent contact is found to depend on fluid characteristics. Such property allows us to examine the crossover between non-coalescing and coalescing droplet microflows by varying the residence time of the dispersion in the microfluidic chamber. This work characterizes droplet interaction and coalescence phenomena during multiphase transport in a simple extensional microgeometry.

/pdf/droplet-arrangement-and-coalescence-in-diverging-converging-3ilyrc14dq.pdf

Droplet arrangement and coalescence in diverging/converging microchannels

Advances in modelling of binary droplet collision outcomes in Sprays: A review of available knowledge

The main objective of the present study is the derivation of models describing the outcome of binary droplet collisions for a wide range of dynamic viscosities in the well-known collision maps (i.e. normalised lateral droplet displacement at collision, called impact parameter, versus collision Weber number). Previous studies by Kuschel and Sommerfeld (Exp Fluids 54:1440, 2013) for different solution droplets having a range of solids contents and hence dynamic viscosities (here between 1 and 60 mPa s) revealed that the locations of the triple point (i.e. coincidence of bouncing, stretching separation and coalescence) and the critical Weber number (i.e. condition for the transition from coalescence to separation for head-on collisions) show a clear dependence on dynamic viscosity. In order to extend these findings also to pure liquids and to provide a broader data basis for modelling the viscosity effect, additional binary collision experiments were conducted for different alcohols (viscosity range 1.2–15.9 mPa s) and the FVA1 reference oil at different temperatures (viscosity range 3.0–28.2 mPa s). The droplet size for the series of alcohols was around 365 and 385 µm for the FVA1 reference oil, in each case with fixed diameter ratio at Δ= 1. The relative velocity between the droplets was varied in the range 0.5–3.5 m/s, yielding maximum Weber numbers of around 180. Individual binary droplet collisions with defined conditions were generated by two droplet chains each produced by vibrating orifice droplet generators. For recording droplet motion and the binary collision process with good spatial and temporal resolution high-speed shadow imaging was employed. The results for varied relative velocity and impact angle were assembled in impact parameter–Weber number maps. With increasing dynamic viscosity a characteristic displacement of the regimes for the different collision scenarios was also observed for pure liquids similar to that observed for solutions. This displacement could be described on a physical basis using the similarity number and structure parameter K which was obtained through flow process evaluation and optimal proportioning of momentum and energy by Naue and Barwolff (Transportprozesse in Fluiden. Deutscher Verlag fur Grundstoffindustrie GmbH, Leipzig 1992). Two correlations including the structure parameter K could be derived which describe the location of the triple point and the critical We number. All fluids considered, pure liquids and solutions, are very well fitted by these physically based correlations. The boundary model of Jiang et al. (J Fluid Mech 234:171–190, 1992) for distinguishing between coalescence and stretching separation could be adapted to go through the triple point by the two involved model parameters C
 a and C
 b, which were correlated with the relaxation velocity $$ u_{\text{relax}} = {\sigma \mathord{\left/ {\vphantom {\sigma \mu }} \right. \kern-0pt} \mu } $$
 . Based on the predicted critical Weber number, denoting the onset of reflexive separation, the model of Ashgriz and Poo (J Fluid Mech 221:183–204, 1990) was adapted accordingly. The proper performance of the new generalised models was validated based on the present and previous measurements for a wide range of dynamic viscosities (i.e. 1–60 mPa s) and liquid properties. Although the model for the lower boundary of bouncing (Estrade et al. in J Heat Fluid Flow 20:486–491, 1999) could be adapted through the shape factor, it was found not suitable for the entire range of Weber numbers and viscosities.

Modelling droplet collision outcomes for different substances and viscosities

The outcomes of binary collisions of water droplets are investigated experimentally for the range of parameters of a spray system used during a severe nuclear reactor accident. Droplets diameters range from 220 to 450 μm with a diameter ratio between 0.5 and 1 and impact velocities between 3 and 10 m s−1. Values of the Weber number based on the small droplet size are between 20 and 280. For droplets with a Weber number up to 120, results in a map of impact parameters versus Weber number show the various regimes, namely, stretching separation, coalescence and reflexive separation. For a higher Weber number, between 120 and 280, the only observed outcomes are the two separation regimes. It is shown that results obtained for unequal droplet sizes match on a single map in terms of the impact parameter and of a new “symmetric” Weber number based on the sum of kinetic energies in the frame of the center of mass and on the sum of surface energies of the two droplets. Ashgriz and Poo [“Coalescence and separation ...

Experimental investigation of water droplet binary collisions and description of outcomes with a symmetric Weber number

Droplet collisions for Weber numbers from 500 up to 2600 have been studied. Experiments have been performed with water and iso-propanol for different impact parameters and different droplet sizes. For higher Weber numbers and in a range of the impact parameter larger than zero a new outcome regime has been observed with larger droplets than found for grazing impacts at impact parameters close to one. Differences for the two liquids and the droplet sizes studied have been identified. Introduction and objectives During the course of a hypothetical severe accident in a Pressurized Water Reactor (PWR), hydrogen can be produced by the core oxidation and distributed into the whole containment. In order to assess the risk of deto- nation, spray systems can be put at the top of the con- tainment to ensure a mixing of the atmosphere, to reduce the total pressure, to cool down the containment walls, and to wash-out the eventually existing fission products present in the air. Spray systems in reactor applica- tions are composed of over 500 interacting water droplet sprays. Droplets are between 100 and 1000 � m large, and are used under pressure (2-3 bars) at water temperatures between 20 and 60 ◦ C, and under gaseous mixture com- posed of water steam, hydrogen and air at temperatures between 60 and 120 ◦ C (1). The droplet size distribution in the containment vessel could have an influence on the spray system efficiency. The droplet size evolution can be modelled by gravity and drag forces, heat and mass trans- fer with the surrounding gas, and droplets interactions. This paper will focus on this latter phenomenon, i.e. on droplet collision. In simulations of interacting sprays, t he modeling of the collision process is absolutely necessary. In order to develop a realistic model of collision, the char- acteristic droplet size distributions are essential.

/pdf/droplet-collision-outcomes-at-high-weber-number-20wfbsb2m8.pdf

Droplet Collision Outcomes at High Weber Number

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Experimental investigation of water droplet binary collisions and description of outcomes with a symmetric Weber number

Droplet Collision Outcomes at High Weber Number