Diffusiophoresis of a Highly Charged Soft Particle in Electrolyte Solutions

Abstract

Diffusiophoresis of a soft particle suspended in an infinite medium of symmetric binary electrolyte solution is investigated theoretically in this study, focusing on the chemiphoresis component when there is no global diffusion potential in the bulk solution. The general governing electrokinetic equations are solved with a pseudo-spectral method based on Chebyshev polynomials, and particle mobility, defined as the particle velocity per unit concentration gradient, is calculated. Parameters of electrokinetic interest are examined, in general, to explore their respective impact upon particle motion, such as the fixed charge density and permeability in the outer porous layer, the surface charge density and size of the inner rigid core, and the electrolyte strength in the solution. Nonlinear phenomena such as the motion-deterring double-layer polarization and the counterion condensation effects are scrutinized, in particular, for highly charged soft particles. Mobility reversal is observed in some range of electrolyte strength for highly charged particles. The generation of an axisymmetric counterclockwise vortex flow across the porous layer is found to be responsible for it. The onset of the mobility reversal is synchronized with the appearance or disappearance of this vortex flow. Mobility reversal may happen more than once, with particle moving toward or away from the region of higher solute concentration. The latter is undesirable in the application of drug delivery and thus should be avoided by delicate control of the electrokinetic environment. A local micro diffusion potential is discovered, which always speeds up the migration of coions and slows down that of counterions to guarantee that there is no net electric current across the double layer. Moreover, multilayer structure of the double-layer polarization is discovered when the electrolyte strength is high. The study presented here provides insight and crucial information for practical applications of soft particles, such as drug delivery.

Analytical solution to dielectric droplet diffusiophoresis under Debye–Hückel approximation

“…On the other hand, diffusiophoresis, the motion of a particle in response to a solute concentration gradient in a solution, has emerged as a competitive driving force to manipulate colloidal particles in colloid science and technology [5]. In particular, it has potential applications in drug delivery due to its self-guiding nature and negligible Joule heating effect [6][7][8], a crucial factor to consider as a raise of 4°C is fatal to mammalian cells [9]. As a result, understanding the diffusiophoretic behavior of a fluid droplet is a very important issue in order to control and convey the drug-carrying droplets like liposomes to their desired destination [10,11].…”

Diffusiophoresis of a highly charged soft particle normal to a conducting plane

“…Hence only the "chemiphoresis component" is present here, which implies the particle motion solely results from the double layer polarization generated by the migration of ions across the borderline of the double layer owing to the imposed concentration gradient in the bulk solution far away from the particle [33,34]. As a result, the particle motion will be fastest in the electrolyte solution with κa around unity, as it implies the double layer thickness is comparable to the particle radius thus the impact of the double layer polarization is most profound in general [21,22,34]. For very thick double layer, indicated by very small κa, the ions in the vicinity of the particle are often too sparse to generate appreciable particle motion.…”

“…The surface potential on the inner rigid core, φ r , on the other hand, is set to 3, the typical value of a highly charged rigid solid particle. The permeability of the outer porous layer, λa, is set to unity as it is the value where particle mobility is most sensitive to the variation of it [21,22,36].…”

“…The extra drag force is proportional to the local fluid velocity with a constant friction coefficient, γ , which is related to the Brinkman screening length λ –1 as . The details can be found elsewhere [21, 22].…”

“…The therapeutic elements are contained in the outer porous layer, which is normally electrically charged [19,20]. Motivated by this application in particular, Lee and his coworkers [21,22] investigated the diffusiophoresis of a soft particle in electrolyte solutions recently, focusing on the unique behaviors of highly charged ones, as they are most often encountered in practice. Suspensions of soft particles were explored by other groups as well [23,24].…”