Katsamba Panayiota, Butler Matthew D, Koens Lyndon, Montenegro-Johnson Thomas D
Computation-based Science and Technology Research Center (CaSToRC), The Cyprus Institute, 20 Constantinou Kavafi Street, 2121 Nicosia, Cyprus.
School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK.
Soft Matter. 2022 Sep 28;18(37):7051-7063. doi: 10.1039/d2sm00942k.
Autophoretic microswimmers self-propel surface interactions with a surrounding solute fuel. Chemically-active filaments are an exciting new microswimmer design that augments traditional autophoretic microswimmers, such as spherical Janus particles, with extra functionality inherent to their slender filament geometry. Slender Phoretic Theory (SPT) was developed by Katsamba to analyse the dynamics of chemically-active filaments with arbitrary three-dimensional shape and chemical patterning. SPT provides a line integral solution for the solute concentration field and slip velocity on the filament surface. In this work, we exploit the generality of SPT to calculate a number of new, non-trivial analytical solutions for slender autophoretic microswimmers, including a general series solution for phoretic filaments with arbitrary geometry and surface chemistry, a universal solution for filaments with a straight centreline, and explicit solutions for some canonical shapes useful for practical applications and benchmarking numerical code. Many common autophoretic particle designs include discrete jumps in surface chemistry; here we extend our SPT to handle such discontinuities, showing that they are regularised by a boundary layer around the jump. Since our underlying framework is linear, combinations of our results provide a library of analytic solutions that will allow researchers to probe the interplay of activity patterning and shape.
自泳微游动器通过与周围溶质燃料的表面相互作用实现自我推进。化学活性细丝是一种令人兴奋的新型微游动器设计，它在传统自泳微游动器（如球形Janus粒子）的基础上，增加了其细长细丝几何形状所固有的额外功能。Katsamba提出了细长泳动理论（SPT），用于分析具有任意三维形状和化学图案的化学活性细丝的动力学。SPT为细丝表面的溶质浓度场和滑移速度提供了线积分解。在这项工作中，我们利用SPT的通用性，为细长自泳微游动器计算了许多新的、非平凡的解析解，包括具有任意几何形状和表面化学性质的泳动细丝的一般级数解、具有直线中心线的细丝的通用解，以及一些对实际应用和数值代码基准测试有用的典型形状的显式解。许多常见的自泳粒子设计包括表面化学的离散跳跃；在这里，我们扩展了我们的SPT来处理这种不连续性，表明它们通过跳跃周围的边界层进行正则化。由于我们的基础框架是线性的，我们结果的组合提供了一个解析解库，这将使研究人员能够探究活性图案和形状之间的相互作用。
