Micromixers based on molecular diffusion - Micromixers Fundamentals Design and Fabrication - page 170

FIGURE 5.7

Micromixers based on viscoelastic instability with: (a) repeated turn and (b) a sudden contraction.

elastic forces. At this high elasticity number, unstable vortices appear before the constriction as
depicted in Fig. 5.7 (b). The asymmetric vortices oscillate from side to side leading to chaotic
advection. Mixing was improved further by molecular-scale effects caused by stretched and collapsed
polymer molecules.

5.2 SEQUENTIAL LAMINATION
Sequential lamination segregates the joined stream into two channels and rejoins them in the next
transformation stage ( Fig. 5.8 ). Because of these characteristics, sequential lamination is also called
split-and-recombine (SAR) concept [21] . Because the SAR process is similar to the stretching and
folding of mixing fluids, this concept is also called the Baker transformation or the Bernoulli trans-
formation [22,23] . Considering the time-dependent striation thickness w ( t ) with initial value w (0)

¼W ,
where W is the width of the microchannel, the decrease of striation thickness is determined by the
function a ( t ):

dln w Þ

d t ¼

ð t

a ð t Þ: (5.9)

In chaotic advection, the function a ( t ) is also called the stretching function and is positive. In the
local coordinate system of the striation, the diffusion process is described by the normalized diffusion
equation:

v 2 c *
vx * 2

vc *
vt * ¼

(5.10)