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54     Cha pte r  T h ree


               3-5-4 Bubble Grating
               So far we have only focused on laminar systems using miscible flu-
               ids. Another interesting system involves the use of immiscible fluids
               to form emulsions and foams in microfluidic channels. These disper-
               sions form periodic, self-assembled geometries that can also be recon-
               figured in real time by varying fluid properties and flow conditions.
               Here we describe a tunable, fluidic, two-dimensional diffraction grat-
               ing based on a microfluidic system comprising a flow-focusing device
               for generating bubbles, and a flowing, regular lattice of bubbles
               formed by dynamic self-assembly [15].
                  As described in Chap. 2, the flow-focusing device consists of two
               inlet channels for the liquid phase, and a single inlet channel for the
               gaseous phase (Fig. 3-13a). The gas and liquid phases meet at a junc-
               tion upstream of a narrow orifice. The gaseous thread periodically



                  Liquid
                                  h
                                       0.59 bar (0.91)
          Gas                    Outlet
                                                                   2 cm



           Liquid
                     (a)                         (c)              (e)
                       Camera

                    Rotating stage  Objective  0.65 bar (0.91)

              Mirror                                               2 cm
          Sample
                              Screen   500 μm          200 μm
           Light source                           (Inset)
                     (b)                         (d)              (f)
          FIGURE 3-13  Schematic representations of the experimental setup. (a) The fl ow-
          focusing bubble generator and self-assembled lattice of bubbles. A tank of nitrogen
          gas connects to the gas inlet, and digitally controlled syringes connect to the liquid
          inlets. The system generates monodisperse bubbles that pack into a quasi-two-
          dimensional sheet. (b) Diffraction and display of incident laser beam. Diffracted laser
          light orthogonal to the plane of bubble lattice is displayed on a white screen. (c) and
          (d) Packing of bubbles in a straight outlet channel that was 1-mm wide and 16-μm
          high. The rate of fl ow of the continuous phase was 0.028 μL/s. The numbers denote
          the input gas pressure and the volume fraction of bubbles (ϕ ) in parentheses.
                                                      vol
          (c) 0.59 bar, ϕ = 0.91, and (d) 0.65 bar, ϕ = 0.91; their corresponding diffraction
                    vol                   vol
          patterns are shown in (e) and (f), respectively. (M. Hashimoto, B. Mayers, P.
          Garstecki, and G. M. Whitesides, “Flowing lattices of bubbles as tunable, self-
          assembled diffraction gratings,” Small, 2, (2006), 1292–1298. Copyright Wiley-VCH
          Verlag GmbH & Co. KGaA. Reproduced with permission.)
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