Interfaces, Capillarity, and Microdrops - Microfluidics for Biotechnology - page 95

And the capillary force that links the plates together is

2 γ θ π cos

2

F » R (3.37)

h

This capillary force can be quite important if the contact angle q is small; for h =
10 m m and R = 1 cm, the force F is of the order of 2.5N. However, if q = π /2, there is
no cohesion between the two plates. Conversely, if q > π /2 the liquid droplet pushes
apart the two plates, and the droplet can be used as a load carrier [17].

3.6.3 Capillary Rise in a Tube—Jurin's Law
When a capillary tube is plunged into a volume of wetting liquid, the liquid rises
inside the tube under the effect of capillary forces (Figure 3.31). It is observed that
the height reached by the liquid is inversely proportional to the radius of the tube.
This property is usually referred to as Jurin's law . Using the principle of minimum
energy, one can conclude that the liquid goes up in the tube if the surface energy
of the dry wall is larger than that of the wetted wall. If we define the impregnation
criterion I by

= - (3.38)
The liquid rises in the tube if I > 0. Upon substitution of the Young law in
(3.38), the impregnation criterion can be written under the form

I γ γ

SG SL

I γ θ = cos

(3.39)

Figure 3.31 Capillary rise is inversely proportional to the capillary diameter.