Wetting Dynamics of Aqueous Surfactant Solutions on Polymer Surfaces - Drops and Bubbles in Contact with Solid Surfaces - page 73

Figure 2. Liquid drop on a solid surface: G, L and S stand for gas, liquid and solid, respectively.

Figure 3. Shape of a liquid drop on a solid surface: P = P i − P e .

For a sufficiently small drop of a partial wetting or non-wetting liquid placed
on a planar surface, gravity effects can be neglected. For such a drop, hydrostatic
pressure inside the drop equilibrates and the drop adopts a shape to conform to the
Laplace law:

γ LG

,

1
R 1 +

1
R 2

P = (2)

where P is the pressure difference between two sides of a curved interface char-
acterized by the principal radii of curvature R 1 and R 2 . The drop shape would be
spherical as shown in Fig. 3. For complete wetting of a flat surface, this pressure can
be reduced towards zero by simultaneously increasing both R 1 and R 2 conserving
the volume of the liquid.
The Young equation (1) describes the mechanical balance at the TPC line for an
ideal surface. However, the equilibrium contact angle Y in the equation can be
obtained only on a perfectly smooth and homogeneous solid surface. In case of the
non-ideality of real solid surfaces, i.e., physical roughness and heterogeneity of sur-
face energy densities across the surface, a given solid-liquid system experimentally
produced different contact angles depending on how the experiment was performed.
In particular, careful experiments have shown two relatively reproducible values of
the contact angle—one as the TPC line advances across the surface and one as it
recedes. Therefore, there is a fundamental issue of how liquid displacement at a
solid surface is to be understood.
3. Contact Angle Hysteresis

Upon causing rapid displacement of a TPC line over a solid surface to a new lo-
cation, experiments have shown static contact angles depend on the direction of