Spatial correlations of hydrodynamic fluctuations in simple fluids under shear flow: A mesoscale simulation study

Area of Science:

• Fluid Dynamics
• Non-equilibrium Statistical Mechanics
• Computational Physics

Background:

• Hydrodynamic fluctuations in equilibrium fluids are well-understood.
• Understanding fluctuations in fluids under shear flow is crucial for many physical processes.
• Previous studies have not fully characterized the spatial correlations of these nonequilibrium fluctuations.

Purpose of the Study:

• To investigate and characterize spatial correlations of hydrodynamic fluctuations in simple fluids subjected to shear flow.
• To compare simulation results with theoretical predictions from fluctuating hydrodynamics.
• To elucidate the behavior of velocity and pressure correlations under shear.

Main Methods:

• Mesoscopic hydrodynamic simulations using multiparticle collision dynamics (MPC).
• Comparison of simulation data with analytical expressions from fluctuating hydrodynamics.
• Analysis of hydrodynamic correlations at various wave vectors and shear rates.

Main Results:

• Demonstrated spatial correlations in hydrodynamic fluctuations under shear flow, absent in equilibrium.
• Identified power-law decay of nonequilibrium contributions to velocity correlations (k^{-4} and k^{-2}) for large wave vectors.
• Observed crossover to slower decay at small wave vectors, indicating long-range correlations.
• Found a k^{-2} dependence for the coupling between transverse velocity components.
• Revealed a quadratic dependence of the nonequilibrium pressure contribution on the shear rate.

Conclusions:

• Shear flow fundamentally alters the nature of hydrodynamic fluctuations, introducing spatial correlations.
• The observed correlations and their wave vector dependencies provide insights into nonequilibrium fluid behavior.
• The findings validate theoretical models and offer a basis for further studies in sheared complex fluids.