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

Area of Science:

• Soft Matter Physics
• Non-equilibrium Statistical Mechanics
• Colloidal Science

Background:

• Driven colloidal suspensions show non-equilibrium ordering, transitioning from uniform mixtures to locally demixed states like lanes or stripes with increasing driving force.
• Previous theoretical work utilized linear stability analysis and deterministic dynamical density functional theory (DFT) to explain these phenomena, introducing advection terms from fluctuating flows.

Purpose of the Study:

• To develop and extend deterministic DFT by incorporating multiplicative noise to create a stochastic DFT model.
• To analyze electric-field-driven binary ionic mixtures as a model system for non-equilibrium ordering phenomena.
• To investigate the emergence of lane formation and stripe-like domains in driven colloidal systems.

Main Methods:

• Development of stochastic dynamical density functional theory (DFT) with multiplicative noise.
• Analysis of fluctuating flows arising from non-Coulombic interactions and oppositely driven migrations.
• Asymptotic analysis of stationary charge-charge correlation functions.
• Application of the pole equation derived from linear stability analysis.
• 2D inverse Fourier transform of charge-charge correlation functions.

Main Results:

• The stochastic DFT successfully models laning phenomena in driven colloidal systems.
• Fluctuating flows are crucial for understanding non-equilibrium ordering.
• The dispersion relation from linear stability analysis is equivalent to the pole equation for charge-charge correlation wavelengths.
• Stripe-like domain formation is confirmed through both the pole equation and correlation function analysis.

Conclusions:

• Stochastic DFT with multiplicative noise provides a robust framework for describing non-equilibrium ordering in driven colloidal suspensions.
• The interplay between fluctuating flows and particle interactions dictates the emergent patterns.
• The study establishes a theoretical link between linear stability analysis and the detailed structure of correlations, explaining pattern formation mechanisms.