Fundamentals and Applications of Microfluidics
This forward-looking book explains how to take advantage of the performance benefits of microfluidics and serves as a reference for technology and applications in this area.
TABLE OF CONTENTS Fundamentals and Applications of Microfluidics
9.3: Micromixers
9.3 Micromixers
In biomedical and chemical analysis, a sample solution is to be tested with a reagent. The two solutions are mixed to make the reaction possible. While in macroscale mixing is achieved with turbulence, mixing in microscale relies mainly on diffusion due to the laminar behavior at low Reynolds numbers. The mixing rate is determined by the flux of diffusion ?:
| (9.6) |  |
where D is the diffusion coefficient in m 2/sec and c is the species concentration in kg/m 3. The diffusion coefficient is a fluid property, which was derived by Einstein as [28]:
| (9.7) |  |
where R is the gas constant, T is the absolute temperature, N A = 6.02 10 23 is the Avogadro number, and f is the friction factor that is proportional to the viscosity ?. At a constant temperature, D is inversely proportional to ?:
| (9.8) |  |
where C D is the constant incorporating all other factors. Figure 9.8 depicts the range of diffusion coefficients of different materials. Tables 9.3 and 9.4 list some typical values for gases and liquids.
| Gas pair | T (K) | D (cm 2 /s) |
|---|---|---|
| Air-CH 4 | 273 | 0.196 |
| Air-H 2 | 273 | 0.611 |
| Air-H 2O | 298.2 | 0.260 |
| Air-benzene | 298.2 | 0.096 |
| Air-butanol | 299.1 | 0.087 |
| CH 4-H 2 | 298.0 | 0.726 |
| CO-H 2 | 295.6 | 0.7430 |
| CO 2-H 2 | 298.0 | 0.6460 |
| CO 2-H 2O | 307.5 | 0.202 |
| H 2-H |
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