Wall effects on self-diffusiophoretic Janus particles: a theoretical study

Abstract

We present a theoretical investigation of the self-diffusiophoresis of a class of twofaced, two-dimensional Janus particles propelled by the production of gradients in the concentration of a solute diffusing into a surrounding fluid at zero Reynolds and Péclet numbers. Those concentration gradients produce a tangential boundary slip resulting in translation and rotation of the particle, as a consequence of the fact that it is free of both force and torque. The model Janus particles studied here have piecewise constant surface mobilities and surface activities over two faces. An isolated circular Janus particle is studied first and its speed of locomotion in free space is found analytically. Confinement effects are then investigated by placing such a Janus particle near a straight no-slip wall. The governing nonlinear dynamical system is found in explicit form. It is used to study how the geometry, location and orientation of the particle relative to the wall affect its motion. It is found that if the particles do not hit the wall in finite time they are eventually repelled away from it.

Dynamics of a treadmilling microswimmer near a no-slip wall in simple shear

“…In principle, we could have simply invoked those results, but the derivation above using the reciprocal theorem and conformal mapping (rather than bipolar coordinates) is novel and is worth reporting in its own right. It is also a natural extension of previous work for swimming near a wall in the absence of shear (Crowdy 2011(Crowdy , 2013.…”

“…where it has already been demonstrated in Crowdy (2011Crowdy ( , 2013 how to compute the speeds U tread , V tread and Ω tread induced by the treadmilling action. Here, we focus on calculating the additional terms U shear , V shear and Ω shear due to the background shear.…”

“…One of the authors (Crowdy 2013) has previously shown that for a general tangential slip profile of the form…”

“…Qualitatively similar nonlinear periodic motions have been found in a three-sphere swimmer (Or, Zhang & Murray 2011), a spheroidal squirmer (Ishimoto & Gaffney 2013) and in experiments , which provides evidence that even idealized two-dimensional models can provide useful insights into more complicated three-dimensional dynamics in certain situations, especially when the physical source of the observed dynamics is not clear. More recently, simple two-dimensional swimmer models have been used to study self-diffusiophoretic Janus particles near a wall (Crowdy 2013), swimmer-swimmer interactions in a film (Clarke, Finn & MacDonald 2014) and wall-bounded motion of swimmers incorporating viscoelastic effects (Yazdi, Ardekani & Borham 2014. Simple two-dimensional modelling has also been widely used to provide insights into electrophoresis near a wall (Keh, Horng & Kuo 1991;Zhao & Bau 2007).…”

“…We also demonstrate, in § 5, the new result that the dynamical system (1.1) has an associated Hamiltonian structure both with and without a background shear flow. It is interesting to note that theoretical models of swimmers in Poiseuille flow derived by previous authors (Zöttl & Stark 2012, 2013 have also been shown to be Hamiltonian; those models do not, however, incorporate hydrodynamic interactions with the wall and assume that the swimmer is sufficiently far from the wall that those interactions can be neglected. An oscillatory swimmer motion in a cylindrical tube has been reported in a detailed numerical calculation incorporating swimmer-wall hydrodynamic interactions by Zhu, Lauga & Brandt (2013).…”