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Chaotic mixing in effective compressible flows.

R Volk1, C Mauger2, M Bourgoin3

  • 1Laboratoire de Physique de l'ENS de Lyon, CNRS UMR5672 and Université de Lyon, Lyon, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary

Salt inhomogeneities in chaotic advection can alter colloid mixing rates. Numerical simulations show that a velocity drift between colloids and fluid particles significantly impacts colloid variance, leading to either delayed or enhanced mixing.

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Area of Science:

  • Fluid dynamics
  • Colloid science
  • Statistical physics

Background:

  • Chaotic advection is a mechanism for mixing substances in fluid flows.
  • Recent experiments suggest salt inhomogeneities induce velocity drift affecting colloid transport.
  • Understanding colloid mixing is crucial in various applications, from environmental science to materials engineering.

Purpose of the Study:

  • To numerically investigate the joint mixing of salt and colloids under chaotic advection.
  • To analyze how salt inhomogeneities, via induced velocity drift, influence colloid mixing dynamics.
  • To elucidate the mechanisms behind accelerated or delayed colloid mixing.

Main Methods:

  • Numerical simulations of chaotic advection.
  • Modeling of salt and colloid transport with velocity drift V(dp).
  • Analysis of colloid variance evolution and its dependence on concentration fields.

Main Results:

  • Velocity drift V(dp) is not divergence-free, significantly affecting colloid variance.
  • Mixing efficiency depends on the coherence between salt and colloid concentration fields.
  • A new variance production term P = -〈C(2)∇ · V(dp)〉/2 governs short-time scalar variance evolution.
  • Mixing can be delayed or enhanced based on initial conditions and the sign of the variance source term.
  • Consecutive regimes of fast and slow mixing are observed for localized Gaussian concentration profiles.

Conclusions:

  • Salt inhomogeneities play a critical role in modulating colloid mixing in chaotic flows.
  • The interplay between velocity drift and concentration fields dictates mixing outcomes.
  • The study provides a theoretical framework for understanding and potentially controlling colloid mixing through engineered salt gradients.