Biomedical Engineering Reference
In-Depth Information
FIGURE 5.3
Dispersion effect in parallel lamination (the interface is arbitrary defined at 20% to 30% of the initial
concentration): (a) Y-mixer and (b) hydrodynamic focusing.
W ), the
difference between the broadening widths at the wall and at the channel center is quickly equalized due
to diffusion in z -direction. The broadening eff ec t is also less dramatic if the mixing time is short. Short
mixing time means a high mean velocity u , which makes convection dominate over molecular
diffusion.
Based on numerical results of Eqn (5.7) , the same relation was obtained by Kamholz et al. [3] .The
square-root relation at the center of the channel reflects the relation between the required length of the
mixing channel and its width L mixer / W
In Eqn (5.8) , the term x
=
u represents the mixing time. For a small channel height ( H
f
Pe W (2.200) derived in Section 2.8. The one-third-power
relation at the channel wall shows that mixing based on molecular diffusion is better, in reality, due to the
distributed velocity profile. According to numerical results presented byKamholz and Yager [3] ,relations
(5.8) are true for a short distance x close to the channel entrance. At an intermediate distance, the
broadening width is proportional to two-thirds power of the distance x . At a long distance, the broadening
width at both the wall and the channel center is again proportional to the square root of the distance x .
As mentioned earlier, fast mixing is achieved in parallel lamination micromixers by decreasing the
mixing path and increasing the contact surface between the solvent and the solute. The simplest
parallel lamination micromixers are T-mixers or Y-mixers. If the aspect ratio of the mixing channel is
small ( W
H ), the inlet streams of a T-mixer can be twisted and laminated as two thin liquid sheets to
reduce the mixing path from the channel width W to the channel height H as shown in Fig. 5.4 (a). The
interface between the two streams also increases by a factor of W / H . Hinsmannn et al. introduced
the streams into the mixing channel through a laminator consisting of many small channels [4] . The
laminator keeps the flow at the entrance on their track and minimizes instability.
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