Mesoscale Modeling of an Active Colloid's Motion

TL;DR

This work addresses mesoscale modeling of active isotropic colloids by coupling a Cahn–Hilliard concentration field to colloid motion. It extends prior particle-based results by showing that concentration-driven phase separation can reproduce single-colloid enhanced diffusion and offers substantial speedups, while also exploring multi-colloid dynamics. The CH-based framework yields good qualitative agreement at low-to-moderate densities, but struggles to capture dense-system phenomena such as complex clustering and solute-ring patterns, indicating areas for refinement and future development. Overall, the approach provides a tractable, physics-informed pathway to study mesoscale collective behavior in active colloids with significant computational efficiency.

Abstract

This paper uses Cahn-Hilliard equations as a mesoscale model of the motion of active colloids. The model attempts to capture the driving mechanisms and qualitative behavior of the isotropic colloids originally proposed by J. Decayeaux in 2021. We compare our model against the single colloid behavior presented in that work, as well as against multi-colloid systems.

Figures (8)

• Figure 1: Chemical potentials showing different stable regions. On the left, two stable regions exist, which drives the system to separation into high and low concentration regions. On the right, only one stable region exists, driving the system to a mixed state. The value of parameter L on the right is half of that for the figure on the left, so the dynamics of the system can be controlled by changing only this parameter.
• Figure 2: Illustration of Force model used in the mesoscale simulation compared to ordinary WCA.
• Figure 3: High concentration regions effectively block the colloid from moving in that direction, so the otherwise random colloid motion becomes directed in the opposite direction. The left plot shows the particle setup, and the right shows the Cahn-Hilliard setup, both demonstrate the high concentration region that is the main driver of the enhanced diffusion.
• Figure 4: Single colloid MSD comparison. The left plot is log-log scale and the right is linear scale. There is good qualitative and quantitative agreement across time scales.
• Figure 5: MSD in log-log scale for four collolids (left) and eight colloids (right.)