Analytical and Computational Studies of Correlations of Hydrodynamic Fluctuations in Shear Flow

Abstract

We study correlations of hydrodynamic fluctuations in shear flow analytically and also by dissipative particle dynamics (DPD) simulations. The hydrodynamic equations are linearized around the macroscopic velocity field and then solved by a perturbation method in Fourier-transformed space. The autocorrelation functions (ACFs) from the analytical method are compared with results obtained from DPD simulations under the same shear-flow conditions. Upto a moderate shear rate, various ACFs from the two approaches agree with each other well. At large shear rates, discrepancies between the two methods are observed, hence revealing strong additional coupling between different fluctuating variables, which is not considered in the analytical approach. In addition, the results at low and moderate shear rates can serve as benchmarks for developing multiscale algorithms for coupling of heterogeneous solvers, such as a hybrid simulation of molecular dynamics and fluctuating hydrodynamics solver, where thermal fluctuations are indispensable.

Theory and simulation of electrokinetic fluctuations in electrolyte solutions at the mesoscale

“…Although both MD and cDPD simulations can be applied easily to electrokinetic problems involving fixed or induced charges on walls, the current theoretical framework cannot be extended to such problems directly. It is also interesting to consider how the fluctuating hydrodynamics is coupled with mesoscale electrokinetics in shear flows, where the current correction functions can be affected by the coupling between fluctuating terms and advection processes (Bian et al 2018), leading to an orientation-dependent decorrelation process of fluctuating variables in the fluid system. and corresponding strengths a ij , γ ij , σ ij , respectively.…”

“…Next, we consider an under-damped solution, where s T is real, that is, k < 2c s /ν L . In particular, we consider the continuum limit, where k 2c s /ν L so that s T ≈ c s , then we arrive at the solutions (De Fabritiis et al 2007;Bian et al 2018)…”

“…Hydrodynamic fluctuations at mesoscopic scales have been studied extensively in the past decade (Bian et al 2015;Péraud et al 2016;Yu et al 2016;Bian, Deng & Karniadakis 2018;Kim et al 2018;Donev et al 2019a). However, the electrokinetic fluctuations in electrolyte solutions have been explored less, especially from a theoretical perspective.…”

Theory and simulation of electrokinetic fluctuations in electrolyte solutions at the mesoscale

“…When the mutual diffusion coefficients of ions become comparable to the self-diffusion terms in concentrated electrolyte solutions (Dufrêche et al 2002;Galindres et al 2021), the contribution of mutual-diffusion on ionic transport should be correctly considered in the fluctuating hydrodynamics and electrokinetics equations. It is also interesting to consider how the fluctuating hydrodynamics is coupled with mesoscale electrokinetics in shear flows, where the current correction functions can be affected by the coupling between fluctuating terms and advection processes (Bian et al 2018), leading to orientation-dependent decorrelation process of fluctuating variables in the fluid system. transport equation (Deng et al 2016):…”

“…Next, we consider an under-damped solution, where s T is real, that is, k < 2c s /ν L . In particular, we consider the continuum limit, where k 2c s /ν L so that s T ≈ c s , then we arrive at the solutions as (De Fabritiis et al 2007;Bian et al 2018)…”