Motion of a particle generated by chemical gradients. Part 2. Electrolytes

Abstract

When immersed in a non-uniform electrolyte solution, a rigid charged sphere migrates toward higher or lower concentration of the electrolyte depending on the relative ionic mobilities and the charge borne by the sphere. This motion has a twofold origin: first, a macroscopic electrolyte gradient produces an electric field which acts on the charged sphere (electrophoresis); secondly, the electrolyte gradient polarizes the cloud of counterions surrounding the charged sphere by making the cloud thinner on the high-concentration side (chemiphoresis). In this paper, we compute the terminal velocity of a non-conductive sphere through a slightly non-uniform solution of a symmetrically charged binary electrolyte. The analysis proceeds through an expansion in the small parameter λ (defined as the ratio of the counterion-cloud thickness to the particle radius). Results to O(λ) are presented. The only property of the sphere's surface that affects the velocity is its zeta potential ζ when the electrolyte gradient vanishes; no information concerning the dependence of ζ upon ionic strength is needed. While the chemiphoretic effect always directs the particle toward higher electrolyte concentration, the electrophoretic contribution can move the particle in either direction depending on the sign of βζ, where β is a normalized difference in mobilities between cation and anion of the elecytrolyte; thus particle movement could be directed toward either higher or lower electrolyte concentration depending on the physical properties of the system. With slight algebraic rearrangement, our results are also applicable to conventional electrophoresis (particle motion in an applied electric field) and show excellent agreement with the numerical calculations of O'Brien & White (1978).

Direct Measurements of Colloidal Solvophoresis under Imposed Solvent and Solute Gradients

“…In this case, the diffusivity of the K + anion is higher than that of the IO 3 − anion, so that the electro-diffusiophoretic and chemi-diffusiophoretic components of eq 2 are oppositely directed. Moreover, the electrodiffusiophoretic component exceeds the chemi-diffusiophoretic component 29 and therefore drives colloids down the ionic strength gradient. Finally, Figure 7e shows diffusiophoretic migration in a nonelectrolyte gradient (sucrose, c mid = 0.5 mM and Δc = 1 mM), wherein PS colloids migrate up the sucrose gradient.…”

“…The first term in eq 2 is the electrophoretic contribution which can be directed either up or down the gradient, and the second term reflects the chemiphoretic contribution, which is always directed up the gradient. Colloidal diffusiophoresis typically proceeds up electrolyte gradients but can in certain circumstances migrate down gradients 29 (e.g., Figure 7d). …”

Efficiency of Surface-Driven Motion: Nanoswimmers Beat Microswimmers

“…For diffusiophoresis of a passive swimmer in an externally maintained concentration gradient the boundary conditions areê r j i | r=R = 0 and (∇c i ) | r→∞ = const.×ê 3 . Also, the boundary conditions of an ionic potential are determined such that the electric current vanishes at infinity (j 1 − j 2 ) | r→∞ = 0 [21]. Both, the ionic and non-ionic solutes mediate a body force b given by − (c 1 − c 2 ) ∇Ψ and −c 1 ∇Ψ, respectively.…”

“…(2), we employ the established theory for diffusiophoresis when l ≪ R [2,21]. The smallness of l implies that the normal concentration profile near the surface is near equilibrium.…”

Motion-based threat detection using microrods: experiments and numerical simulations

“…First, we note that the classical expression for the diffusiophoretic velocity used here was originally derived for spherical particles. 29, 30 While we do not expect the dependence on s to change significantly for rod-like particles such as the micromotors considered here, diffusiophoresis may also lead to a rotational flux contribution, though this flux is negligible unless strong gradients exist on the scale of the particles, which is not the case here. Second, we have neglected the effect of the microrods on the distribution of silver ions.…”