Page 36 - Optofluidics Fundamentals, Devices, and Applications

Basic Micr ofluidic and Soft Lithographic Techniques 17

x (0, 0, 0) Fluo-3 CaCl 2
H/2
y
H/2
z

Fluorescent
complex
W
(a)

10 μm

10 μm 10 μm
(b) (c)

FIGURE 2-4 (a) Schematic drawing of the experiment used to generate
fl uorescence in the microchannel, and the coordinate system employed. The
dashed lines indicate the internal edges of the channel. H is the height of
the channel. The origin of the coordinate system is located in the middle of
the vertical edge shared by both channels in the Y junction. (b) and (c) Data
2+
obtained for the fl uo-3/Ca system by confocal fl uorescence microscopy in:
2
(b) A 100 × 250 μm y-z slice obtained 12 μm from the top of the channel.
2
(c) Corresponding 90 × 90 μm cross sections in the x-y plane of the channel
obtained 50 μm (top) and 200 μm (bottom) from the Y junction (Reprinted
with permission from R. F. Ismagilov, A. D. Stroock, P. J. A. Kenis,
G. Whitesides, and H. A. Stone, “Experimental and theoretical scaling laws
for transverse diffusive broadening in two-phase laminar flows in
microchannels,” Appl. Phys. Lett., 76, (2000), 2376–2378. Copyright
(2000), American Institute of Physics.)
with width w = 100 μm at velocity v = 100 μm/s, it would take a time
2
of t ~ w /D = 5 s for the ions to diffuse across the entire width of the
channel. During this time, the stripe will have moved a distance Z ~
vw /D = 500 μm down the channel. The number of channel widths
2