Computational transport processes for micromixers* - Micromixers Fundamentals Design and Fabrication - page 73

CHAPTER

3

Computational transport
processes for micromixers *

CHAPTER OUTLINE

3.1 Introduction ................................................................................................................................... 74
3.2 Problem Description ....................................................................................................................... 75
3.3 Mathematical Formulation............................................................................................................... 75
3.3.1 Species transport.........................................................................................................75
3.3.2 Fluid transport.............................................................................................................76
3.3.3 Energy transport ..........................................................................................................77
3.3.4 Electric and magnetic fields .........................................................................................77
3.3.4.1 Electroosmotic flows ................................................................................................78
3.3.4.2 Ferrofluid flows ........................................................................................................79
3.3.5 Two-fluid flows ............................................................................................................80
3.4 Solution Procedure......................................................................................................................... 82
3.4.1 General transient convection-diffusion equation.............................................................82
3.4.2 Finite volume formulation.............................................................................................82
3.4.2.1 Higher-order schemes .............................................................................................86
3.4.2.2 Remarks .................................................................................................................87
3.4.3 Solution algorithm .......................................................................................................88
3.5 Verifications and Validations........................................................................................................... 88
3.5.1 Verification - solution procedure of the general transient convection diffusion equation .....89
3.5.2 Validation - solution procedure of the Navier-Stokes equations .......................................90
3.5.3 Validation - solution procedure of the level-set method ...................................................91
3.6 Examples ....................................................................................................................................... 92
3.6.1 Mixing in a micro-enclosure..........................................................................................92
3.6.2 Mixing in a lid-driven microcavity..................................................................................92
3.6.3 Mixing in a straight microchannel .................................................................................96
3.6.4 Mixing in winding microchannels ..................................................................................96
3.6.5 Mixing within a droplet flowing in a straight microchannel ...............................................97
3.6.6 Mixing within a droplet flowing through a micro-U-bend ................................................100
3.6.7 Mixing in three thermocapillary merged droplets...........................................................101
3.6.8 Mixing within a droplet driven by electroosmotic flow in an enclosure.............................104
3.6.9 Mixing within a ferrofluid droplet.................................................................................107

* This chapter is contributed by Yit Fatt Yap (Petroleum Institute, United Arab Emirates), Jing Liu (Nanyang Technological
University, Singapore), and John Chee Kiong Chai (Petroleum Institute, United Arab Emirates).