Chemically active filaments: analysis and extensions of slender phoretic theory

Area of Science:

• Physics, Applied Mathematics
• Soft Matter Physics
• Microfluidics

Background:

• Autophoretic microswimmers utilize surface interactions with solute fuel for self-propulsion.
• Chemically-active filaments represent an advanced microswimmer design, offering enhanced functionality due to their geometry.
• Traditional models often focus on simpler shapes like spherical Janus particles.

Purpose of the Study:

• To develop and present new analytical solutions for the dynamics of chemically-active filaments using Slender Phoretic Theory (SPT).
• To extend SPT to handle arbitrary filament shapes, chemical patterning, and surface chemistry discontinuities.
• To provide a versatile framework for analyzing microswimmer behavior and benchmarking numerical simulations.

Main Methods:

• Application of Slender Phoretic Theory (SPT) to analyze solute concentration fields and slip velocity on filament surfaces.
• Derivation of a general series solution for arbitrary filament geometries and surface chemistries.
• Development of a universal solution for straight-centerline filaments and explicit solutions for canonical shapes.
• Extension of SPT to incorporate discrete jumps in surface chemistry via boundary layer analysis.

Main Results:

• A library of new, non-trivial analytical solutions for slender autophoretic microswimmers.
• Demonstration of how surface chemistry discontinuities are regularized within the SPT framework.
• Provision of solutions for filaments with arbitrary shapes and chemical patterns.
• Universal solution for straight filaments and specific solutions for benchmarkable shapes.

Conclusions:

• The generalized SPT framework provides powerful analytical tools for studying complex microswimmer dynamics.
• The developed solutions facilitate research into the relationship between microswimmer shape, surface activity, and propulsion.
• This work offers a valuable resource for both theoretical analysis and numerical code validation in microswimmer research.