Biomedical Engineering Reference
In-Depth Information
Figure 3.52
The different approaches to the calculation of the volume of a droplet between two
parallel horizontal plates.
3.8.1.3 Droplet in a Corner: The Concus-Finn Relation
Microfluidic channels and chambers are etched in silicon, glass, or plastic. Let us
investigate first the effect of a corner—or a wedge—on the droplet interface. Take
the case of a 90° wedge. The shape of the droplet is shown in Figure 3.53 depend-
ing on the Bond number
Bo
=
ρgR
2
/
g
where
R
is a characteristic dimension of the
droplet, which can be scaled as the 1/3 power of the value of the volume of liquid
R
3
= 3Vol/
π
.
Let us consider now microdrops in which the Bond number is small. It has been
observed that liquid interfaces in contact with highly wetting solid walls forming a
Figure 3.53
The shape of a liquid drop in a 90° wedge. (a) A small volume droplet of 0.125
m
l tends
to take the form of a sphere despite the different contact angles on the two planes, with a Bond
number of the order of 0.04. (b) A larger droplet of 1.25
m
l—Bond number 4—is flattened by gravity
(Surface Evolver calculation).
