Modelling interacting diffusiophoretic filaments in viscous fluids

  • Makanga, Ursy (Flatiron Institute)
  • Montenegro-Johnson, Thomas (University of Warwick)
  • Marangos, Christos (The Cyprus Institute)
  • Katsamba, Panayiota (Cyprus University of Technology)

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Active diffusive fibres are pervasive across a wide range of applications, spanning from environmental, biomedical and industrial applications. Examples include environmental microfibres, dissolvable biomedical sutures, smart textiles, fibrous electrodes and catalysts, microbiological filaments, and phoretic filaments in active matter. In general, diffusive filaments are slender particles with chemically active surfaces that release or consume dissolved species, whose transport in the surrounding fluid is governed primarily by diffusion. In autophoretic filaments, the resulting concentration gradients drive surface slip flows and, in turn, propulsion, with strong sensitivity to the filament shape and surface patterning. While modelling passive slender particles in viscous fluids has been a major area of research over the past few decades, methodologies for active particles such as diffusiophoretic filaments are scarce. The resulting three-dimensional chemo-hydrodynamic problem is challenging to tackle analytically and can be computationally costly. Recently, Katsamba et al., 2020, developed a Slender Phoretic theory (SPT) – that reduces the complexity of the phoretic problem from three dimensions to one – using a matched asymptotic expansion of the boundary integral solution. SPT has enabled the simulation of diverse filamentous morphologies, such as filaments of arbitrary centreline in 3D space, spatially-varying surface activity profiles and varying cross-sectional radii. Here, we extend SPT to a general modelling framework for interacting active diffusive filaments, accounting for chemical, hydrodynamic, and geometric coupling between multiple bodies. The resulting computational tool enables efficient simulation of multibody interactions, that will allow the exploration of collective filament dynamics, emergent self-organisation, and cooperative propulsion and pumping in complex configurations.