Diffusiophoretic velocity of a spherical soft particle

The general expression is derived for the diffusiophoretic velocity of a spherical soft particle (that is, a spherical hard particle consisting of the particle core covered with an ion-penetrable surface layer of polyelectrolytes) in an electrolyte concentration gradient. For a weakly charged soft particle, the obtained general expression for the diffusiophoretic velocity is shown to reproduce the results derived by Huang and Keh (J Phys Chem B (2012) 116: 7575–7589). A simple approximate analytic expression is obtained for the diffusiophoretic velocity applicable for the case where the particle core radius and the thickness of the polyelectrolyte layer are much larger than the Debye length and the Brinkman screening length.