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Experiment of drop diameter impact velocity roughness
mm m/s µm
Stow and Hadfield [142] 1.65 3.62 to 3.82 3 to 12
Range and Feuillebois [115] 1.94 2.16 12 to 23
Xu et al. [166, 167] 3.4 4.3 5 to 78
Pan et al. [103] 0.5 29.6 to 32.5 0.003 to 0.2
Mehdizadeh et al. [83] 0.55 30 0.03
our experiment 0.2 11 to 18 0.75 to 1.25
Table 6.1.: Summary of the conditions of the prompt splash.
Figure 6.9.: Force field analysis on the spreading lamella.
the aerodynamic force are dependent on the lamella thickness and the spreading
velocity. Beside the necessity of sufficiency, the lamella thickness and the spreading
velocity correlate to each other in a complementary manner that a thicker lamella
requires a lower spreading velocity to create the uprising liquid film. For a certain
lamella thickness, there exists a minimum spreading velocity, above which the
liquid corona forms. This velocity is named as the critical spreading velocity. The
viscosity does not enter this hypothesis explicitly, however it influences both the
lamella thickness and the spreading velocity.
Two submodels are desired for the thickness of the lamella, and the corresponding
critical spreading velocity. Ruiter et al. [124] shows that the thickness of the
lamella for the normal impact is multiple times thicker than the boundary layer
which grows proportional to ν water t, where ν is the kinematic viscosity. Furthermore,
the lamella thickness is dependent on the impact velocity. Far away from
splash threshold, the lamella thickness decreased with the increasing impact velocity.
While approaching the splash threshold, the lamella thickness increased, probably
due to the aerodynamic pressure which stalls the spreading of the lamella.
172 6. Results and Discussion