Impact of droplets on inclined flowing liquid films

The impact of droplets on an inclined falling liquid film is studied experimentally using high-speed imaging. The falling film is created on a flat substrate with controllable thicknesses and flow rates. Droplets with different sizes and speeds are used to study the impact process under various Ohnesorge and Weber numbers, and film Reynolds numbers. A number of phenomena associated with droplet impact are identified and analyzed, such as bouncing, partial coalescence, total coalescence, and splashing. The effects of droplet size, speed, as well the film flow rate are studied culminating in the generation of an impact regime map. The analysis of the lubrication force acted on the droplet via the gas layer shows that a higher flow rate in the liquid film produces a larger lubrication force, slows down the drainage process, and increases the probability of droplet bouncing. Our results demonstrate that the flowing film has a profound effect on the droplet impact process and associated phenomena, which are markedly more complex than those accompanying impact on initially quiescent films.

Figure 1

Schematic diagram of the experimental setup for droplet impact on falling liquid films which comprises a falling film rig, a droplet-generation unit, and a high-speed imaging system.

Figure 2

Typical images of the wavy flow in the falling liquid films at different Reynolds numbers: (a) $\text{Re}=54$, (b) $\text{Re}=245$, and (c) $\text{Re}=636$. The flow rates are 0.9, 4.1, and 10.7 l/min, respectively.

Figure 3

Time-space plots showing the evolution of the wavy flow in the falling liquid films at different Reynolds numbers: (a) $\text{Re}=54$, (b) $\text{Re}=245$, and (c) $\text{Re}=636$. The flow rates are 0.9, 4.1, and 10.7, l/min respectively. The speeds of the waves can be estimated from the gradient of the dashed lines of the waves.

Figure 4

“Bouncing” of a droplet on a falling liquid film. The dimensionless parameters are $\text{Oh}=0.0021, \text{We}=4$, and $\text{Re}=636$. The droplet speed is 0.3 m/s, the flow rate of the falling film is 10.7 l/min, and the droplet diameter is 3.3 mm. See Ref. [62], Movie 1.

Figure 5

“Partial coalescence” of a droplet on a falling liquid film. The dimensionless parameters are $\text{Oh}=0.0021, \text{We}=4$, and $\text{Re}=54$. The droplet speed is 0.3 m/s, the flow rate of the falling film is 0.9 l/min, and the droplet diameter is 3.3 mm. See Ref. [62], Movie 2.

Figure 6

Formation and propagation of capillary waves immediately after the collapse of the gas layer between the droplet and the liquid film. The dimensionless parameters are $\text{Oh}=0.0021, \text{We}=4$, and $\text{Re}=54$. The droplet speed is 0.3 m/s, the flow rate of the falling film is 0.9 l/min, and the droplet diameter is 3.3 mm.

Figure 7

“Total coalescence” of a droplet on a falling film. The dimensionless parameters are $\text{Oh}=0.0021, \text{We}=76$, and $\text{Re}=636$. The droplet speed is 1.3 m/s, the flow rate of the falling film is 10.7 l/min, and the droplet diameter is 3.3 mm. See Ref. [62], Movie 3.

Figure 8

“Splashing” during droplet impact on a falling film. The dimensionless parameters are $\text{Oh}=0.0021, \text{We}=316$, and $\text{Re}=636$. The droplet speed is 2.67 m/s, the flow rate of the falling film is 10.7 l/min, and the droplet diameter is 3.3 mm. See Ref. [62], Movie 4.

Figure 9

Regime map for droplet impact on falling liquid films. Here, S, T, and M designate splashing, total coalescence, and multiple phenomena as described in Fig. 10. The Ohnesorge number is fixed at $\text{Oh}=0.0021$. The droplet speed is in the range of 0.30–2.99 m/s, the flow rate of the falling film is in the range of 0.9–10.7 l/min, and the droplet diameter is 3.3 mm. The lines are used only to guide readers' eyes.

Figure 10

Probability of occurrence of different phenomena as a function of $\text{Re}$ with $\text{Oh}=0.0021$ and $\text{We}=4$. The droplet speed is 0.30 m/s, the flow rate of the falling film is in the range of 0.9–10.7 l/min, and the droplet diameter is 3.3 mm.

Figure 11

Schematic diagram of the flow in the gas layer and the liquid film beneath the droplet during the impact on flowing liquid film.

Figure 12

Estimation of the lubrication force normalised by the gravitational force normal to the film, $F_{\text{gravity}}=\frac{1}{6}\pi d^3\rho gcos\left(\theta \right)$, as a function of the flow rate of the liquid film at different thicknesses of the gas layer.

Figure 13

Schematic diagram of the droplet deformation and the pressure.

Figure 14

Histogram of the lifetime of the gas layer for three impact phenomena: bouncing, partial coalescence, and total coalescence. The dimensionless parameters are $\text{Oh}=0.0021, \text{We}=4$, and $\text{Re}$ in the range of 54–636. The droplet speed is 0.30 m/s, the flow rate of the falling film is in the range of 0.9–10.7 l/min, and the droplet diameter is 3.3 mm.

Figure 15

Dimple formation and droplet ejection during the impact of a large droplet on a falling film. The dimensionless parameters are $\text{Oh}=0.0016, \text{We}=6.5$, and $\text{Re}=54$. The droplet speed is 0.3 m/s, the flow rate of the falling film is 0.9 l/min, and the droplet diameter is 5.2 mm. See Ref. [62], Movie 5.

Figure 16

Effects of the droplet size, the droplet speed, and the film flow rate on the propagation of the baseline during droplet splashing. (a) Schematic diagram of the definition of the coordinate system. (b) Effect of the droplet size. The droplet speed is 1.87 m/s, the film flow rate is 0.9 l/min, and correspondingly $\text{Re}=54$ and $\text{We}$ in the range of 156–254. (c) Effect of the droplet speed. The film flow rate is 4.1 l/min, the droplet diameter is 3.3 mm, and correspondingly $\text{Re}=245$ and $\text{Oh}=0.0021$. (d) Effect of the film flow rate. The droplet speed is 2.67 m/s, and the droplet radius is 3.3 mm, and correspondingly $\text{Oh}=0.0021$ and $\text{We}=316$. The inset shows two images of crowns at different film flow rates.