A self consistent theory for phonon propagation in a suspension of one-dimensional filaments

Abstract

Using a self consistent, field theoretic multiple scattering theory in a viscous, acoustic fluid, we have developed a mean field model to describe the propagation of phonons in suspensions of one dimensional filaments. This geometry is approximately realized by the cytoskeleton in generic cells and can be studied in a controlled manner using suspensions of carbon nanotubes. We have extended the coherent potential approximation method, typically used for point scatterers, to the case of one dimensional filaments using the supersymmetric method, an approach employed with great success in disordered electronic systems. Unlike similar systems involving suspensions of effectively point scatterers, viscosity is found to play an important role in determining the observed wave speed because of both the high density and the one dimensional nature of the scatterers. We have carried out Brillouin light scattering measurements on both live cells, for which we believe the observed frequency shifts result from coupling to the cytoskeleton, and carbon nanotube suspensions. By varying the temperature, we may approach the glass transition of the fluid and substantially change the viscosity to directly test our predictions. Preliminary measurements show frequency shifts in accord with the predictions. [Research funded by the Office of Naval Research.]