Microfluidics for Biologists Fundamentals and Applications

D diffusion coefficientðÞ¼w^2 ðÞwidth to diffuse=2tdiffðÞðtime to diffuse 1 : 85 Þ

The time to diffuse is dependent on the particle velocity in the fluid (U 0 ) and the
length (L) it will travel before diffusing completely to the adjacent stream. Thus,
eq. (1.85) can be written as

D¼w^2 U 0 =2L ð 1 : 86 Þ

However, the particle has to diffuse through only half of the total width of the
H-connecting arm because the other half is filled with different liquid. Due to this
w becomes w/2 and eq. (1.86) will be

D¼w^2 U 0 =4L ð 1 : 87 Þ

Also, particles in liquid flow experience convection along with the diffusion.
The time of particle convection become important as referred in Table1.8. Thus the
particle diffusivity becomes crucial as well. Typical diffusivities for common
biological moieties are mentioned in Table1.7.
As mentioned in Table1.8, for particle to diffuse into the other half across the
channel width filled with different liquid, then the prerequisite must be the diffu-
sivity of the particle should be high; the aspect ratio of channel length to its width
should be smaller along with flow velocity. This all will result in low Pẻclet number
and smaller diffusion time. The opposite will be true for a particle not to diffuse into
the adjacent fluid across its width.

3 Conclusion

This chapter provides basic information, such as basic principles and related theory,
for developing a fundamental background to understand the so-looking complex
physics of microfluidics. On the contrary, the foundation of fluid mechanics starts

Table 1.8 Conditions for particle separation in no-membrane H-filter

tconv

(time of particle

convection)

tdiff

(time of particle

diffusion)

PeMass

(Pẻclet number)

L/U 0 w^2 /4D RePr¼U 0 L/D

For

diffusion

tconvtdiff Low Pe,

For no

diffusion

tconv>>tdiff High Pe

Either longer channel length or slower flow

velocity or both are required to achieve

diffusion

30 C.K. Dixit

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