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Diffusiophoresis of a dielectric fluid droplet with constant surface charge density in a symmetric binary electrolyte solution is investigated theoretically in this study, focusing on the chemiphoresis component, the very heart of diffusiophoresis. The resultant electrokinetic equations are solved with a pseudo-spectral method based on Chebyshev polynomial in the spirit of a computational fluid dynamic simulation. Reversions of moving directions are found for droplets less viscous than ambient solution when the electrolyte strength is increased due to the buildup of osmosis pressure in front of the moving droplets leading to an osmosis pressure gradient upon the droplet. The upward spouting effect of the spinning droplet surface is also responsible this buildup, which hinders the downward migration of ions and holds them up there. A solid particle may move faster than a gas bubble due to the energy consumption in the formation of an induced exterior vortex flow nearby surrounding the gas bubble. The less viscous the droplet is, the more severe this consumption is. A “solidification” phenomenon is observed where all the droplets move at the same speed with their surfaces and interior fluids motionless like rigid particles. Funnel-shape local extrema of mobility profiles provide solid evidence that the diffusion-induced double layer polarization is the very cause of the droplet motion in chemiphoresis. Excellent agreement with experimental data for a rigid particle is obtained. The study provides insights and guidelines in practical applications like drug delivery and other dead-end-pore types of operations such as EOR.

A simple analytical formula is obtained for the diffusiophoresis of a dielectric fluid droplet in symmetric binary electrolyte solutions under Debye-Hückel approximation valid for weakly charged droplets. The chemiphoresis is found to yield negative mobilities most of the time for droplets of constant surface charge density, which implies that the droplets tend to move away from the source releasing ionic chemicals. This is undesirable in some practical applications like drug delivery with liposomes in terms of conveying the drugcarrying liposomes to the desired area in the human body releasing specific ionic chemicals utilizing the self-guiding nature of diffusiophoresis. The further involvement of the electrophoresis component, however, may change the scenario via the oriented electric field generated by the induced diffusion potential. The lesson here is that while the impact of the chemiphoresis component is determined by nature and uncontrollable, the electrophoresis component serves as an artificially adjustable factor via choosing droplets with the surface charge of appropriate sign in practical applications. The results here have potential use in practical applications such as drug delivery. The portable simple analytical formula is a powerful asset to experimental researchers and design engineers in colloid science and technology to facilitate their works.

Diffusiophoresis of a dielectric fluid droplet in electrolyte solutions is investigated theoretically, focusing on the electrophoresis component resulting from the induced diffusion potential in the electrolyte solution when the diffusivities of cations and anions there are different. The resultant electrokinetic equations are solved with a pseudo-spectral method based on the Chebyshev polynomials. We found, among other things, that the electrophoresis component dominates at a larger Debye length, whereas the chemiphoresis component at a smaller Debye length for a dielectric droplet of a constant surface charge density. The two components are of comparable magnitudes in the NaCl solution. The dual between the spinning electric driving force tangent to the droplet surface and the hydrodynamic drag force reinforced by the motion-deterring electrokinetic Maxwell traction from the surrounding exterior osmosis flow is crucial in the determination of the ultimate droplet motion. Unlike the chemiphoresis component, which is independent of the sign of charges carried by the droplet, the droplet moving direction as well as its magnitude in the electrophoresis component depends on the sign of charges carried by the droplet as well as the direction of the electric field induced by the diffusion potential. This gives the electrophoresis component excellent maneuverability in practical applications like drug delivery and enhanced oil recovery, where migration of droplets toward regions of higher solute concentrations is often desired.

Diffusiophoresis of a single soft particle in an electrolyte solution with induced diffusion potential is investigated theoretically in this study. A pseudo-spectral method based on Chebyshev polynomials is adopted to solve the resultant governing electrokinetic equations. Parameters of electrokinetic interest are examined extensively to explore their respective effect upon the particle motion, such as the fixed charge density and the permeability of the outer porous layer, the surface potential and size of the inner rigid core, and the electrolyte strength and magnitude of the induced diffusion potential in the solution. The nonlinear effects pertinent to highly charged particles, such as the double layer polarization effect and the counterion condensation effect, are scrutinized, in particular. Here, nonlinear effects refer to the effects that can only be properly revealed by accurately solving the complete nonlinear Poisson–Boltzmann equation governing the electric potential instead of the simplified linear Helmholtz equation under the Debye–Hückel approximation, valid for lowly charged particles only. We found, among other things, that characteristic local extrema in mobility profiles are mainly due to these two effects. Moreover, a soft particle moves fastest in dilute electrolyte solutions, in general. The smaller the soft particle is, the faster it moves under otherwise identical structural and electrokinetic conditions, provided that the particle radius is smaller than the Debye length, the characteristic thickness of the double layer. The shape of the double layer polarization takes an undulating multilayer form at large electrolyte strength. The results provided here are useful in practical applications such as drug delivery as well as microfluidic and nanofluidic operations.