Diffusiophoretic mobility of charge‐regulating porous particles

Abstract

The diffusiophoresis of a charge-regulating porous sphere, such as polyelectrolyte coil, with an arbitrary thickness of the electric double layer in an electrolyte solution prescribed with a concentration gradient is analytically studied for the first time. The ionogenic functional groups and hydrodynamic frictional segments distribute uniformly within the permeable particle, and a charge regulation model for the association and dissociation reactions of the functional groups relates the fixed charge density to the local electric potential. The electrokinetic equations governing the electric potential, ionic electrochemical potential, and fluid velocity distributions are solved as power-series expansions in the basic fixed charge density. An explicit formula for the diffusiophoretic mobility of the particle, which vanishes at the isoelectric point, is derived from a force balance. The effects of charge regulation on the diffusiophoretic mobility, which depend on various particle and electrolyte characteristics such as the reaction equilibrium constants of the ionogenic functional groups, are significant and interesting. The variation in the bulk concentration of the charge-determining ions can produce more than one reversal in the direction of the diffusiophoretic velocity. The obtained results differ conspicuously from those of impermeable particles and provide valuable information for the interpretation of experimental data.

Diffusiophoresis: a novel transport mechanism - fundamentals, applications, and future opportunities

“…Several derivations exist for both electrolytic and non-electrolytic solutes. Recent work in the area focuses on diffusiophoresis in concentrated electrolytes (Prieve et al, 2019), multiple electrolytes (Chiang and Velegol, 2014;Gupta et al, 2019), dependence of mobility on solute concentration (Gupta et al, 2020;Lee et al, 2023b), multivalent electrolytes (Wilson et al, 2020), particle shape (Doan et al, 2023) and composite particles (Li and Keh, 2016;Mondal et al, 2023).…”

“…Several derivations exist for both electrolytic and non-electrolytic solutes. Recent work in the area focuses on diffusiophoresis in concentrated electrolytes(Prieve et al, 2019), multiple electrolytes(Chiang and Velegol, 2014;Gupta et al, 2019), dependence of mobility on solute concentration(Gupta et al, 2020;Lee et al, 2023b), multivalent electrolytes(Wilson et al, 2020), particle shape(Doan et al, 2023) and composite particles(Li and Keh, 2016;Mondal et al, 2023).Observation in experiments: The most striking feature of passive diffusiophoresis is the "focusing" effect where a region of high colloid concentration is observed. This, in effect, is as if diffusiophoresis imparts a "negative diffusion" coefficient to colloids(Murray, 2003).…”

Diffusiophoresis of a charged particle in a microtube

“…Diffusiophoresis of a charged particle under macroscopic electrolyte concentration gradients interacting with the electric double layer encompassing the particle, accompanied by the relative diffusioosmotic flow of the ambient fluid, is a well–known electrokinetic phenomenon applied to solid–liquid separations . In an unbounded solution of a symmetric electrolyte with a uniform concentration gradient , the diffusiophoretic velocity of a particle is as follows : where η and ε are the viscosity and dielectric permittivity, respectively, of the fluid, ζ is the zeta potential of the particle surface, Z is the valence of the symmetric electrolyte, and are the diffusivities of the anion and cation, respectively, is the prescribed electrolyte concentration at the particle center, e is the elementary electric charge, k is the Boltzmann constant, and T is the absolute temperature.…”

“…Diffusiophoresis of a charged particle under macroscopic electrolyte concentration gradients interacting with the electric double layer encompassing the particle, accompanied by the relative diffusioosmotic flow of the ambient fluid, is a well-known electrokinetic phenomenon applied to solidliquid separations [1,2]. In an unbounded solution of a symmetric electrolyte with a uniform concentration gradient ∇n ∞ , the diffusiophoretic velocity of a particle is as follows [3]:…”

Nano‐Structured Materials as Separation Media

“…They also demonstrated that the diffusion of 45‐nm nanoparticles in 300 nm pores can be satisfactorily explained by hydrodynamic frictions . Along these lines, the diffusiophoresis of a charge‐regulating porous sphere is analytically described for the first time by Keh's group . Specifically, the electrokinetic equations governing the electric potential, ionic electrochemical potential, and fluid velocity distributions were solved as power‐series expansions in the basic fixed charge density and highlighted the differences between these particles and those with impermeable properties.…”