Biomedical Engineering Reference
In-Depth Information
C h a p t e r 3
Interfaces, Capillarity, and Microdrops
3.1 Introduction
Microfluidics in biotechnological systems are not limited to microflows. Each time
that a liquid is in contact with another fluid or liquid, such as air or another im-
miscible liquid, an interface forms. This interface is associated to surface tension
forces which can be very important at the microscale, compared to the other forces
such as gravity and inertia, as shown in Chapter 1. At the contact of a solid surface,
capillarity forces appear and play an important role. They may even dominate or
govern the flow. In this section we present the notion of interface and the theory of
capillarity, and we apply it to the physics of microdrops, which are frequently found
in microfluidic systems.
3.2 Interfaces and Surface Tension
Fluids can be miscible or immiscible. When they are immiscible, an interface sepa-
rates the two fluids.
3.2.1 The Notion of Interface
An interface is the geometrical surface that delimits two immiscible fluid domains.
This is a mathematical definition which implies that an interface has no thickness
and is smooth (i.e. has no roughness). As practical as it is, this definition is a sche-
matic concept. The reality is much more complex, and the separation of two im-
miscible fluids (water/air, water/oil, and so forth) depends on molecular interactions
between the molecules of each fluid [1] and on Brownian diffusion (thermal agita-
tion). A microscopic view of the interface between two fluids looks more like the
scheme of Figure 3.1. In the presence of a wall, the interface contacts the wall along
a triple line.
However, in engineering applications, the mathematical concept regains its util-
ity. At a macroscopic size, the picture of Figure 3.1(b) can be replaced by that of
Figure 3.2, where the interface is a mathematical surface without thickness and
the contact angle
q
is uniquely defined by the tangent to the surface at the contact
line.
In a condensed state, molecules attract each other. Molecules located in the
bulk of a liquid have isotropic interactions with all the neighboring molecules; these
interactions are mostly van der Waals attractive interactions for organic liquids and
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