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Evidence for Marginal Stability in Emulsions.

Jie Lin1,2, Ivane Jorjadze1, Lea-Laetitia Pontani1,3

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We measured how pressure affects vibrations in emulsions, modeling soft spheres. Increased pressure linearly shifts the vibrational cutoff frequency and enhances low-frequency modes beyond Debye theory, indicating marginal stability.

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Area of Science:

  • Soft matter physics
  • Condensed matter physics
  • Rheology

Background:

  • Emulsions serve as model systems for understanding the behavior of granular materials and soft amorphous solids.
  • Vibrational properties are crucial for characterizing the mechanical stability and response of these systems.
  • Debye theory provides a baseline for understanding vibrational density of states in solids.

Purpose of the Study:

  • To experimentally measure the effect of applied pressure on vibrational modes in emulsions.
  • To investigate the low-frequency vibrational density of states and its dependence on pressure.
  • To explore the localization properties of vibrational modes under compression.

Main Methods:

  • Utilized emulsions as a model system for soft frictionless spheres at zero temperature.
  • Performed measurements of vibrational modes as a function of applied pressure.
  • Analyzed the vibrational density of states D(ω) and the participation ratio.

Main Results:

  • Observed a low-frequency cutoff ω* in the density of states, scaling linearly with the number of extra contacts per particle (δz).
  • Found that for frequencies below ω*, D(ω) exhibits quadratic behavior (D(ω)∼ω²/ω*²), exceeding Debye theory predictions.
  • Demonstrated that the localization of softest low-frequency modes increases with applied pressure.

Conclusions:

  • Emulsions exhibit marginal stability, characterized by non-plane-wave modes extending to vanishing frequencies.
  • The observed vibrational behavior deviates from standard Debye theory, aligning with recent theoretical predictions for soft amorphous solids.
  • Pressure plays a critical role in governing the vibrational dynamics and localization in emulsions.