Motility-induced inter-particle correlations and dynamics: a microscopic approach for active Brownian particles.

Area of Science:

• Physics
• Soft Matter Physics
• Statistical Mechanics

Background:

• Theoretical models for active Brownian particles (ABPs) lack detailed descriptions of inter-particle correlations.
• The pair-correlation function is essential for understanding the dynamics and phase behavior of ABP suspensions.

Purpose of the Study:

• To derive expressions for the pair-correlation function of ABPs with short-ranged interactions.
• To analyze the behavior of the pair-correlation function at low concentrations for small and large swimming velocities.
• To generalize Fick's diffusion equation to incorporate motility and study mass transport.

Main Methods:

• Solving a differential equation derived from the Fokker-Planck equation for ABP positions and orientations.
• Analyzing the pair-correlation function for different swimming Peclet numbers (λ).
• Generalizing Fick's diffusion equation to include motility effects.

Main Results:

• Derived expressions for the pair-correlation function for ABPs at low concentrations.
• Found that for large swimming velocities (high λ), the pair-correlation function is highly asymmetric: large near contact upon approach (∼λ) and small upon separation (∼λ^1/3).
• Showed that mass transport is dominated by a concentration-gradient-induced swimming direction at high velocities.

Conclusions:

• The derived pair-correlation function provides a quantitative description of motility-induced correlations in ABPs.
• The generalized diffusion equation highlights the impact of directed motion on mass transport.
• These results offer a foundation for analyzing ABP behavior at higher concentrations and complex phase transitions.