Generic theory of colloidal transport

We discuss the motion of colloidal particles relative to a two component fluid consisting of solvent and solute. Particle motion can result from (i) net body forces on the particle due to external fields such as gravity; (ii) slip velocities on the particle surface due to surface dissipative phenomena. The perturbations of the hydrodynamic flow field exhibits characteristic differences in cases (i) and (ii) which reflect different patterns of momentum flux corresponding to the existence of net forces, force dipoles or force quadrupoles. In the absence of external fields, gradients of concentration or pressure do not generate net forces on a colloidal particle. Such gradients can nevertheless induce relative motion between particle and fluid. We present a generic description of surface dissipative phenomena based on the linear response of surface fluxes driven by conjugate surface forces. In this framework we discuss different transport scenarios including self-propulsion via surface slip that is induced by active processes on the particle surface. We clarify the nature of force balances in such situations.Comment: 22 pages, 1 figur

Phoretic Motion of Spheroidal Particles Due To Self-Generated Solute Gradients

We study theoretically the phoretic motion of a spheroidal particle, which generates solute gradients in the surrounding unbounded solvent via chemical reactions active on its surface in a cap-like region centered at one of the poles of the particle. We derive, within the constraints of the mapping to classical diffusio-phoresis, an analytical expression for the phoretic velocity of such an object. This allows us to analyze in detail the dependence of the velocity on the aspect ratio of the polar and the equatorial diameters of the particle and on the fraction of the particle surface contributing to the chemical reaction. The particular cases of a sphere and of an approximation for a needle-like particle, which are the most common shapes employed in experimental realizations of such self-propelled objects, are obtained from the general solution in the limits that the aspect ratio approaches one or becomes very large, respectively.Comment: 18 pages, 5 figures, to appear in European Physical Journal