Computational transport processes for micromixers* - Micromixers Fundamentals Design and Fabrication - page 74

3.7 Concluding Remarks..................................................................................................................... 110
References ......................................................................................................................................... 111
3.1 INTRODUCTION
With a great variety of potential applications, transport processes in a micromixer are often rich in
physics. Understanding these processes is crucial to the design of a good micromixer. As both the time
and length scales involved are small, experimental investigations of these processes become
increasingly challenging. Expensive high-resolution measurement equipment are required to provide
data with time and length scales convincingly resolved. In view of this problem, theoretical investi-
gations play an essential complementary role in the design of micromixers. Theoretical investigations
provide useful detailed insights into the physics of the transport processes. It offers the ability to
predict these transport processes.
Of particular interest in this chapter is the prediction of transport processes in micromixers.
Generally, these processes involve the transport of physically and/or chemically distinct species.
These processes can be affected by, among others, the flow, temperature, electric, and magnetic
fields. These physical fields are often interrelated. As a result, the mixing process is governed by
a system of strongly coupled partial differential equations (PDEs). These PDEs can be highly
nonlinear. The geometries of the domain in which the solutions are sought for this system of PDEs
are mostly irregular, in the sense that the boundary of the domain cannot be conveniently repre-
sented using an ordinary or even general curvilinear coordinate system. Attempting an analytical
solution for this system of PDEs in irregular domains is mathematically very demanding. It is,
therefore, not surprising that there are only a limited number of analytical solutions available, often
at the cost of having assumptions that over-simplify the systems of PDEs. For such types of
problems, a numerical solution is one of the most viable options leading to the subject of this
chapter.
This chapter presents a general computational framework for the prediction of mixing process at
the continuum level (see Chapter 2). The numerical engine for the framework is based on the finite
volume method. This is the authors' biased personal choice after having worked on the finite volume
method in recent years. Such a framework is equally applicable to other numerical engines based on
the finite difference or the finite element method. This chapter focuses on the framework, for which
solutions for the system of PDEs can be made, rather than on the various numerical approaches.
Therefore, a comprehensive review of all the available literature related to various numerical
approaches will not be attempted here. In the interest of providing a concise description of the
computational framework implemented by the authors, it is possible that many significant papers
might be omitted. Any such omissions are unintentional and do not imply any judgment as to the
quality and usefulness of these works.
The remaining chapter is divided into five sections. A description of the problem is given in Section
3.2 . In Section 3.3 , the mathematical formulation of the problem is presented, including a discussion of
an outline for incorporating various additional physics. The numerical solution procedure is given in
Section 3.4 . Section 3.5 is devoted to the verifications and validations of the solution procedures.
Examples of mixing problems solved with the current framework are then presented and discussed in