Chapter 3
Computational Analysis of Flow
and Mixing in Micromixers
Abstract This chapter introduces the computational framework and provides a
detailed analysis on the different numerical techniques for the analyses of flow
and mixing in micromixers. Flow and mixing analyses are based on both the Eulerian and Lagrangian approaches; relative advantages and disadvantages of these
two approaches and suitability to different types of mixing problems are analyzed.
This chapter also discusses the various facets of numerical schemes subjected to
discretization errors and computational grid requirements. Since a large number of
studies are based on commercial CFD packages, relevant details of these packages
to the mixing problem are presented. This chapter concludes with mixing characterization technique using concentration data obtained on a computational grid, and
provides the basis for performance evaluation of different micromixer designs. This
chapter consists of three sections. Section 3.1 presents the Eulerian approach for
flow and mixing analyses, different mixing models, boundary conditions, and the
numerical approach employed in obtaining solutions of the governing equations.
The Lagrangian approach is presented in Sect. 3.2. In the final section, the method
for mixing quantification is discussed.
3.1 Eulerian Approach to Mixing
The following assumptions are made to obtain the simplified governing equations
for flow dynamics in micromixers:
1. Smooth and isothermal walls
2. Incompressible and Newtonian fluid flow
3. Constant diffusion coefficient for the two mixing fluids
4. Negligible wall surface tension
The continuity and Navier–Stokes equations can be written as follows:
∂U i
∂ x i
= 0
(3.1)
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
A. Afzal and K.-Y. Kim, Analysis and Design Optimization of Micromixers,
SpringerBriefs in Computational Mechanics,
https://doi.org/10.1007/978-981-33-4291-0_3
35
Computational Analysis of Flow
and Mixing in Micromixers
Abstract This chapter introduces the computational framework and provides a
detailed analysis on the different numerical techniques for the analyses of flow
and mixing in micromixers. Flow and mixing analyses are based on both the Eulerian and Lagrangian approaches; relative advantages and disadvantages of these
two approaches and suitability to different types of mixing problems are analyzed.
This chapter also discusses the various facets of numerical schemes subjected to
discretization errors and computational grid requirements. Since a large number of
studies are based on commercial CFD packages, relevant details of these packages
to the mixing problem are presented. This chapter concludes with mixing characterization technique using concentration data obtained on a computational grid, and
provides the basis for performance evaluation of different micromixer designs. This
chapter consists of three sections. Section 3.1 presents the Eulerian approach for
flow and mixing analyses, different mixing models, boundary conditions, and the
numerical approach employed in obtaining solutions of the governing equations.
The Lagrangian approach is presented in Sect. 3.2. In the final section, the method
for mixing quantification is discussed.
3.1 Eulerian Approach to Mixing
The following assumptions are made to obtain the simplified governing equations
for flow dynamics in micromixers:
1. Smooth and isothermal walls
2. Incompressible and Newtonian fluid flow
3. Constant diffusion coefficient for the two mixing fluids
4. Negligible wall surface tension
The continuity and Navier–Stokes equations can be written as follows:
∂U i
∂ x i
= 0
(3.1)
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
A. Afzal and K.-Y. Kim, Analysis and Design Optimization of Micromixers,
SpringerBriefs in Computational Mechanics,
https://doi.org/10.1007/978-981-33-4291-0_3
35