TY - JOUR

T1 - Hydrodynamic fluctuations in quasi-two dimensional diffusion

AU - Peláez, Raul P.

AU - Usabiaga, Florencio Balboa

AU - Panzuela, Sergio

AU - Xiao, Qiyu

AU - Delgado-Buscalioni, Rafael

AU - Donev, Aleksandar

N1 - Funding Information:
We thank Eric Vanden-Eijnden and Johannes Bleibel for informative discussions. This work was supported in part by the National Science Foundation under collaborative award DMS-1418706 and by DMS-1418672, and by the US Department of Energy Oce of Science, Oce of Advanced Scientific Computing Research, Applied Mathematics program under award DE-SC0008271. We thank the NVIDIA Academic Partnership program for providing GPU hardware for performing some of the simulations reported here. RD-B and SP acknowledge the support of the Spanish Ministry of
Funding Information:
Science and Innovation MINECO (Spain) under grant FIS2013-47350-C5-1-R and the ‘María de Maeztu’ Programme for Units of Excellence in R&D (MDM-2014-0377). Part of the simulations were done in Marenostrum under grant FI-2017-2-0023. RD-B and RP acknowledges support the donors of The American Chemical Society Petroleum Research Fund for partial support of this research via PRF-ACS ND9 grant.

PY - 2018/6/18

Y1 - 2018/6/18

N2 - We study diffusion of colloids on a fluid-fluid interface using particle simulations and fluctuating hydrodynamics. Diffusion on a two-dimensional interface with three-dimensional hydrodynamics is known to be anomalous, with the collective diffusion coefficient diverging like the inverse of the wavenumber. This unusual collective effect arises because of the compressibility of the fluid flow in the plane of the interface, and leads to a nonlinear nonlocal convolution term in the diffusion equation for the ensemble-averaged concentration. We extend the previous hydrodynamic theory to account for a species/color labeling of the particles, as necessary to model experiments based on fluorescent techniques. We study the magnitude and dynamics of density and color density fluctuations using a novel Brownian dynamics algorithm, as well as fluctuating hydrodynamics theory and simulation. We find that hydrodynamic coupling between a single tagged particle and collective density fluctuations leads to a reduction of the long-time self-diffusion coefficient, even for an ideal gas of non-interacting particles. This unexpected finding demonstrates that density functional theories that do not account for thermal fluctuations are incomplete even for ideal systems. Using linearized fluctuating hydrodynamics theory, we show that for diffusion on a fluid-fluid interface, nonequilibrium fluctuations of the total density are small compared to the equilibrium fluctuations, but fluctuations of color density are giant and exhibit a spectrum that decays as the inverse cubed power of the wavenumber. We confirm these predictions through Brownian dynamics simulations of diffusive mixing with two indistinguishable species. We also examine nonequilibrium fluctuations in systems with two-dimensional hydrodynamics, such as thin smectic films in vacuum. We find that nonequilibrium fluctuations are colossal and comparable in magnitude to the mean, and can be accurately modeled using numerical solvers for the nonlinear equations of fluctuating hydrodynamics.

AB - We study diffusion of colloids on a fluid-fluid interface using particle simulations and fluctuating hydrodynamics. Diffusion on a two-dimensional interface with three-dimensional hydrodynamics is known to be anomalous, with the collective diffusion coefficient diverging like the inverse of the wavenumber. This unusual collective effect arises because of the compressibility of the fluid flow in the plane of the interface, and leads to a nonlinear nonlocal convolution term in the diffusion equation for the ensemble-averaged concentration. We extend the previous hydrodynamic theory to account for a species/color labeling of the particles, as necessary to model experiments based on fluorescent techniques. We study the magnitude and dynamics of density and color density fluctuations using a novel Brownian dynamics algorithm, as well as fluctuating hydrodynamics theory and simulation. We find that hydrodynamic coupling between a single tagged particle and collective density fluctuations leads to a reduction of the long-time self-diffusion coefficient, even for an ideal gas of non-interacting particles. This unexpected finding demonstrates that density functional theories that do not account for thermal fluctuations are incomplete even for ideal systems. Using linearized fluctuating hydrodynamics theory, we show that for diffusion on a fluid-fluid interface, nonequilibrium fluctuations of the total density are small compared to the equilibrium fluctuations, but fluctuations of color density are giant and exhibit a spectrum that decays as the inverse cubed power of the wavenumber. We confirm these predictions through Brownian dynamics simulations of diffusive mixing with two indistinguishable species. We also examine nonequilibrium fluctuations in systems with two-dimensional hydrodynamics, such as thin smectic films in vacuum. We find that nonequilibrium fluctuations are colossal and comparable in magnitude to the mean, and can be accurately modeled using numerical solvers for the nonlinear equations of fluctuating hydrodynamics.

KW - Brownian motion

KW - bio-colloids and nano-colloids

KW - colloids

KW - diffusion

KW - fluctuating hydrodynamics

UR - http://www.scopus.com/inward/record.url?scp=85049679386&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049679386&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/aac2fb

DO - 10.1088/1742-5468/aac2fb

M3 - Article

AN - SCOPUS:85049679386

VL - 2018

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 6

M1 - 063207

ER -