Abstract

Ubiquitous in the microcosmos, chemically active filaments are breaming with rich coupled dynamics arising from the interplay of (bio)chemical activity, fluid flow and elasticity. This talk presents a unified mathematical modelling framework for diffusive filaments interacting with their microscale environment through surface fluxes, with applications ranging from catalytic microbots to degrading microplastic fibres. At the heart of this framework lies Slender Phoretic Theory (SPT)—a reduced-order, asymptotically derived approach for modelling solute dynamics around thin, chemically active filaments. By exploiting the filament’s slender geometry, SPT reduces the complex boundary value problem of solving Laplace equation for the solute dynamics to a line integral along the filament’s centerline. The theory accommodates general centreline geometries, spatially varying surface flux, and non-uniform cross-sectional profiles. SPT predictions have been rigorously validated against full numerical solutions using Boundary Element Methods with regularised singularities. Originally developed to model autophoretic and catalytic microswimmers, we now extend SPT to explore solute release from degrading microplastic fibres—bridging a conceptual and technical pathway from synthetic active matter to pollutant transport in environmental systems.

Key words: asymptotic modelling, slender body theory, diffusion, boundary element methods, microplastic fibres, microfibres, active matter, colloids, self-diffusiophoresis,, microbots