# Interfacial Polygonal Nanopatterning of Stable Microbubbles

(in progress...)

Authors: E. Dressaire, R. Bee, D. C. Bell, A. Lips, and H. A. Stone.

Science 320 (5880), 1198-1201 (2008).

## Keywords

Ostwald ripening,

## Summary

The article presents a new method to stabilize micron-size bubbles by adding a surfactant layer covering the surface of the microbubbles. It also reports the formation of hexagonal and pentagonal surface patterning of the microbubbles. The pattern size and bubbles radius depend on how long the sample was sheared and the shear rate used. The size of the bubbles decreased as the shearing time was increased and as the shear rate increased. The concentration of surfactant was also varied but this showed no effect on bubble radius and only a small change in pattern size was observed. A molecular model describing this phenomenon was also developed and it predicts that the packing of the surfactant molecules is what controls the pattern structure and stability of the bubbles.

## Soft Matter Connection

The patterning observed on the surface of the bubbles is quantitatively explained by the molecular model developed. Initially the bubbles are covered smoothly by surfactant, as time progresses the smooth surface begins to buckle at 120 degree angles until eventually the hexagonal patterning forms. The model assumes each hexagon or pentagon in the pattern to have a spherical cap of radius <math>R_c</math> and a bubble radius of *a*. The domain size can be estimated by the following equation describing the minimization of energy of the microbubbles:

<math>E(a, R_c) = n(A \frac{\kappa}{2} (\frac{2}{R_c} - \frac{2}{R_{sp}})^2 + \lambda \pi a) - pV</math>

where <math>\kappa</math> is the bending rigidity, <math>R_sp</math> is the spontaneous radius of curvature of the surfactant layer, *p* is the Laplace pressure, *n* is the total number of domains, *V* is volume, and <math>\lambda</math> is the line tension energy.