Interfaces, Capillarity, and Microdrops - Microfluidics for Biotechnology - page 104

Figure 3.42 Pinning of a drop moving from a hydrophobic area towards a hydrophilic surface due
to a defect of the surface.

droplet cannot move even if capillary forces are applied on it. We show in Figure
3.42 a Surface Evolver numerical simulation of pinning of a droplet during its mo-
tion from a hydrophobic to a hydrophilic substrate.

3.7.4 Pinning of a Microdroplet—Quadruple Contact Line
Pinning may also occur at a transition line between two surfaces with different
chemical coatings, inducing a sharp transition of wettability [8]. This effect is due to
the fact that, when the contact line reaches the separation line, we have a four-phase
contact line. The canthotaxis condition states that there is equilibrium as long as
the contact angle is comprised between the Young angles on both sides q 1 and q 2 as
shown in Figure 3.43 [8, 9]

θ θ θ £ £ (3.62)

1 2

Equation (3.62) can be written in terms of surface energy

æ ö æ ö

γ - γ γ - γ

S G 1 S L 1 S G 2 S L 2

arccos £ £ θ arccos (3.63)

ç ÷ ç ÷

è γ ø è γ ø

Figure 3.43 Quadruple contact line pinning on a wettability boundary. (a) Vertical cross section of
the droplet with the limiting contact angles q 1 and q 2 . (b) An Evolver simulation of the droplet.