Osmotic self-propulsion of slender particles

We consider self-diffusiophoresis of axisymmetric particles using the continuum description of Golestanian et al. [“Designing phoretic micro-and nano-swimmers,” New J. Phys. 9, 126 (2007)], where the chemical reaction at the particle boundary is modelled by a prescribed distribution of solute absorption and the interaction of solute molecules with that boundary is represented by diffusio-osmotic slip. With a view towards modelling of needle-like particle shapes, commonly employed in experiments, the self-propulsion problem is analyzed using slender-body theory. For a particle of length 2L, whose boundary is specified by the axial distribution κ(z) of cross-sectional radius, we obtain the approximation $− μ 2 D L ∫ − L L j ( z ) d κ ( z ) d z dz$ for the particle velocity, wherein j(z) is the solute-flux distribution, μ the diffusio-osmotic slip coefficient, and D the solute diffusivity. This approximation can accommodate discontinuous flux distributions, which are commonly used for describing bimetallic particles; it agrees strikingly well with the numerical calculations of Popescu et al. [“Phoretic motion of spheroidal particles due to self-generated solute gradients,” Eur. Phys. J. E: Soft Matter Biol. Phys. 31, 351–367 (2010)], performed for spheroidal particles.