Evidence for marginal stability in emulsions

TL;DR

This study investigates how pressure influences vibrational modes in emulsions, revealing a linear relationship between a low-frequency cutoff and contact number, and demonstrating that emulsions are marginally stable with non-plane-wave modes.

Contribution

First measurements of pressure effects on vibrational modes in emulsions, showing marginal stability and deviations from Debye behavior in soft frictionless spheres.

Findings

Density of states exhibits a low-frequency cutoff omega* proportional to dz.

D(omega) scales as omega^2/omega*^2 below omega*.

Softest modes become more localized with increased compression.

Abstract

We report the first measurements of the effect of pressure on vibrational modes in emulsions, which serve as a model for soft frictionless spheres at zero temperature. As a function of the applied pressure, we find that the density of states D(omega) exhibits a low-frequency cutoff omega*, which scales linearly with the number of extra contacts per particle dz. Moreover, for omega<omega*, D(omega)~ omega^2/omega*^2; a quadratic behavior whose prefactor is larger than what is expected from Debye theory. This surprising result agrees with recent theoretical findings. Finally, the degree of localization of the softest low frequency modes increases with compression, as shown by the participation ratio as well as their spatial configurations. Overall, our observations show that emulsions are marginally stable and display non-plane-wave modes up to vanishing frequencies.