Abstract
The impact of the drop on an immiscible liquid surface is common in many applications, where differences in physical properties like viscosity and thickness of the target liquid layer are crucial to the impact outcomes. We experimentally investigate the effect of dimensionless thickness \(\beta\) (ratio of film thickness to drop diameter) and dimensionless viscosity (ratio of film viscosity to drop viscosity) on the water drop impact upon silicone oil surfaces. For the ultra-thin film (\(\beta\) = 0.002), drop bouncing resembles when impinging on superhydrophobic surfaces, except that the rupture of oil film results in a residual drop liquid. The dimensionless viscosity determines the receding contact angle, maximum retraction velocity and drop contact time. For the thin film (\(\beta\) = 0.1), we observe capillary climbing of oil film due to Neumann’s condition and the subsequent compound central jet. In addition, film viscosity plays a significant role in the number of fingers and crown emergence. For the thick film (\(\beta\) = 1) and pool (\(\beta\) = 5), we derive a theoretical model to predict the maximum penetration depth of the crater in the pool and the maximum expansion width of the crater in the thick film, which is validated by experimental results.
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Abbreviations
- D :
-
The equivalent diameter of drop
- U :
-
The impact velocity of drop
- \(\rho _{{\textrm{d}}}\) :
-
Density of drop fluid
- \(\nu _{{\textrm{d}}}\) :
-
Kinematic viscosity of drop fluid
- \(\sigma _{{\textrm{d}}}\) :
-
Surface tension of drop fluid
- \(\rho _{{\textrm{f}}}\) :
-
Density of film fluid
- \(\nu _{{\textrm{f}}}\) :
-
Kinematic viscosity of film fluid
- \(\sigma _{{\textrm{f}}}\) :
-
Surface tension of film fluid
- \(\sigma _{{\textrm{df}}}\) :
-
Interface tension between drop and film liquid
- \(H_{{\textrm{f}}}\) :
-
Thickness of liquid film
- \(\beta\) :
-
Dimensionless film thickness
- \(\eta\) :
-
Ratio of film viscosity to drop viscosity
- \({\text {We}}_{{\textrm{d}}}\) :
-
Weber number of drop
- \({\text {Oh}}_{{\textrm{d}}}\) :
-
Ohnesorge number of drop
- \({\text {Fr}}_{{\textrm{d}}}\) :
-
Froude number of drop
- \({\text {Re}}_{{\textrm{f}}}\) :
-
Reynold number of liquid film
- t :
-
Time
- \(\tau\) :
-
Dimensionless time
- \(D_{{\textrm{s}}}\) :
-
Spreading diameter of drop
- \(U_{{\textrm{s}}}\) :
-
Spreading velocity of drop
- \(D_{\textrm{max}}\) :
-
The maximum spreading diameter
- \(U_{\textrm{rmax}}\) :
-
The maximum receding velocity of drop
- \(t_{{\textrm{c}}}\) :
-
Contact time between drop and film
- \(\theta _{{\textrm{r}}}\) :
-
Receding contact angle of drop
- \(t_{{\textrm{i}}}\) :
-
The capillary-inertial time
- S :
-
Spreading parameter
- \(\alpha\) :
-
Dimensionless radial radius of crater
- \(\zeta\) :
-
Dimensionless translation distance of crater center
- \(H_{{\textrm{c}}}\) :
-
Penetration depth of crater
- \(\alpha _0\) :
-
Numerical constant
- \(D_{{\textrm{c}}}\) :
-
Expanding width of crater
- \(H_{\textrm{cmax}}\) :
-
The maximum penetration depth in the pool
- \(D_{\textrm{cmax}}\) :
-
The maximum expanding width in thick film
- \(E_{{\textrm{k}}}\) :
-
The initial kinematic energy of drop
- \(E_{{\textrm{s}}}\) :
-
The initial surface energy of drop
- \(E_{{\textrm{p}}}\) :
-
The potential energy of thinly spread drop
- \(E_{{\textrm{d}}}\) :
-
The dissipated energy in the pool liquid during impact
- \(t_\textrm{crater}\) :
-
The time to reach the maximum impact crater
- \(\Omega\) :
-
Volume of the maximum impact crater
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Funding
This study was supported by the National Natural Science Foundation of China (11972339, 12302350, 11932019, 12388101), Natural Science Basic Research Plan in Shaanxi Province of China (S2023-JC-QN-0752), the Fundamental Research Funds for the Central Universities (WK2090000023), and the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB22040403).
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Luo, L., Tian, Y. & Li, E. Experimental study on the impact behaviors of a water drop on immiscible oil surfaces: bouncing, compound central jet formation and crater evolution. Exp Fluids 65, 40 (2024). https://doi.org/10.1007/s00348-024-03781-5
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DOI: https://doi.org/10.1007/s00348-024-03781-5