Page 60 - Optofluidics Fundamentals, Devices, and Applications

Optical Components Based on Dynamic Liquid-Liquid Interfaces 41

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3-4-3 L Interface between Miscible Liquids Is Diffuse
2
The L interface between miscible liquids is diffuse—it is a gradient of
chemical/physical composition and refractive indices. Diffusion of
molecules or ions between different liquids broadens the interface
between the streams. This diffusion creates a graded profile of refrac-
tive index across the interface. This feature is attractive for applica-
tions that require a gradient of refractive index, such as GRIN lenses,
and diffusive splitters. This graded profile is more difficult to gener-
ate, and almost impossible to modify in solid-state systems.
Diffusion, when sufficiently extended, flattens the contrast in
chemical/physical composition (e.g., salt concentration, tempera-
ture) of the respective fluids, and therefore the contrast in the refrac-
tive index that defines the fluidic-optical interface. As described in
Chap. 2, for solute ions flowing through a channel with width w =
−1
100 μm at velocity v = 100 μms , it would take only 5 s for the ions to
diffuse across the width of the entire channel. That is, within 500 μm
down the channel, the contrast in concentration and refractive index
will be flattened. The use of a more viscous liquid, or a higher rate of
flow of liquids, can mitigate this effect. Increasing the rate of flow
reduces the residence time of the liquids inside the channel, and
therefore reduces diffusive broadening for the same length of the
channel. Figure 3-5 shows the simulations for the profile of refractive
index at different rates of flow. In principle, the use of immiscible
liquids can eliminate diffusion completely, but different wetting
properties of the liquids on the PDMS wall and surface tension
between the liquids (leading to droplet formation) can complicate the
2
flow and make the manipulation of the L interface more difficult.

3-5 Liquid-Liquid Optical Devices

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3-5-1 L Waveguides
Design and Construction
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L waveguides consist of two streams of liquids with lower refractive
index (the cladding), sandwiching a stream of liquid with higher refrac-
tive index (the core) flowing in a microchannel [1] (Fig. 3-6). In principle,
2
any liquid that does not swell PDMS [4] can be used in L waveguides,
as long as the contrast in index of refraction between the core and the
cladding streams are large enough to sustain the propagation of light. In
much of our work, we used a 5-M aqueous solution of calcium chloride
(n = 1.45) as the core liquid, and water as the cladding (n = 1.33).
d d
To introduce light into the device, an optical fiber is inserted into
the PDMS device through a fiber port fabricated at the end of the
2
channel. The guided light exits the L waveguide when the core fluid
is forced to turn by 90° with a radius of ~ 0.5 mm (much less than the
2
critical radius) [10]. The output of the L waveguide can then be