Single Drop Impacts of Complex Fluids: A Review - Drops and Bubbles in Contact with Solid Surfaces - page 273

This work studies the impact of a model viscoplastic fluid (vaseline) on a Plexi-
glas surface, for different impact velocities. The rheological behavior of the fluid
was modeled using a Cross model, modified to include a yield-stress component.
This was found to provide a good fit with viscometric measurements in the range
10 − 2 10 3 s − 1 .

Upon impact at low velocities ( v i =

˙ γ

0 . 67 ms − 1 ), drops decrease sharply in
height, however inertial spreading is small with no lamella formation: drops appear
to be gently deposited on the surface and behave like a deformable solid. A slow
creeping flow is observed thereafter until drops assume a sessile state after approx-
imately 5 minutes. At slightly larger velocities ( v i = 0 . 85 ms − 1 ), drops retract after

maximum inertial spreading and oscillations of the drop height are observed. After
retraction, the diameter continues to spread at a near constant rate. At high impacts
( v i = 2 . 3ms − 1 ), recoil is inhibited with wetted area retractions of no greater than

5% of the maximum spreading. Again, creeping flow is observed, however this is
small and does not affect the maximum drop diameter.
The variation in final drop shape with respect to the impact velocity, which be-
comes noticeable only above the value v i = 0 . 85 ms − 1 , was characterized with

respect to the Bingham number:

τ c D 0
μv i ,

Bm = (3)

where μ is defined as the zero shear rate viscosity μ 0 ; however, such definition of
the viscosity term is not well posed because whilst the Bingham number charac-
terizes the ratio of viscous to yield-stress forces, viscous dissipation only occurs
during fluid motion therefore the μ 0 term is only valid at zero shear rate.
Because surface forces play an important role in all drop impact phenomena, it
is interesting to observe what happens when the yield stress magnitude is compara-
ble with the capillary (Laplace) pressure [16, 17]. This leads to the definition of a
capillary regime and a viscoplastic regime, which can be characterized through the
Bingham-capillary number [19]:

τ c D 0
σ

B

=

. (4)

Whilst in the capillary regime the impact morphology is qualitatively similar to that
of simple liquids, in the viscoplastic regime one can sometimes observe perma-
nent deformations that do not disappear upon impact or under the action of surface
forces.
For example, if drops are produced from a capillary nozzle, the prolate shape
that creates during the fluid extrusion [20-22] remains partly visible after impact,
as shown in Fig. 5, which displays the impact morphology of hairgel-water drops
for different yield stress magnitudes. This phenomenon is also influenced by in-
ertia, and becomes less and less pronounced at higher impact Weber numbers. The
droplets symmetry can be improved significantly if the dispensing nozzle has a very