8
1 Mixing at Microscale
Decrease in Re:
Increased
Residence time
Increase in Re:
Enlarged interfacial area
by Stretching & Folding
Re = 10
Re = 50
Fig. 1.6 Variations of mixing index with Reynolds number for serpentine micromixers
3. Schmidt number (Sc) ≡
ν
D
where L and U are the characteristic length and velocity scales of the micromixer,
respectively. The kinematic viscosity and coefficient of mass diffusivity are denoted
by ν and D, respectively.
The Reynolds number represents the ratio of inertial to viscous force. In most
microfluidics applications, due to low Reynolds numbers, laminar flow is expected.
The Peclet number represents the relative importance of the mass transfer by convection compared to that of diffusion. Convection is dominated at high Peclet numbers.
For water flows at room temperature, the kinematic viscosity ν and diffusion coefficient D are 10
–6 m
2 s
−1 and 10
–10 m
2 s
−1 , which correspond to the Reynolds and
Peclet numbers of 0.1 and 1000, respectively, for the cross-sectional dimension, L
= 100 μm and velocity, U = 1 mm s
−1 . The Schmidt number represents the ratio of
momentum to mass transport, and thus the ratio of Peclet to Reynolds number.
1 Mixing at Microscale
Decrease in Re:
Increased
Residence time
Increase in Re:
Enlarged interfacial area
by Stretching & Folding
Re = 10
Re = 50
Fig. 1.6 Variations of mixing index with Reynolds number for serpentine micromixers
3. Schmidt number (Sc) ≡
ν
D
where L and U are the characteristic length and velocity scales of the micromixer,
respectively. The kinematic viscosity and coefficient of mass diffusivity are denoted
by ν and D, respectively.
The Reynolds number represents the ratio of inertial to viscous force. In most
microfluidics applications, due to low Reynolds numbers, laminar flow is expected.
The Peclet number represents the relative importance of the mass transfer by convection compared to that of diffusion. Convection is dominated at high Peclet numbers.
For water flows at room temperature, the kinematic viscosity ν and diffusion coefficient D are 10
–6 m
2 s
−1 and 10
–10 m
2 s
−1 , which correspond to the Reynolds and
Peclet numbers of 0.1 and 1000, respectively, for the cross-sectional dimension, L
= 100 μm and velocity, U = 1 mm s
−1 . The Schmidt number represents the ratio of
momentum to mass transport, and thus the ratio of Peclet to Reynolds number.