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promoted the prompt splash. Interestingly, the textured surface with regular roughness
elements exhibited less prompt splash than with the random roughness [166].
More interestingly, both the roughness height and width of the textured surface
promoted the prompt splash at lower values and began to affect reversely at larger
values. Prompt splash was completely suppressed with a dimensionless roughness
height R ∗ z = 0.036.
The finding that the random roughness enhanced the splash is in accordance with
the empirical correlation from Stow and Hadfield [142]:
Re 0.31 We 0.69 = K crit , (2.10)
where K crit is a roughness dependent threshold value. Mundo et al. proposed the
following splash threshold for random roughness height between R ∗ z
= 0.018 and
1.3 [99],
OhRe 1.25 = We 1/2 Re 1/4 = K crit = 57.7, (2.11)
where the K crit was equal for all the roughnesses. Cossali et al. [34] suggested later
that the applied roughness by Mundo et al. were in an asymptotic regime, where
the K crit of Stow and Hadfield achieved a nearly constant value. These models are
however empirical correlations which base on an average point of view of both the
prompt splash and the corona splash, because these experiments were conducted
at normal atmosphere pressure, where the both types of splash occur. It should
be noted that the substrate condition in the experiment of Mundo et al. could be
very different from the topic of the roughness, because the roughness height was
comparable with the drop size. It is arguable whether it was a rough surface, or
a randomly uneven surface. Furthermore the impact surface was unlikely to be
dry as we found out by repeating the same impact conditions in our experiment:
a drop train impacted on a rotating cylinder, and the cylinder was cleaned by a
rubber wiper.
Rein et al. [119] summarized the available splash thresholds by expressing a
critical Ohnesorge number as a function of the Reynolds number, as Figure 2.9
exhibits. These semi-empirical correlations can be divided into two categories: one
is for the drop impact on smooth surfaces, the other is for drop impacts on rough
or slightly wetted surfaces.
The threshold from Cossali et al. [34] is for drop impacts on a thin liquid film of
80 µm, which was 2.5% of the drop diameter. Hardalupas et al. [47] conducted
2.2. Drop Impact on Dry Surfaces 21