Splash of a drop impacting onto a solid substrate wetted by a thin film of another liquid

In this study, the impact of a liquid drop onto a thin liquid film of a different fluid is investigated experimentally using a high-speed video system and analysed theoretically to obtain expressions for predicting splashing thresholds. The study focuses on impact conditions leading to one of four outcomes: deposition, corona without splash, corona splash, and partial rebound. In addition to the conventional influencing parameters, which are usually described by combinations of impact Weber and Reynolds numbers and dimensionless film thickness, also the ratio of the drop and film liquid viscosities have been systematically varied over a wide range. The results of the theoretical analysis, in good agreement with the experimental observations, show that the well-known $K$ number determines the splashing threshold only if the viscosity of the film is much larger or much smaller than the drop viscosity. If the drop and film viscosities are comparable, a critical modified $K$ number is introduced, which is a function of the viscosity ratio.

Figure 1

Different impact outcomes: (a) deposition, (b) corona (without splash), (c) corona splash, (d) corona detachment, and (e) partial rebound.

Figure 2

Schematic illustration of the experimental setup.

Figure 3

Drop size influence on corona development: S65 drop impacting onto a water film with $\kappa =0.015$, $U_0=2.3$ m/s, and $h=0.5$ mm. Drop diameter is $D_0=1.8$ mm (left) and $2.2\mathrm{mm}$ (right), resulting in dimensionless film thicknesses of $\delta =0.28$ and 0.23.

Figure 4

Impact velocity influence on corona development: water drop ($D_0=2$ mm) impacting onto a S10 film with $h=0.5$ mm and $\kappa =9.9$. Impact velocity is $U_0=1.7$ (left) and 2.3 m/s (right).

Figure 5

Film thickness influence on the corona development: A S5 drop impacting onto a S10 wall film with from left to right $\delta =0.04$, 0.11, and 0.23. The impact velocity is $U_0=3.2$ m/s, the drop diameter is $D_0=2.2$ mm, and the viscosity ratio is $\kappa =0.5$. Relevant movies can be found at Ref. [34].

Figure 6

Influence of fluid combination on the corona development: Impact of a S5 drop onto a S65 film (left) with $\kappa =13$ and of a S65 drop impacting onto a S5 film (right) with $\kappa =0.08$ for $\delta =0.25$, $U_0=2.3$ m/s, and $D_0=2$ mm.

Figure 7

Temporal development of the spreading of a S350 drop impacting onto wall films ($\delta =0.23$) of different viscosities: (a) wall film of S1000; (b) wall film of S100000; and (c) impact onto glass for comparison. The impact velocity is $U_0=3.2$ m/s and drop diameter is $D_0=2.3$ mm.

Figure 8

Temporal development of the corona evolution of a S350 drop impacting onto different wall films: (a) S5; (b) S10; and (c) S20 for the same dimensionless film thickness $\delta =0.04$, impact velocity of $U_0=3.2$ m/s, and drop diameter of $D_0=2.3$ mm.

Figure 9

Effect of viscosity ratio ($\kappa$) on the outcome of drop impact with $\delta =0.25$, $D_0=2$ mm, and $U_0=2.3$ m/s.

Figure 10

Consecutive stages of drop impact onto a wetted substrate: (a) initial drop deformation and penetration into the wall film, inception of the viscous boundary layer on the wall; (b) boundary-layer growth leads to intersection with the drop/film liquid interface; and (c) liquid layer in the crater is thinner than the viscous boundary layer.

Figure 11

Map of the experimentally observed outcomes of drop impact. Region I of splash occurrences corresponds to very viscous drops, and region II corresponds to splash occurrences on a very viscous wall film. The relative film thickness varies in the range $0.036<\delta <0.29$ and the viscosity ratio in the range ${10}^{-4}<\kappa <{10}^4$.

Figure 12

Map of the experimentally observed outcomes of drop impact for region III, when the viscosities of the drop and wall film liquids are comparable and $K_{\text{d}}>100$ and $K_{\text{f}}>100$. The relative initial wall film thickness varies in the range $0.05<\delta <0.22$. The data belonging to regions I and II (determined from Fig. 11) are not included.