Correlated fluctuating hydrodynamics. II. Scale-dependent Reynolds numbers

Area of Science:

• Fluid dynamics
• Soft-matter physics
• Biophysics

Background:

• Many chemical and biological systems use low-Reynolds-number (Re ≪ 1) linearization of Navier-Stokes equations.
• This approximation assumes viscous dissipation dominates inertial effects, valid when viscous forces are much larger than inertial forces.
• Internal fluid structure can modify momentum transport, potentially invalidating this assumption.

Purpose of the Study:

• Investigate the impact of scale-dependent viscous dissipation on the validity of low-Re linearization.
• Determine if spatial correlations in structured fluids alter the balance between inertial and viscous effects.
• Assess the sufficiency of a single Reynolds number for linearization validity in fluctuating fluids.

Main Methods:

• Utilized a thermodynamically consistent fluctuating-hydrodynamic framework for structured fluids.
• Performed direct numerical simulations in one and two dimensions.
• Analyzed nonlinear mode coupling and particle transport dynamics.

Main Results:

• Scale-dependent viscous dissipation was shown to alter the inertia-viscosity balance across scales.
• Direct numerical simulations confirmed the invalidation of conventional low-Re linearization.
• In 1D, nonlinear coupling accelerated high-wavenumber mode relaxation; in 2D, particle velocity autocorrelation decayed slower, leading to up to 90% diffusion coefficient discrepancies.

Conclusions:

• The classical low-Re linearization is insufficient for spatially correlated fluctuating fluids.
• Scale-dependent viscous dissipation invalidates the standard justification for linearization.
• Linearization validity depends on a scale-dependent spectrum of effective Reynolds numbers, not a single value.