# Flowing Lattices of Bubbles as Tunable, Self-Assembled Diffraction Grating

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Original entry: Sorell Massenburg, APPHY 226, Spring 2009

Michinao Hashimoto, Brian Mayers, Piotr Garstecki, and George M. Whitesides. 2006, 2, No. 11, 1292 – 1298

# Soft Matter Keywords

Bubbles, Surface Tension, PDMS

# Abstract

We demonstrate tunable, fluidic, two-dimensional diffraction gratings based on a microfluidic platform comprising a flow-focusing bubble generator and flowing, regular lattices of bubbles formed by dynamic self-assembly. The structure of these lattices can be tuned with switching times of less than ten seconds by changing the pressures and rates of flow applied to the device. These diffraction gratings exhibit high stability (over hours of operation if properly designed and operated). For our devices, we achieved tunable ranges in pitch from 12 to 51 mm, corresponding to first-order diffraction angles from 3.28 to 0.78 for light with a wavelength of 632 nm.

# Soft Matters

The authors use flow focusing devices to make monodisperse air bubbles which then form regular lattices at high volume fractions. By approaching a volume fraction 0.91 (disks on a plane), dislocations and defects were minimized and flowed out of the lattice. But when the volume fraction became too high, the round bubbles deformed to be hexagonally shaped and became hexagonally close packed.

Schematic of bubble maker and optical setup.

The monodispersity and periodicity of the bubble lattice diffracted light. Here, the authors used channel sizes heights $10-20\mu m$, water for the continuous phase and a 632 HeNe laser. Changing these parameters would modify the phase shift of the diffracted light. However in this paper, the authors focused on controlling the diffraction pattern by modulating the flow rates which changed the lattice. The authors obtained diffraction patterns for varying volume fractions as shown in the second figure to the left.

Bubble lattices, at varying pressures (associated volume fraction in parenthesis). Pressure (N2) range from 0.43 (0.66 volume fraction) to 0.65 (0.91 volume fraction). Also shown in the bottom image is impact of the defect on the angle of diffraction pattern.

Like slits in a standard diffraction grating, the menisci of the bubbles diffract light with periodicity. Like standard diffraction gratings, the generated diffraction pattern is effected by irregularities. The effect of the defects on the angle of diffraction pattern decreases with increasing volume fraction. As one approaches the disk packing fraction, 0.91, the lattice achieves minimum defects and maximum stability.

Temporal stability of diffraction pattern angle for volume fractions 0.82 and 0.91.

The authors also report diffraction efficiencies of (ratio of single spot intensity to incident beam intensity) 3% as compared to 17% from commercial suppliers like Thor Labs. The authors make no mention of brownian motion, which the reviewer presumes might have an effect for small bubble sizes.