On the Hydrodynamic Stability of a Lennard-Jones Molecular Fluid

Bharath Venkatesh Raghavan, Martin Ostoja Starzewski

Research output: Contribution to journalArticle

Abstract

As a central concept in fluid dynamics stability is fundamental in understanding transitions from laminar to turbulent flow. In continuum flows, it is well-established that a transition to turbulence can occur at subcritical Reynolds numbers, in contrast to theoretical predictions. In non-equilibrium molecular dynamics (NEMD), it has been widely observed that at a critical Reynolds number the fluid undergoes an ordering transition from an amorphous phase to a ‘string’ phase. Using the fluctuation theorem (FT) and the dissipation function, we generalize the classical continuum Reynolds-Orr equation to sheared molecular fluids by ascribing a natural description to the nature of stochastic perturbations, i.e. fluctuations in shear stress. Via the Poincaré inequality, we arrive at a new stability criterion by providing a lower bound on the exponential decay of perturbations, which reduces to the classical continuum result in the limit of infinite system size. We investigate the nature of these velocity perturbations and conditions necessary for growth in the kinetic energy of perturbations. We obtain a fluid dependent estimate for the critical Reynolds number by which one may estimate the critical Reynolds number at which the fluid transitions to the string phase, thus providing a framework for generalizing classical continuum theories to the microscale.

Original languageEnglish (US)
JournalJournal of Statistical Physics
DOIs
StatePublished - Jan 1 2019

Fingerprint

Hydrodynamic Stability
flow stability
Lennard-Jones
Reynolds number
Continuum
Fluid
perturbation
fluids
continuums
Perturbation
strings
Strings
continuum flow
Transition to Turbulence
Non-equilibrium Molecular Dynamics
Fluctuation Theorem
dynamic stability
Stochastic Perturbation
Infinite Systems
estimates

Keywords

  • Fluctuation theorem
  • Phase transition
  • Poincaré inequality
  • Stability
  • Subcritical
  • Turbulence

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

On the Hydrodynamic Stability of a Lennard-Jones Molecular Fluid. / Raghavan, Bharath Venkatesh; Starzewski, Martin Ostoja.

In: Journal of Statistical Physics, 01.01.2019.

Research output: Contribution to journalArticle

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