Ion size effect on the diffusiophoretic mobility of a large colloidal particle

Diffusiophoresis of Weakly Charged Fluid Droplets in a General Electrolyte Solution: An Analytical Theory

Owing to the importance of analytical results for electrokinetics of colloidal entities, we performed a mathematical analysis to determine the closed form analytical results for the diffusiophoretic velocity of a hydrophobic and polarizable fluid droplet. A comprehensive mathematical model is developed for diffusiophoresis, considering the background aqueous medium as general electrolytes (e.g., binary valence-symmetric/asymmetric electrolytes and a mixed solution of binary electrolytes). We performed our analysis under a weak concentration gradient, and the analytical results for diffusiophoretic velocity are calculated within the Debye-Hückel electrostatic framework. The exact form of the diffusiophoretic velocity is further approximated with negligible error, and the approximate form is found to be free from any of the cumbersome exponential integrals and thus very convenient for practical use. The present theory also covers the diffusiophoresis of perfectly dielectric as well as perfectly conducting droplets as its limiting case. In addition, we have further derived a number of closed form expressions for diffusiophoretic velocity pertaining to several particular cases, and we observed that the derived limit correctly recovers the available existing analytical results for diffusiophoretic velocity. Thus, the present analytical theory for diffusiophoresis can be applied to a wide class of fluidic droplets, e.g., hydrophobic and dielectric oil/conducting mercury droplets, air bubbles, nanoemulsions, as well as any polarizable and hydrophobic fluidic droplet suspended in a solution of general electrolytes.

Two-dimensional diffusiophoretic colloidal banding: optimizing the spatial and temporal design of solute sinks and sources

Diffusiophoresis refers to the phenomenon where colloidal particles move in response to solute concentration gradients. Existing studies on diffusiophoresis, both experimental and theoretical, primarily focus on the movement of colloidal particles in response to one-dimensional solute gradients. In this work, we numerically investigate the impact of two-dimensional solute gradients on the distribution of colloidal particles, i.e., colloidal banding, induced via diffusiophoresis. The solute gradients are generated by spatially arranged sources and sinks that emit/absorb a time-dependent solute molar rate. First we study a dipole system, i.e., one source and one sink, and discover that interdipole diffusion and molar rate decay timescales dictate colloidal banding. At timescales shorter than the interdipole diffusion timescale, we observe a rapid enhancement in particle enrichment around the source due to repulsion from the sink. However, at timescales longer than the interdipole diffusion timescale, the source and sink screen each other, leading to a slower enhancement. If the solute molar rate decays at the timescale of interdipole diffusion, an optimal separation distance is obtained such that particle enrichment is maximized. We find that the partition coefficient of solute at the interface between the source and bulk strongly impacts the optimal separation distance. Surprisingly, the diffusivity ratio of solute in the source and bulk has a much weaker impact on the optimal dipole separation distance. We also examine an octupole configuration, i.e., four sinks and four sources, arranged in a circle, and demonstrate that the geometric arrangement that maximizes enrichment depends on the radius of the circle. If the radius of the circle is small, it is preferred to have sources and sinks arranged in an alternating fashion. However, if the radius of the circle is large, a consecutive arrangement of sources and sinks is optimal. Our numerical framework introduces a novel method for spatially and temporally designing the banded structure of colloidal particles in two dimensions using diffusiophoresis and opens up new avenues in a field that has primarily focused on one-dimensional solute gradients.

Diffusiophoresis of a Soft Particle as a Model for Biological Cells

We derive the general expression for the diffusiophoretic mobility of a soft particle (i.e., polyelectrolyte-coated hard particle) in a concentration gradient of electrolytes for the case in which the particle’s core size is large enough compared with the Debye length. Therefore, the particle surface can be regarded as planar, and the electrolyte concentration gradient is parallel to the core surface. The obtained expression can be applied for arbitrary values of the fixed charge density of the polyelectrolyte layer and the surface charge density of the particle core. We derive approximate analytic mobility expressions for soft particles of three types, i.e., (i) weakly charged soft particles, (ii) soft particles with a thick polyelectrolyte layer, in which the equilibrium electric potential deep inside the polyelectrolyte layer is equal to the Donnan potential, and (iii) soft particles with an uncharged polymer layer of finite thickness.