From a practical viewpoint, the two superhydrophobic states thus
appear to be extremely different: although the apparent (advancing)
contact angles remain comparable, the adhesion is dramatically
increased in the Wenzel state.
In a second series of experiments, we tried to induce direct
transitions between both states.We started from a drop deposited on the
microtextured surface, and increased the pressure exerted by this drop
on its substrate. Two different methods can be used for this purpose.
(1) We varied the drop size:the larger the drop,the smaller the pressure.
Large drops are flattened by gravity
g
to a thickness
h
first described by
Taylor
13
:
h
= 2
a
sin(
θ
*/2), where
a
is the capillary length (
a
= (
γ
/
ρ
g
)
1/2
,
with
γ
the liquid surface tension and
ρ
its density;
a
is 2.7mm for water).
Such a flattened drop exerts a hydrostatic pressure
ρ
gh
on its substrate—
ofthe order of50Pa in our case.For drops small enough that the effect of
gravity is negligible (that is, radius
R
smaller than
a
), the internal
pressure,
∆
P
, in the superhydrophobic limit is given by the Laplace law
(
∆
P
= 2
γ
/
R
), which is also the pressure exerted by the drop on its
substrate, hence the smaller the drop, the larger the pressure. We let
R
vary between 4 and 0.9mm,which allowed us to increase the pressure up
to 150Pa.(2) To reach higher pressures,we placed the drop between two
identical substrates, and compressed it by using a micrometric screw,
which also allowed us to measure the gap
x
between the plates.
The pressure was simply deduced using the Laplace equation
(
∆
P
= 2
γ

cos
θ
*

/
x
, for
x
<<
R
). Figure 2 shows a sequence of these
experiments (note that because of the texture, the surface is iridescent
and reflects in the drop, giving the colours). For each pressure
∆
P
, we
took numerical micrographs of the edge of the drop, from which we
could deduce the contact angle
θ
* with a precision of 5
°
; its value is
plotted as a function of
∆
P
in the same figure.
It is observed that the contact angle first has a plateau value,which
corresponds to the airpocket regime described above. The contact
angle then decreases, which can be interpreted as a progressive
sinking of the drop inside the texture (as seen in equation 2,exploring
the textures, that is, increasing
φ
s
, leads to a decrease of
θ
*). For high
pressures, the contact angle tends towards
θ
* = 145
±
3
°
, in close
agreement with the value obtained by condensing a water drop.
We thus interpret this limit as a Wenzel state.
We then monitored what happens when relaxing the pressure.
In Fig. 3 is a series of snapshots showing the separation between the
plates after imposing a pressure of about 250Pa.Although the contact
angle hysteresis was very small in the Cassie regime, a huge hysteresis
is observed here, which reveals the irreversibility of the transition.