Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation

Abstract

Simulation and experimental studies have demonstrated non-equilibrium ordering in driven colloidal suspensions: with increasing driving force, a uniform colloidal mixture transforms into a locally demixed state characterized by the lane formation or the emergence of strongly anisotropic stripe-like domains. Theoretically, we have found that a linear stability analysis of density dynamics can explain the non-equilibrium ordering by adding a non-trivial advection term. This advection arises from fluctuating flows due to non-Coulombic interactions associated with oppositely driven migrations. Recent studies based on the dynamical density functional theory (DFT) without multiplicative noise have introduced the flow kernel for providing a general description of the fluctuating velocity. Here, we assess and extend the above deterministic DFT by treating electric-field-driven binary ionic mixtures as the primitive model. First, we develop the stochastic DFT with multiplicative noise for the laning phenomena. The stochastic DFT considering the fluctuating flows allows us to determine correlation functions in a steady state. In particular, asymptotic analysis on the stationary charge-charge correlation function reveals that the above dispersion relation for linear stability analysis is equivalent to the pole equation for determining the oscillatory wavelength of charge--charge correlations. Next, the appearance of stripe-like domains is demonstrated not only by using the pole equation but also by performing the 2D inverse Fourier transform of the charge--charge correlation function without the premise of anisotropic homogeneity in the electric field direction.

17 pages, 6 figures

References in corpus (31)

• Nanofluidics, from bulk to interfaces
• Electrostatic correlations: from Plasma to Biology
• Classical dynamical density functional theory: from fundamentals to applications
• Scaling analysis of the screening length in concentrated electrolytes
• Screening length for finite-size ions in concentrated electrolytes
• Reentrance effect in the lane formation of driven colloids
• Influence of hydrodynamic interactions on lane formation in oppositely charged driven colloids
• Primitive Model Electrolytes in the Near and Far Field: Decay Lengths from DFT and Simulations
• A dynamic density functional theory for particles in a flowing solvent
• Density profiles of a colloidal liquid at a wall under shear flow
• Universal Long Ranged Correlations in Driven Binary Mixtures
• On the microscopic origin and macroscopic implications of lane formation in mixtures of oppositely-driven particles
• Stresses in non-equilibrium fluids: Exact formulation and coarse grained theory
• Nonequilibrium Tuning of the Thermal Casimir Effect
• Long-range fluctuation-induced forces in driven electrolytes
• Driven colloidal suspensions in confinement and density functional theory: Microstructure and wall-slip
• Introduction to colloidal dispersions in external fields
• Controlling colloidal sedimentation using time dependent shear
• Mean-field electrostatics beyond the point-charge description
• Instabilities and turbulence-like dynamics in an oppositely driven binary particle mixture
• A Gaussian theory for fluctuations in simple liquids
• Nonequilibrium phase transitions of sheared colloidal microphases: Results from dynamical density functional theory
• Transient fluctuation-induced forces in driven electrolytes after an electric field quench
• Dynamical density functional theory analysis of the laning instability in sheared soft matter
• Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis
• Transverse density fluctuations around the ground state distribution of counterions near one charged plate: stochastic density functional view
• Stochastic dynamics and thermodynamics around a metastable state based on the linear Dean-Kawasaki equation
• Length-scales of Dynamic Heterogeneity in a Driven Binary Colloid
• Non-hyperuniform metastable states around a disordered hyperuniform state of densely packed spheres: stochastic density functional theory at strong coupling
• Length-scales in sheared soft matter depend sensitively on molecular interactions
• On the equivalence of self-consistent equations for nonuniform liquids: a unified description of the various modifications

Cited by in corpus (5)

• Perspective: New directions in dynamical density functional theory
• Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis
• Perpendicular and Parallel Phase Separation in Two Species Driven Diffusive Lattice Gases
• Competition between lanes and transient jammed clusters in driven binary mixtures
• Theoretical Basis for Classifying Hyperuniform States of Two-Component Systems