Diffusiophoresis of colloidal particles in neutral solute gradients at finite Péclet number

Abstract

The role of neutral solute advection on the diffusiophoretic motion of colloidal particles is quantified. Theoretical analyses of this phenomenon usually assume that the solute concentration evolves solely via diffusion; that is, the Péclet number (Pe) for solute transport is identically zero. This leads to the conclusion that the translational diffusiophoretic velocity of a colloid is independent of its size, shape, and orientation with respect to the imposed solute gradient, provided that the colloid has uniform surface properties and that the length scale of interaction between the solute and the particle surface is much smaller than the particle size (Morrison, J. Colloid Interface Sci. vol. 34, 1970, p. 210). For a single spherical colloid, we show that the particle velocity decreases monotonically with increasing Pe. Moreover, the solute concentration and fluid flow around the colloid become markedly fore-aft asymmetric as Pe is increased. Next, an asymptotic expansion at small Pe predicts that solute advection leads to relative phoretic motion between two identical spherical colloids, which ultimately align in a plane normal to the imposed gradient (there is no relative motion at Pe = 0). Finally, asymptotic analysis of the diffusiophoretic motion of a slightly non-spherical colloid at small Pe demonstrates that advection leads to a shape-and orientation-dependent particle velocity, in contrast to the insensitivity of the velocity to shape and orientation at Pe = 0.

Effect of the interaction strength and anisotropy on the diffusio-phoresis of spherical colloids

“…The conventional theoretical description of phoretic transport combines a local thermodynamics description of the fluid around a colloidal particle with Stokesian hydrodynamics 2,6,14,[33][34][35] . Whilst such a continuum description is usually adequate for electrophoresis, it is less applicable in the case of diffusio-and thermo-phoresis, where the characteristic length-scales are often too small to justify local hydrodynamics/thermodynamics.…”

Electrophoresis of bubbles

“…This reduces the problem to an infinite system of (coupled and nonlinear) ordinary differential equations (ODEs) in r, which may be solved by a controlled truncation procedure. This procedure is essentially the same as that detailed by Khair (2013) in the context of a different physical problem.…”

Autophoretic flow on a torus

“…Autophoretic microswimmers are artificial microscale particles that self propel via slip flows at their surface created through self-generated, rather than externally imposed [1,2], field gradients such as heat [3,4] or solute concentration [5]. Such particles have potential biomedical [6] and microfluidics applications [7], and may perform intricate microscale tasks, for example directed cargo transport and assembly [8,9].…”