Binary droplet collision at high Weber number

By using the techniques developed for generating high-speed droplets, we have systematically investigated binary droplet collision when the Weber number (We) was increased from the range usually tested in previous studies on the order of 10 to a much larger value of about 5100 for water (a droplet at 23 m/s with a diameter of 0.7 mm). Various liquids were also used to explore the effects of viscosity and surface tension. Specifically, beyond the well-known regimes at moderate We’s, which exhibited coalescence, separation, and separation followed by satellite droplets, we found different behaviors showing a fingering lamella, separation after fingering, breakup of outer fingers, and prompt splattering into multiple secondary droplets as We was increased. The critical Weber numbers that mark the boundaries between these impact regimes are identified. The specific impact behaviors, such as fingering and prompt splattering or splashing, share essential similarity with those also observed in droplet-surface impacts, whereas substantial variations in the transition boundaries may result from the disparity of the boundary conditions at impacts. To compare the outcomes of both types of collisions, a simple model based on energy conservation was carried out to predict the maximum diameter of an expanding liquid disk for a binary droplet collision. The results oppose the dominance of viscous drag, as proposed by previous studies, as the main deceleration force to effect a Rayleigh-Taylor instability and ensuing periphery fingers, which may further lead to the formations of satellite droplets.

Figure 1

Schematic of the experimental setup for droplets carried by a high-speed flow. 1: air compressor; 2: pressure controlling valve; 3: flow meter; 4 and 5: droplet generators; 6: contraction and acceleration sections; 7: enclosed test section; 8: upstream tank with porous medium filter; 9: high-speed camera; 10: LED lamp; 11: personal computer; 12: electronic control box.

Figure 2

The collision sequence between two water droplets showing temporary coalescence followed by separation and satellite droplets $\left(\text{We}=58,V_r=2.45\text{m}/\text{s},D=0.7\text{mm}\right)$.

Figure 3

The collision sequence between two water droplets showing (a) fingering $\left(\text{We}=210,V=3.89\text{m}/\text{s},D=1.0\text{mm}\right)$; (b) fingering and separation $\left(\text{We}=277,V_r=4.26\text{m}/\text{s},D=1.10\text{mm}\right)$; (c) breakup $\left(\text{We}=878,V_r=9.50\text{m}/\text{s},D=0.70\text{mm}\right)$; (d) prompt splattering $\left(\text{We}=1593,V_r=12.80\text{m}/\text{s},D=0.70\text{mm}\right)$; (e) prompt splattering $\left(\text{We}=5144,V_r=23.00\text{m}/\text{s},D=0.70\text{mm}\right)$.

Figure 4

(Color online) The collision sequences of two water droplets for (a) splattering at the receding phase $\left(\text{We}=442.3,V_r=5.13\text{m}/\text{s},D=1.21\text{mm}\right)$ and (b) splattering at the expanding phase with radius about the maximum $\left(\text{We}=805.2,V_r=9.10\text{m}/\text{s},D=0.70\text{mm}\right)$. $\text{Scale}\text{bar}=0.50\text{mm}$.

Figure 5

(Color online) The variation in breakup diameter $\left(D_b\right)$ normalized by droplet diameter $\beta$ versus Weber number, fitted with a third-order polynomial. The boundaries separating different regimes are also marked at the axis, indicating Regime I: coalescence, II: separation, III: separation with satellite droplets, IV: fingering, V: fingering and separation, VI: breakup, and VII: prompt splattering.

Figure 6

The collision sequences of two water droplets for (a) splattering at the expanding stage $\left(\text{We}=1176,V_r=11.00\text{m}/\text{s},D=0.70\text{mm}\right)$ and (b) prompt splattering $\left(\text{We}=1520,V_r=12.50\text{m}/\text{s},D=0.70\text{mm}\right)$. (c) shows the transient image that was once captured almost immediately after the impact at the same condition as (b).

Figure 7

(Color online) (a) The variation in normalized breakup diameter $\left(\beta =D_b/D\right)$ with respect to We for different fluids, also fitted by polynomial lines; (b) critical We’s versus Oh, also fitted by straight lines.

Figure 8

(Color online) The variation in maximum spread factor $\left(\xi =D_e/D\right)$ versus the Reynolds number. The triangles represent the measured data for collisions between two droplets made of water and the circles represent those made of water-57% glycerine. The solid lines are the predictions of Pasandideh-Fard et al. [19] for droplet-surface collision and the dashed lines are those of our present model in the corresponding ranges of measured We and Re for binary droplet collision.

Figure 9

Impact configuration of the model for expansion of coalesced droplets.

Figure 10

(Color online) The variation in maximum spread factor $\left(\xi =D_e/D\right)$ versus the Weber number. The triangles represent the measured data for collisions between two droplets made of water and the circles represent those made of water-57% glycerine. The solid and the dashed lines are the predictions of our present model, respectively, for these two liquids.