Interfaces, Capillarity, and Microdrops - Microfluidics for Biotechnology - page 85

Figure 3.14 Sketch of a liquid plug moving under capillary forces between two plates. The contact
angle is q < 90°.

γ

P - P =

(3.17)

0 1

R

1

with the notations of Figure 3.15.
For the right side interface

γ

P - P =

(3.18)

0 2

R

2

Subtraction of the two relations leads to

γ æ

1 1 ö

P - P = -

(3.19)

ç ÷

1 2

è R R ø

2 1

Next, we show that R 2 < R 1 . Looking at Figure 3.15, we have

R sin β = d

2 2

where d is the half-distance between the plates.
The angle b is linked to q and a by the relation

π

β = + α θ -

2

Figure 3.15 Curvature of the interface in a dihedral.