TY - JOUR

T1 - On the Hydrodynamic Stability of a Lennard-Jones Molecular Fluid

AU - Raghavan, Bharath Venkatesh

AU - Ostoja-Starzewski, Martin

N1 - Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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.

AB - 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.

KW - Fluctuation theorem

KW - Phase transition

KW - Poincaré inequality

KW - Stability

KW - Subcritical

KW - Turbulence

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U2 - 10.1007/s10955-019-02357-6

DO - 10.1007/s10955-019-02357-6

M3 - Article

AN - SCOPUS:85069973599

SN - 0022-4715

VL - 177

SP - 61

EP - 77

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 1

ER -