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Donev, Aleksandar

Publications and source records attributed to Donev, Aleksandar.

12 records
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DOE OSTI2019

Fluctuating hydrodynamics of electrolytes at electroneutral scales

At mesoscopic scales electrolyte solutions are modeled by the fluctuating generalized Poisson-Nernst-Planck (PNP) equations. However, at length and time scales larger than the Debye scales, electrolytes are effectively electroneutral, and the charged-fluid PNP equations become too stiff to solve numerically. Here we formulate the isothermal incompressible equations of fluctuating hydrodynamics for reactive multispecies mixtures involving charged species in the electroneutral limit, and design a numerical algorithm to solve these equations. Our model does not assume a dilute electrolyte solution but rather treats all species on an equal footing, accounting for cross-diffusion and non-ideality using Maxwell-Stefan theory. By enforcing local electroneutrality as a constraint, we obtain an elliptic equation for the electric potential that replaces the Poisson equation in the fluctuating PNP equations. We develop a second-order midpoint predictor-corrector algorithm to solve either the charged-fluid or electroneutral equations with only a change of the elliptic solver. We use the electroneutral algorithm to study a gravitational fingering instability, triggered by thermal fluctuations, at an interface where an acid and base react to neutralize each other. Our results demonstrate that, because the four ions diffuse with very different coefficients, one must treat each ion as an individual species, and cannot treat the acid, base, and salt as neutral species. This emphasizes the differences between electrodiffusion and classical Fickian diffusion, even at electroneutral scales.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Fluctuating Hydrodynamics and Debye-Hückel-Onsager Theory for Electrolytes

We apply fluctuating hydrodynamics to strong electrolyte mixtures to compute the concentration corrections for chemical potential, diffusivity, and conductivity. We show these corrections to be in agreement with the limiting laws of Debye, Hückel, and Onsager. We compute explicit corrections for a symmetric ternary mixture and find that the co-ion Maxwell-Stefan diffusion coefficients can be negative, in agreement with experimental findings.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Stochastic Simulation of Complex Fluid Flows (Progress Report for period 07/01/2016 - 06/30/2018)

At a microscopic scale, fluids are composed of molecules whose positions and velocities are random. This gives rise to thermal fluctuations that span the whole range of scales from the microscopic through the mesoscopic, and even the macroscopic. The inclusion of thermal fluctuations is crucial in multi-scale models, which are an important theme in the research program of the DOE Office of Science, and in particular the ASCR Applied Mathematics program's priority focus area on modeling of complex systems involving processes that span vastly different time and/or length scales. In this five-year Early Career project, the PI Aleksandar Donev and collaborators developed computational algorithms for modeling complex fluid mixtures at small scales using a formulation based on fluctuating hydrodynamics. Novel computational methods were developed to model complex fluids with increasing physical complexity, starting from binary miscible and immiscible mixtures, going through multispecies non-reactive and reactive mixtures, and culminating with reactive electrolytes mixtures of neutral molecules and ions. In close collaboration with the group of John Bell at Lawrence Berkeley National Laboratory, the methods were implemented in a scalable computational framework suitable for modern parallel supercomputers, and made publicly available on github. A number of physical examples in which giant nonequilibrium fluctuations are improtant were studied, with a special focus on instabilities at a liquid-liquid interface driven by gravity, diffusion, reactions, and/or electric fields. The methods and codes developed in this project are expected to enable other novel applications in the DOE Basic Energy Sciences program, and engineering sciences more broadly.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Fluctuating hydrodynamics of reactive liquid mixtures

Fluctuating hydrodynamics (FHD) provides a framework for modeling microscopic fluctuations in a manner consistent with statistical mechanics and nonequilibrium thermodynamics. This paper presents an FHD formulation for isothermal reactive incompressible liquid mixtures with stochastic chemistry. Fluctuating multispecies mass diffusion is formulated using a Maxwell-Stefan description without assuming a dilute solution, and momentum dynamics is described by a stochastic Navier-Stokes equation for the fluid velocity. We consider a thermodynamically consistent generalization for the law of mass action for non-dilute mixtures and use it in the chemical master equation (CME) to model reactions as a Poisson process. The FHD approach provides remarkable computational efficiency over traditional reaction-diffusion master equation methods when the number of reactive molecules is large, while also retaining accuracy even when there are as few as ten reactive molecules per hydrodynamic cell. We present a numerical algorithm to solve the coupled FHD and CME equations and validate it on both equilibrium and nonequilibrium problems. We simulate a diffusively driven gravitational instability in the presence of an acid-base neutralization reaction, starting from a perfectly flat interface. We demonstrate that the coupling between velocity and concentration fluctuations dominates the initial growth of the instability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Efficient reactive Brownian dynamics

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and dissociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently process reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as reaction-diffusion master equation algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction-limited and diffusion-limited irreversible association in three dimensions and compare to existing theoretical predictions at low and moderate densities. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium and compare to recent theoretical predictions. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. Our studies reinforce the common finding that microscopic mechanisms and correlations matter for diffusion-limited systems, making continuum and even mesoscopic modeling of such systems difficult or impossible. We also find that for models in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Stochastic Hybrid Models and Algorithms for Fluids (FHDeX) v1

This software contains numerical modules and application codes for studying the behavior of fluid dynamical systems where fluctuations play an important role in the dynamics. There is support for finite-volume/finite-difference solvers for partial differential equations, particle methods, and hybrid fluid-particle approaches.

Bell, JohnB.↗
DOE OSTI2017

Large scale Brownian dynamics of confined suspensions of rigid particles

We introduce methods for large-scale Brownian Dynamics (BD) simulation of many rigid particles of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid multiblob method [F. Balboa Usabiaga et al., Commun. Appl. Math. Comput. Sci. 11(2), 217–296 (2016)] at a cost comparable to the cost of deterministic simulations. We demonstrate that we can efficiently generate deterministic and random displacements for many particles using preconditioned Krylov iterative methods, if kernel methods to efficiently compute the action of the Rotne-Prager-Yamakawa (RPY) mobility matrix and its “square” root are available for the given boundary conditions. These kernel operations can be computed with near linear scaling for periodic domains using the positively split Ewald method. Here we study particles partially confined by gravity above a no-slip bottom wall using a graphical processing unit implementation of the mobility matrix-vector product, combined with a preconditioned Lanczos iteration for generating Brownian displacements. We address a major challenge in large-scale BD simulations, capturing the stochastic drift term that arises because of the configuration-dependent mobility. Unlike the widely used Fixman midpoint scheme, our methods utilize random finite differences and do not require the solution of resistance problems or the computation of the action of the inverse square root of the RPY mobility matrix. We construct two temporal schemes which are viable for large-scale simulations, an Euler-Maruyama traction scheme and a trapezoidal slip scheme, which minimize the number of mobility problems to be solved per time step while capturing the required stochastic drift terms. We validate and compare these schemes numerically by modeling suspensions of boomerang-shaped particles sedimented near a bottom wall. Using the trapezoidal scheme, we investigate the steady-state active motion in dense suspensions of confined microrollers, whose height above the wall is set by a combination of thermal noise and active flows. We find the existence of two populations of active particles, slower ones closer to the bottom and faster ones above them, and demonstrate that our method provides quantitative accuracy even with relatively coarse resolutions of the particle geometry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Fluctuation-enhanced electric conductivity in electrolyte solutions

Significance Using fluctuating hydrodynamics, we demonstrate that thermal fluctuations contribute to charge transport in binary electrolyte solutions. We show the existence of an enhancement, or renormalization, of the electric conductivity due to the coupling between fluctuations of charge and fluid velocity. This coupling results in nontrivial corrections to the classical Poisson–Nernst–Planck equations, which are of the order of the square root of the salt concentration and therefore significant even for dilute solutions. Our calculations predict a cation–anion cross-diffusion coefficient that is in quantitative agreement with experimental measurements. Our findings have important implications for the fields of both mesoscale hydrodynamics and electrolyte transport.

97 MATHEMATICS AND COMPUTING↗