Electrophoresis of tightly fitting spheres along a circular cylinder of finite length

Electrophoresis of a tightly fitting sphere of radius $a$ along the centreline of a liquid-filled circular cylinder of radius $R$ is studied for a gap width $h_0=R-a\ll a$ . We assume a Debye length $\kappa ^{-1}\ll h_0$ , so that surface conductivity is negligible for zeta potentials typically seen in experiments, and the Smoluchowski slip velocity is imposed as a boundary condition at the solid surfaces. The pressure difference between the front and rear of the sphere is determined. If the cylinder has finite length $L$ , this pressure difference causes an additional volumetric flow of liquid along the cylinder, increasing the electrophoretic velocity of the sphere, and an analytic prediction for this increase is found when $L\gg R$ . If $N$ identical, well-spaced spheres are present, the electrophoretic velocity of the spheres increases with $N$ , in agreement with the experiments of Misiunas & Keyser (Phys. Rev. Lett., vol. 122, 2019, 214501).

Nonlinear electrophoresis of a tightly fitting sphere in a cylindrical tube

We investigate electrophoresis of a tightly fitting sphere of radius $R-h_{0}$ on the axis of a circular tube of radius $R$, using lubrication theory and ideas due to Schnitzer & Yariv (Phys. Fluids, vol. 26, 2014, 122002). The electrical charge clouds on both the cylindrical wall and the surface of the sphere are assumed thin compared to the gap between the sphere and cylinder, so that charge clouds do not overlap and ion exclusion effects are minimal. Nevertheless, non-uniform pumping of counter-ions within the charge clouds leads to a change in the ionic concentration outside the charge clouds in the narrow gap between sphere and cylinder. The electro-osmotic slip velocities at the two surfaces are modified, leading to a decrease in the electrophoretic velocity of the sphere at low Péclet numbers and an increase in the velocity at high Péclet numbers. When the field strength $E_{0}$ is low, it is known that the electrophoretic velocity $U_{0}$ is proportional to $E_{0}(\unicode[STIX]{x1D701}_{s}-\unicode[STIX]{x1D701}_{c})$ which is zero when the zeta potential $\unicode[STIX]{x1D701}_{s}$ on the sphere surface is equal to the zeta potential $\unicode[STIX]{x1D701}_{c}$ on the cylinder. The perturbation to the above low field strength electrophoretic velocity (at high Péclet number) is predicted to be proportional to $E_{0}^{3}(\unicode[STIX]{x1D701}_{s}+\unicode[STIX]{x1D701}_{c})^{2}(\unicode[STIX]{x1D70E}_{s}+\unicode[STIX]{x1D70E}_{c})$, where $\unicode[STIX]{x1D70E}_{s}$ and $\unicode[STIX]{x1D70E}_{c}$ are the surface charge densities on the sphere and cylinder. The choice of materials with similar or identical zeta potentials (and surface charge densities) for the cylinder and sphere should therefore facilitate the observation of velocities nonlinear in the field strength $E_{0}$, since the reference linear electrophoretic velocity will be small.

Modeling of Electro-Kinetic Motion of Janus Droplet

Electro-kinetic manipulation Janus particles and droplets has attracted attention in recent years due to their potential application in microfluidics. Due to the presence of two different zone on the surface of particles with different charge distribution, the motion of the Janus particles are quite different than the that of regular particles. Therefore; the fundamental understanding of this motion is the key element for the further development of the microfluidic systems with Janus particles. In present study, electro-kinetic motion of Janus droplets inside a micro-channel is modeled using boundary element formulation. 2D formulation is verified against the reported experimental data in the literature. Results show that the 2D boundary element formulation is successful for the prediction of the electrophoretic velocity of the Janus droplets. The current formulation has a potential to model non-spherical particles and to study particle-particle and particle-wall interactions.

Strong-field electrophoresis

We analyse particle electrophoresis in the thin-double-layer limit for asymptotically large applied electric fields. Specifically, we consider fields scaling as ${\delta }^{\ensuremath{-} 1} $, $\delta ~(\ll \hspace *{-2pt}1)$ being the dimensionless Debye thickness. The dominant advection associated with the intense flow mandates a uniform salt concentration in the electro-neutral bulk. The $O({\delta }^{\ensuremath{-} 1} )$ large tangential fields in the diffuse part of the double layer give rise to a novel ‘surface conduction’ mechanism at moderate zeta potentials, where the Dukhin number is vanishingly small. The ensuing $O(1)$ electric current emerging from the double layer modifies the bulk electric field; the comparable $O(1)$ transverse salt flux, on the other hand, is incompatible with the nil diffusive fluxes at the homogeneous bulk. This contradiction is resolved by identifying the emergence of a diffusive boundary layer of $O({\delta }^{1/ 2} )$ thickness, resembling thermal boundary layers at large-Reynolds-number flows. The modified electric field within the bulk gives rise to an irrotational flow, resembling those in moderate-field electrophoresis. At leading order, the particle electrophoretic velocity is provided by Smoluchowski’s formula, describing linear variation with applied field.