Session E13: Electrokinetics: Phoresis Phenomenon

Autophoresis of two dissolving particles with surface chemical reactions

Classic diffusiophoresis describes the motion of charged particles in an electrolyte solution with an imposed concentration gradient. We investigate the autophoresis of two particles where the concentration gradient is induced by the dissolution and chemical reaction on the particle surfaces. Analytical results of the interactions are given in bi-spherical coordinates. We find that when the chemical reactions are fast relative to the diffusion of ions, the ion concentration near the particle surfaces is strongly modified and a significant local concentration gradient is generated, which results in large deviations from the conventional expression of the autophoresis where the diffusiophoretic slip velocity on the particle surface is assumed to be proportional to the concentration gradient. In particular, we show that the effective diffusiophoretic mobility is enchanced when the surface chemical reaction results in an absorption of ions from solution, while a much smaller mobility results from the reaction depositing ions into solution.   

Diffusiophoresis in one-dimensional solute gradients

We solve for the diffusiophoretic motion of suspended colloidal particles that are exposed to 1D solute gradients using numerical and analytical techniques. Similarity solutions are developed that govern the particle dynamics in a semi-infinite domain. The method of characteristics is also used to describe a diffusion-free transport model for the particles. In the limit of small particle diffusiophoretic mobility, relative to the solute diffusivity, analytical solutions are determined for the particle motions in both finite and semi-infinite domains. Results demonstrate the presence of local maxima and minima in the particle concentrations and confirm the traveling particle front dynamics. Results can inform the design of particle injection and withdrawal applications in pores and other quasi-1D geometries.   

Cleaning by surfactant gradients: the importance of rinsing in fabric cleaning

Removing particles from fibrous materials involves loosening via surfactants followed by particle transfer in a flow. While flow advection is commonly believed to be the major driver for pore-scale transport, small pores within the fabric do not allow any significant fluid flow inside them, thus significantly reducing the role of advection. However, rinsing the fabric with fresh water naturally establishes a surfactant gradient within the pore space, providing a suitable environment for particles to undergo diffusiophoresis. We demonstrate that this mechanism can remove particles from deep within narrow fabric pores. Moreover, the non-linear aspect of diffusiophoresis significantly prolongs the lifetime of the phoretic motion beyond the naive solute diffusion timescale, allowing long-lasting, continuous removal of particles.   

Electrophoretic mobility of a particle attached to a fluid interface in the thin Debye layer limit.

We consider the electrophoretic mobility of a particle attached to an interface between an electrolyte and a dielectric fluid, assuming a large viscosity and dielectric permittivity ratio. We further assume a constant zeta potential at the particle surface and that the Debye layer around the particle is much thinner than the particle diameter. Based on that, the electrostatic and the hydrodynamic stresses at the particle surface locally balance. As a result, no torque is exerted on the particle. In the absence of gravity, the electrodipping force is the only potential cause for the deformation of the fluid interface. We show that at lowest order, the interface deformation is proportional to the equilibrium electrocapillary number. Further, the solution of the Young-Laplace equation indicates that the interface only gets deformed in the close vicinity of the particle surface. As a result, to a good approximation, during the electrophoretic transport of a particle along a fluid interface, the interface deformation is negligible. This allows relating its electrophoretic mobility to the mobility in the bulk electrolyte, indicating that the two are identical. Finally, we discuss potential applications in electrophoretic separation processes.   

The Leaky Dielectric Model as a Weak Electrolyte Limit of an Electrodiffusion Model

The Taylor-Melcher (TM) model is the standard model for the electrohydrodynamics of poorly conducting leaky dielectric fluids under an electric field. The TM model treats the fluid as an ohmic conductor, without modeling ion dynamics. On the other hand, electrodiffusion models, which have been successful in describing electokinetic phenomena, incorporates ionic concentration dynamics. Mathematical reconciliation between electrodiffusion and the TM models has been a major issue for electrohydrodynamic theory. Here, we derive the TM model from an electrodiffusion model where we explicitly model the electrochemistry of ion dissociation. We introduce salt dissociation reaction in the bulk and take the limit of weak salt dissociation (corresponding to poor conductors in the TM model.) Assuming small Debye length we derive the TM model with or without the surface charge advection term depending upon the scaling of relevant dimensionless parameters. Our analysis also gives a description of the ionic concentration distribution within the Debye layer, which hints at possible scenarios for electrohydrodynamic singularity formation. In our analysis we also allow for a jump in voltage across the liquid interface which causes a drifting velocity for a liquid drop under an electric field.   

The impact of electrostatic correlations on Dielectrophoresis of Non-conducting Particles

The dipole moment of a charged, dielectric, spherical particle under the influence of a uniform alternating electric field is computed theoretically and numerically by solving the modified continuum Poisson-Nernst-Planck (\textbf{PNP}) equations accounting for ion-ion electrostatic correlations that is important at concentrated electrolytes (Phys. Rev. Lett. 106, 2011). The dependence on the frequency, zeta potential, electrostatic correlation lengths, and double layer thickness is thoroughly investigated. In the limit of thin double layers, we carry out asymptotic analysis to develop simple models which are in good agreement with the modified PNP model. Our results suggest that the electrostatic correlations have a complicated impact on the dipole moment. As the electrostatic correlations length increases, the dipole moment decreases, initially, reach a minimum, and then increases since the surface conduction first decreases and then increases due to the ion-ion correlations. The modified PNP model can improve the theoretical predictions particularly at low frequencies where the simple model can't qualitatively predict the dipole moment.