By considering an ion moving inside an imaginary sphere filled with a power-law fluid, we bring out the implications of the fluid rheology and the influence of the proximity of the other ions towards evaluating the conduction current in an ionic solution. We show that the variation of the conductivity as a function of the ionic concentration is both qualitatively and quantitatively similar to that predicted by the Kohlrausch law. We then utilize this consideration for estimating streaming potentials developed across narrow fluidic confinements as a consequence of the transport of ions in a convective medium constituting a power-law fluid. These estimates turn out to be in sharp contrast to the classical estimates of streaming potential for non-Newtonian fluids, in which the effect of rheology of the solvent is merely considered to affect the advection current, disregarding its contributions to the conduction current. Our results have potential implications of devising a new paradigm of consistent estimation of streaming potentials for non-Newtonian fluids, with combined considerations of the confinement effect and fluid rheology in the theoretical calculations.

Consistent prediction of streaming potential in non-Newtonian fluids: the effect of solvent rheology and confinement on ionic conductivity.

Molecular dynamics simulations were used to investigate the electric field-induced migration of nanoparticles in a nanochannel grafted with a polymer brush. The distribution of nanoparticles, brush monomer density and migration velocity are addressed at different electric field strengths and grafting densities. The increase of the grafting density leads to a decrease of the effective radius of the nanochannel. At high grafting density, the distribution of nanoparticles is shifted significantly towards the center of the channel. Enhancing the electric field leads to a very slight change of brush monomer density. The migration velocity increases with the electric field rapidly at weak electric fields, while a slow increase is observed at strong electric fields. Additionally, it is found that the migration velocity of nanoparticles exhibits a nonlinear dependence on the grafting density.

Charged Nanoparticle Transport in Polymer-Grafted Nanochannels

Electrophoresis of Bottle‐Brush Polyelectrolytes in an Attractive Nanochannel

We study the stretching of a surface-tethered polyelectrolyte confined between parallel surfaces under the application of a dc electric field. We explore the influence of the electric-field strength, the length of the polyelectrolyte, and the degree of confinement on the conformation of the polyelectrolyte by single-molecule experiments and coarse-grained coupled lattice-Boltzmann molecular-dynamics simulations. The fractional extension of the polyelectrolyte is found to be a universal function of the product of the applied electric field and the molecular contour length, which is explained by simple scaling arguments. The degree of confinement does not have any significant influence on the stretching. We also confirm that an electrohydrodynamic equivalence principle relating the stretching in an electric field to that in a flow field is applicable.

Electric-field-induced stretching of surface-tethered polyelectrolytes in a microchannel.

By molecular dynamics simulations, we investigated the transport of charged polymers in applied electric fields in confining environments, which were straight cylinders of uniform or non-uniform diameter. In the simulations, the solvent was modeled explicitly and, also, the counterions and coions of added salt. The electrophoretic velocities of charged chains in relation to electrolyte friction, hydrodynamic effects due to the solvent, and surface friction were calculated. We found that the velocities were higher if counterions were moved away from the polymeric domain, which led to a decrease in hydrodynamic friction. The topology of the surface played a key role in retarding the motion of the polyelectrolyte and, even more so, in the presence of transverse electric fields. The present study showed that a possible way of improving separation resolution is by controlling the motion of counterions or electrolyte friction effects.

https://www.mdpi.com/1996-1944/6/7/3007/pdf

Charged Polymers Transport under Applied Electric Fields in Periodic Channels

We consider the dynamics of charged polymers in free solution in a slit geometry under the influence of an electrical field, applied at an angle to the plane parallel walls of the confinement. The simulations are carried out using the Brownian dynamics method with explicit counterions and implicit hydrodynamics. The hydrodynamic interactions between all the particles and the plane parallel walls are taken into account using a diffusion matrix which depends on slit geometry and the actual polyelectrolyte-solute conformations. We observe a selective transport of the charged polymers, as a function of the degree of polymerization and slit height.

Simulations of polyelectrolyte dynamics in an externally applied electric field in confined geometry.

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Simulations of polyelectrolyte dynamics in an externally applied electric field in confined geometry.