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Optical Components Based on Dynamic Liquid-Liquid Interfaces     55


               enters the orifice, breaks, and releases a bubble into the outlet chan-
               nel. As low gas pressures, the volume fraction (ϕ ) of the bubbles
                                                          vol
               formed is low, and the bubbles flow in disordered packs.  As  ϕ
                                                                       vol
               increases, the bubbles organize into hexagonally packed domains. As
               ϕ  approaches 0.91, the limit of packing of disks on the plane, the
                vol
               domains become a single lattice extending throughout the outlet
               channel. At ϕ  ~ 0.91, the bubbles fill the entire plane of the channel;
                          vol
               the defects in the lattices are minimized.
                  Figure 3-13b shows the optical setup to characterize the diffrac-
               tion patterns from the bubble lattices. A He/Ne laser (λ = 632.8 nm)
               illuminates the center of the bubble lattice. The direction of the beam
               is perpendicular to the plane of the device 1-cm downstream from the
               flow-focusing nozzle. Diffraction patterns are projected onto a white
               screen.
                  Figure 3-13c to f shows the bubble lattices and their correspond-
               ing diffraction patterns. These bubble lattice gratings can be mod-
               eled as both amplitude gratings and phase gratings. The menisci of
               the bubbles refract light radially, in a way that is similar to diffrac-
               tion gratings formed from periodic arrays of dots or holes—that is,
               amplitude gratings. The bubbles and the carrying fluid also repre-
               sent periodic arrays of alternating refractive indices—phase grat-
               ings. Changing the pressure of the gas and rate of flow of the liquid
               applied to the flow-focusing device changes the structure of the
               bubble lattices, and the diffraction patterns generated. The switch-
               ing time is less than 10 s.



          3-6 Conclusions
               Dynamic optofluidic components based on liquid-liquid interfaces
               are simple to design, fabricate, and operate. They are adaptive and
               reconfigurable; the range of tuning is large, and only limited by the
               choice of liquids that can be injected into the microfluidic systems.
               Fluidic optical systems are also readily integrable with microanalyti-
               cal and lab-on-a-chip systems for biochemical detection, where the
               analytes of interest are usually in the liquid phase.
                  The main disadvantage of these optofluidic components is the
               need for a constant supply of fluids. The range of refractive index
               available in fluids is also limited: the highest is around 1.75; this value
               is much lower than that in solids. They have limited transparency in
               the infrared, and are therefore mostly used in the visible region of the
               spectrum. In addition, the speed of optical switching is slow (on the
               order of seconds) compared to conventional optical devices. Never-
               theless, these devices should still be useful for applications that do
               not require fast switching, such as optical sensing.
                  Optical systems based on liquid-liquid interfaces are still in their
               infancy of development. There are enough data to show that these
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