Inferring Surface Slip in Active Colloids from Flow Fields Using Physics-Informed Neural Networks

TL;DR

The work tackles the challenge of inferring slip velocity and interfacial stresses at active colloid boundaries from partial flow measurements, addressing an inverse Stokes problem that is ill-posed and difficult to constrain near surfaces. It introduces a physics-informed neural network framework that embeds the Stokes equations and boundary conditions into the learning loss to recover slip velocity and reconstruct the full velocity and pressure fields from sparse velocity data. Validation against analytical solutions and boundary-element method results for squirmer and phoretic Janus particles shows quantitative agreement in both unbounded and wall-bounded geometries, with slip recovered even when near-surface data are unavailable. The approach links bulk hydrodynamic observations to microscopic interfacial physics, offering a general and extensible tool for characterizing interfacially driven transport in active matter and potentially guiding experiments and design of microfluidic systems.

Abstract

The directed motion of active colloids is governed by spatial variations in surface chemistry and interfacial stress, yet these properties remain extremely difficult to measure directly. We introduce a physics-informed neural network framework that infers the slip distribution driving propulsion from partial observations of the surrounding flow. By combining sparse fluid velocity measurements with the Stokes equations and boundary constraints, the method reconstructs both the near-surface slip and the full velocity and pressure fields. Validation against analytical solutions and Boundary Element Method calculations for canonical active colloid models shows quantitative agreement in both unbounded and confined geometries. Crucially, the framework recovers the surface slip even when no flow data are available near the particle, demonstrating that accessible bulk measurements encode the interfacial stresses responsible for active motion. These results establish physics-informed inference as a powerful tool for characterizing and ultimately controlling interfacially driven transport in colloidal active matter.

Figures (2)

• Figure 1: (a) Bulk flow around an active colloid can be measured accurately, but data within the near-surface region (red hatched band) are typically noisy or missing, obscuring the slip velocity and interfacial stresses that generate propulsion. (b) Spatial coordinates $\boldsymbol r=(x,y,z)$ serve as inputs, and the network outputs $(u_x^{nn},u_y^{nn},u_z^{nn},p^{nn})$. Physics-based losses enforce the Stokes equations, incompressibility, force- and torque-free conditions, boundary constraints, and no-slip walls when present, while a data-loss term penalizes deviations from measured velocities. Minimizing the total loss yields physically consistent reconstructions of the flow field and surface slip distribution.
• Figure 2: Comparison of PINN-predicted (blue) and BEM (pink) flow fields in the $yz$-plane for squirmer and phoretic Janus particles in the laboratory frame. Panels (a,c) show unbounded cases: a puller squirmer with $\beta_s = 5$ and a Janus particle with $\beta_p = -10$. Panels (e,g) show corresponding near-wall configurations, with the particle centered at $z_0/a = 2$; the squirmer is oriented normal to the wall, and the Janus particle is oriented at $\mathrm{rot}_x = \pi/3$. Panels (b,f) report the surface slip velocity for squirmers with $\beta_s =\{-5, 0, 5\}$, and panels (d,h) report slip velocities for Janus particles with $\beta_p = \{-10, 1, 10\}$. In all cases, open symbols denote BEM results and filled symbols denote PINN predictions. For the squirmer, solid curves in panels (b,f) show the analytical slip distribution used as reference. Velocities are normalized by the swimming speed $|\bm{U}|$.