Biomedical Engineering Reference
In-Depth Information
substrate). Apparently, it should result in a unique value of the static contact angle.
However, it happens frequently that the static contact angle is not uniquely defined,
because a static angle is obtained after stopping a moving interface [33-35]. It can
be comprised between two values, the first obtained by slowing down to a stop at
an advancing front
q
s,a
, and another value (smaller) obtained by slowing down to a
stop at a receding front
q
s,r
as shown in Figure 4.41.
4.3.5 Interface and Meniscus
The shape of liquid plug in a capillary tube depends on the capillary forces. A liquid
plug moving inside a capillary tube (or between two parallel plates) is limited by
two meniscus, one corresponding to the advancing front (index
a
), the other one
corresponding to the receding front (index
r
) as shown in Figure 4.42. In microcap-
illaries, because the gravity force is negligible, menisci have spherical shapes. Note
that receding, advancing, and static contact angles are not identical.
4.3.6 Microflow Blocked by Plugs
In this section we analyze the motion of one or more liquid plugs inside a cylindrical
capillary tube. We use a lumped model and we show that Bernoulli's equation com-
bined with Tanner's law explains the main features of the behavior of liquid plugs
moving inside capillary tubes [36]. Flow regions may be decomposed in two steps
(Figure 4.43); first the regions where a fluid moves inside the capillary, inducing a
friction pressure drop; second, the interfaces that induce a capillary pressure drop.
The total pressure drop in the capillary is then
D
P
= D
P
+ D
P
(4.60)
channel
cap
drag
Figure 4.41
Hoffman-Tanner law for advancing and receding contact angles versus capillary num-
ber. The advancing contact angle is larger than the receding contact angle and there is a static
hysteresis at zero velocity.
