Travelling wave dipolophoresis of ideally polarizable nano-particles with overlapping electric double layers in cylindrical pores

Abstract

Regimes of streaming potential in cylindrical nano-pores in presence of finite sized ions and charge induced thickening: An analytical approach T. Miloh and A. Boymelgreen Phys. Fluids 26, 072101 (2014) case, the Helmholtz-Smoluchowski (HS) slip-velocity may be implemented as a boundary condition in the Stokes equation, effectively bypassing the need to consider the electrostatic (Coulomb) forces in the momentum equation, thus considerably simplifying the analysis. However, if the particle radius or channel width is of the same order as the EDL (nano-size), this approximation ceases to be valid and it becomes necessary to resolve the EDL as well as any remaining bulk solute according to the full Poisson-Nernst-Planck (PNP) formulation together with the inhomogeneous Stokes equation, incorporating the Coulombic force density. Further complication arises if the suspended particles are conducting or polarizable, in which case the applied field will "induce" polarization within each particle, which is then shielded by a corresponding electric double layer. 14-17 In a confined system, this double layer formed around the colloid can interact with the EDL at the channel wall, resulting in a highly nonlinear problem. It is emphasized here that in contrast to the more well-known "linear" electroosmotic effect, the "induced-charge" effect is dependent only on the polarizability of the particle or wall and not on its native charge. Thus, in order to focus on the induced contribution, bounding surfaces are generally considered initially uncharged. In fact, it is well known that under the application of AC fields, the linear effects average to zero over a single cycle, while for the case of DC or biased AC forcing, it is possible -at least to first-order -to superimpose the linear and nonlinear solutions.Our ambitious goal in the present study is to develop a general framework for evaluating the phoretic motion (translation and rotation), induced by an arbitrary externally applied electric field, on polarizable (uncharged) nano particles, freely suspended in a nano-channel with conducting walls and filled with an electrolyte. It is important to note that no restrictions are imposed on the geometrical shape of the particle or the enclosing nanopore.The consideration of a conducting wall boundary condition, which results in a background induced electroosmotic flow (EOF) that is nonlinear in the applied field, is the first factor which differentiates this work from the classical approach to other bounded cases, wherein the channel walls are generally considered to be insulating and subject to linear electroosmosis (see, for example, Refs. 5 and 6). Practically, such a boundary condition accounts for geometries in which the active electrodes are embedded in the channel wall. In order to solve this nonlinear ambient electroosmotic flow in a nanochannel, the potential overlap of the EDLs induced at the channel walls must be accounted for in such a way that equilibrium cannot be assumed a priori to occur away (e.g., along the ch...

Pair interactions in induced charge electrophoresis of conducting cylinders

“…particles move due to both the DEP and the ICEP when the applied electric field is nonuniform. Such particle motion is referred to as dipolophoresis (DIP), plenty of studies have been carried out on the DIP and can be referred from [29][30][31].…”

Travelling-Wave Dipolophoresis: Levitation and Electrorotation of Janus Nanoparticles

“…The idea of pumping fluids by means of travelling-wave electro-osmosis, using an array of equally spaced planar or spiral elec-trodes, was proposed in several studies [ 22 , 23 , 24 , 25 ]. The corresponding twDIP axisymmetric problem of freely suspended perfectly conducting spherical NP, placed along the center of a cylindrical pore, was analyzed by Miloh and Boymelgreen [ 26 ]. Recently, a theoretical/numerical twDIP study of free metallic spherical (or cylindrical) NP’s, lying in unbounded space and subject to a sinusoidal travelling wave AC electric forcing, has been also presented by Flores et al [ 27 ].…”

Dipolophoresis and Travelling-Wave Dipolophoresis of Metal Microparticles

“…In particular, we assume that the metal particles are subjected to travelling-wave electric fields and the motion that emerges is named as travelling-wave DIP (twDIP). Travelling-wave dipolophoresis of a polarizable colloid in a pore was considered by Miloh and Boymelgreen [39] in the case of EDL overlapping between particles and walls. Here, we consider thin double layers and the electrokinetic flow induced on a single particle.…”