Computational transport processes for micromixers* - Micromixers Fundamentals Design and Fabrication - page 80

3.3.5 Two-fluid flows
The flows of two different immiscible fluids are often encountered in micromixers, for example,
droplets in a carrier fluid. Such a droplet in a carrier fluid system forms the basis of droplet-based (or
digital) microfluidics. In the context of micromixers, the droplets serve as container for the trans-
portation of chemical or biological agents with excellent physical and chemical isolation and as
microreaction chambers. The motion of the droplets in microchannels results in a circulatory flow
within the droplets and therefore enhances mixing and chemical reaction of their contents. Central to
the investigation of the transport processes involved in such configurations is the prediction of
a dynamically evolving interface between the two fluids. The aim of this section is to incorporate such
a two-fluid flow feature into the current computational framework.
Figure 3.2 shows the domain of interest consisting of two fluids, i.e., the -ve and the

þ ve fluids,

U and the U þ regions, respectively. The subregion U D with species X

with each occupying the

U þ region. These fluids are separated by the interface G

concentrated is now contained within the . The

evolution of the interface is treated with the level-set method [6] . The level-set function is defined
mathematically as

8
<

d;
0

if x˛U
if x˛G
if x˛U þ

f ¼ ;

þ

(3.33)

:

d ;

where d is the shortest normal distance from the interface. The domain of interest is visualized as
consisting of a single special fluid. This fluid is special in the sense that its properties at a given time
and location are set to the properties of either the -ve or the

ve fluids, depending on whichever
occupies that particular location at that particular time. The properties of the special fluid can be
conveniently expressed using the level-set function as either an arithmetic mean of the form

þ

aðfÞ¼ð 1 H Þa þ Ha þ (3.34a)

or a harmonic mean of the form

1
aðfÞ ¼

1 H

a

H
a þ

þ (3.34b)

FIGURE 3.2

Domain of interest consisting of two immiscible fluids.