Diffusiophoresis of a highly charged soft particle in electrolyte solutions induced by diffusion potential

Abstract

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.

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

“…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].…”

“…Hence some coordinate transformation is necessary for the boundary conditions across the interface between the soft particle and the solution, as shown in Eq. (21). The details can be found elsewhere [27].…”

“…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].…”