Fundamentals of mass transport in the microscale - Micromixers Fundamentals Design and Fabrication - page 9

CHAPTER

2

Fundamentals of mass transport
in the microscale

CHAPTER OUTLINE

2.1 Transport Phenomena ..................................................................................................................... 10
2.1.1 Molecular level ............................................................................................................10
2.1.2 Continuum level ..........................................................................................................14
2.1.2.1 Conservation of mass...............................................................................................14
2.1.2.2 Conservation of momentum .....................................................................................15
2.1.2.3 Conservation of energy.............................................................................................21
2.1.2.4 Conservation of species ...........................................................................................22
2.2 Molecular Diffusion ........................................................................................................................ 22
2.2.1 Random walk and Brownian motion...............................................................................22
2.2.2 Stokes-Einstein model of diffusion ...............................................................................23
2.2.3 Diffusion coefficient.....................................................................................................24
2.2.3.1 Diffusion coefficient in gases....................................................................................24
2.2.3.2 Diffusion coefficient in liquids ..................................................................................25
2.2.3.3 Diffusion coefficient of electrolytes ...........................................................................26
2.3 Taylor Dispersion ........................................................................................................................... 28
2.3.1 Two-dimensional analysis .............................................................................................28
2.3.2 Three-dimensional analysis...........................................................................................34
2.4 Chaotic Advection .......................................................................................................................... 36
2.4.1 Basic terminologies .....................................................................................................36
2.4.2 Examples of chaotic advection ......................................................................................40
2.4.2.1 Lorentz's convection flow .........................................................................................40
2.4.2.2 Dean flow in curved pipes........................................................................................40
2.4.2.3 Flow in helical pipes ................................................................................................46
2.4.2.4 Flow in twisted pipes ...............................................................................................47
2.4.2.5 Flow in a droplet ......................................................................................................50
2.5 Viscoelastic effects........................................................................................................................ 53
2.6 Electrokinetic Effects ..................................................................................................................... 55
2.6.1 Electroosmosis ............................................................................................................55
2.6.1.1 The Debye layer ......................................................................................................55
2.6.1.2 Electroosmotic transport effect .................................................................................57
2.6.1.3 Electrokinetic flow between two parallel plates ..........................................................58
2.6.1.4 Electrokinetic flow in a cylindrical capillary ...............................................................60
2.6.1.5 Electrokinetic flow in a rectangular microchannel......................................................61