Motion of a particle generated by chemical gradients Part 1. Non-electrolytes

When a particle is placed in a fluid in which there is a non-uniform concentration of solute, it will move toward higher or lower concentration depending on whether the solute is attracted to or repelled from the particle surface. A quantitative understanding of this phenomenon requires that the equations representing conservation of mass and momentum within the fluid in the vicinity of the particle are solved. This is accomplished using a method of matched asymptotic expansions in a small parameter L/a, where a is the particle radius and L is the length scale characteristic of the physical interaction between solute and particle surface. This analysis yields an expression for particle velocity, valid in the limit L/a → 0, that agrees with the expression obtained by previous researchers. The result is cast into a more useful algebraic form by relating various integrals involving the solute/particle interaction energy to a measurable thermodynamic property, the Gibbs surface excess of solute Γ. An important result is that the correction for finite L/a is actually O(Γ/C∞a), where C∞ is the bulk concentration of solute, and could be O(1) even when L/a is orders of magnitude smaller.