Diffusiophoresis of a spherical particle in porous media

Travelling-wave gel dipolophoresis of hydrophobic conducting colloids

A unified 'weak-field' formulation is provided for calculating the combined nonlinear effect of dielectrophoresis and the induced-charge electrophoresis (dipolophoresis) of polarized rigid hydrophobic spherical colloids freely suspended in an electrolyte-saturated Brinkman-hydrogel (porous) medium under a general (direct or alternating currents) non-uniform electric forcing. Explicit expressions for the modified total dipolophoretic mobility of a conducting (metallic) spherical colloid are given in terms of the Brinkman (Darcy), Navier slip, and Debye (screening) length scales. Also presented is a rigorous derivation of the Helmholtz-Smoluchowski slip velocity in terms of these three length scales, including the induced electroosmotic flow field around a hydrophobic rigid colloid embedded in a Brinkman medium that is forced by an arbitrary (non-uniform) ambient electric field. The available solutions for a free (non-porous) electrolyte solution under a uniform forcing and no-slip surface are obtained as limiting cases. For the purpose of illustration, we present and analyse some newly explicit solutions for the mobility and the associated induced-charge electroosmotic velocity field of a slipping colloid set in an effective (hydrogel) porous medium, which is exposed to an ambient 'sinusoidal' travelling-wave excitation depending on frequency and wave number.

Diffusiophoresis in porous media saturated with a mixture of electrolytes

Current theories of diffusiophoresis in porous media are limited to a porous medium saturated with a valence symmetric electrolyte. A predictive model for diffusiophoresis in porous media saturated with a valence asymmetric electrolyte, or a general mixture of valence symmetric and asymmetric electrolytes, is lacking. To close this knowledge gap, in this work we develop a mathematical model, based upon the regular perturbation method and numerical integration, to compute the diffusiophoretic mobility of a colloid in porous media saturated with a general mixture of electrolytes. We model the electrokinetics using the Poisson-Nernst-Planck equations and the fluid transport in porous media using the Brinkman equation with an electric body force. We report three novel key findings. First, we demonstrate that, in the same electrolyte concentration gradient, lowering the permeability of the porous medium can significantly weaken the colloid diffusiophoretic motion. Second, we show that, surprisingly, by using a valence asymmetric electrolyte the colloid diffusiophoretic motion in a denser porous medium can be stronger than that in a less dense porous medium saturated with a symmetric electrolyte. Third, we demonstrate that varying the composition of an electrolyte mixture does not only change the strength of the colloid diffusiophoretic motion drastically, but also qualitatively its direction. The model developed from this work can be used to understand and predict natural phenomena such as intracellular transport, as well as design technological applications such as enhanced oil recovery, nanoparticle drug delivery, and colloidal species separation.

Diffusioosmotic Reversal of Colloidal Focusing Direction in a Microfluidic T-Junction

Solute gradients next to an interface drive a diffusioosmotic flow, the origin of which lies in the intermolecular interactions between the solute and the interface. These flows on the surface of colloids introduce an effective slip velocity, driving their diffusiophoretic migration. In confined environments, the interplay between diffusiophoresis and diffusioosmosis governs the motion of colloids. Previous studies have indeed demonstrated the quantitative modulation of phoretic migration by the osmotic flows. Here, we show that diffusioosmotic flows can lead to qualitatively distinct outcomes, reversing the direction of colloidal focusing expected from diffusiophoresis alone. Using microfluidic experiments in a T-junction, numerical simulations, and theoretical modeling, we explain our observations to be due to an interplay between diffusiophoretic migration of colloids toward the walls and their entrainment in a diffusioosmotic vortex. We show this focusing to be persistent for a range of salt types, salt gradients, and flow rates, and establish a criterion for its emergence. Our work sheds light on how boundaries modulate the solute-mediated transport of colloids in confined environments and how the colloidal trajectories can be utilized to infer the surface properties.

Transient Gel Diffusiophoresis of a Spherical Colloidal Particle

A general theory is presented to analyze the time-dependent, transient diffusiophoresis of a charged spherical colloidal particle in an uncharged gel medium containing a symmetrical electrolyte when an electrolyte concentration gradient is suddenly applied. We derive the inverse Laplace transform of an approximate expression for the relaxation function R(t), which describes the time-course of the ratio of the diffusiophoretic mobility of a weakly charged spherical colloidal particle, possessing a thin electrical double layer, to its steady-state diffusiophoretic mobility. The relaxation function depends on the mass density ratio of the particle to the electrolyte solution, the particle radius, the Brinkman screening length, and the kinematic viscosity. However, it does not depend on the type of electrolyte (e.g., KCl or NaCl), which affects only the steady-state gel diffusiophoretic mobility. It is also found that the expression for the relaxation function in transient gel diffusiophoresis of a weakly charged spherical colloidal particle with a thin electrical double layer takes the same form as that for its transient gel electrophoresis.

Competition between ion-ion electrostatic correlations and hydrodynamic slip radically changes diffusioosmosis

Existing theories can predict separately the effects of hydrodynamic slip and ion-ion electrostatic correlations on diffusioosmosis. However, a predictive model for the coupled dynamics of hydrodynamic slip and electrostatic correlations in diffusioosmosis is lacking. In this work, we develop a mathematical model to compute the diffusioosmotic mobilities of valence-symmetric electrolytes in a charged parallel-plate channel. We employ the Navier slip condition to model the hydrodynamic slip at the channel walls and the modified Poisson equation to model ion-ion electrostatic correlations. We report two key findings arising from the competition between electrostatic correlations and hydrodynamic slip, which radically change diffusioosmosis. First, in a divalent electrolyte, a minute hydrodynamic slip defers the reversal in the direction of diffusioosmosis caused by electrostatic correlations to a higher concentration. Hydrodynamic slip can even eliminate the diffusioosmosis reversal in a monovalent electrolyte. Second, electrostatic correlations limit the change in the mobility due to hydrodynamic slip, by hindering the slip-enhanced ionic transport via surface charge overscreening. Electrostatic correlations can reduce the change in the mobility by ≈60% in a monovalent electrolyte, whereas the stronger electrostatic correlations in a divalent electrolyte can even reduce the change by an order of magnitude. The model developed from this work can be used to understand and predict diffusioosmosis in natural settings such as metamorphic transformation, in addition to that in applications such as colloidal species separation, nanoparticle drug delivery, and enhanced oil recovery.

Diffusioosmotic flow reversals due to ion-ion electrostatic correlations

Existing theories of diffusioosmosis have neglected ion-ion electrostatic correlations, which are important in concentrated electrolytes. Here, we develop a mathematical model to numerically compute the diffusioosmotic mobilities of binary symmetric electrolytes across low to high concentrations in a charged parallel-plate channel. We use the modified Poisson equation to model the ion-ion electrostatic correlations and the Bikerman model to account for the finite size of ions. We report two key findings. First, ion-ion electrostatic correlations can cause a unique reversal in the direction of diffusioosmosis. Such a reversal is not captured by existing theories, occurs at ≈ 0.4 M for a monovalent electrolyte, and at a much lower concentration of ≈ 0.003 M for a divalent electrolyte in a channel with the same surface charge. This highlights that diffusioosmosis of a concentrated electrolyte can be qualitatively different from that of a dilute electrolyte, not just in its magnitude but also its direction. Second, we predict a separate diffusioosmotic flow reversal, which is not due to electrostatic correlations but the competition between the underlying chemiosmosis and electroosmosis. This reversal can be achieved by varying the magnitude of the channel surface charge without changing its sign. However, electrostatic correlations can radically change how this flow reversal depends on the channel surface charge and ion diffusivity between a concentrated and a dilute electrolyte. The mathematical model developed here can be used to design diffusioosmosis of dilute and concentrated electrolytes, which is central to applications such as species mixing and separation, enhanced oil recovery, and reverse electrodialysis.

Unidirectional drying of a suspension of diffusiophoretic colloids under gravity

Recent experiments (K. Inoue and S. Inasawa, RSC Adv., 2020, 10, 15763-15768) and simulations (J.-B. Salmon and F. Doumenc, Phys. Rev. Fluids, 2020, 5, 024201) demonstrated the significant impact of gravity on unidirectional drying of a colloidal suspension. However, under gravity, the role of colloid transport induced by an electrolyte concentration gradient, a mechanism known as diffusiophoresis, is unexplored to date. In this work, we employ direct numerical simulations and develop a macrotransport theory to analyze the advective-diffusive transport of an electrolyte-colloid suspension in a unidirectional drying cell under the influence of gravity and diffusiophoresis. We report three key findings. First, drying a suspension of solute-attracted diffusiophoretic colloids causes the strongest phase separation and generates the thinnest colloidal layer compared to non-diffusiophoretic or solute-repelled colloids. Second, when colloids are strongly solute-repelled, diffusiophoresis prevents the formation of colloid concentration gradient and hence gravity has a negligible effect on colloidal layer formation. Third, our macrotransport theory predicts new scalings for the growth of the colloidal layer. The scalings match with direct numerical simulations and indicate that the colloidal layer produced by solute-repelled diffusiophoretic colloids could be an order of magnitude thicker compared to non-diffusiophoretic or solute-attracted colloids. Our results enable tailoring the separation of colloid-electrolyte suspensions by tuning the interactions between the solvent, electrolyte, and colloids under Earth's or microgravity, which is central to ground-based and in-space applications.