Electroosmotic Flow in a Capillary Annulus with High Zeta Potentials

Velocity slip in electroosmotic flows (EOF) is investigated using an analytical solution of Poisson–Boltzmann and Stokes (PB-S) equations with slip correction, and the results are compared with the predictions from molecular dynamics (MD) simulations. Particularly, EOFs of NaCl solution in silicon nanochannels are simulated, and channel dimensions are picked to exhibit plug flow behavior in the bulk region. Electrochemical conditions are specified within the validity region of PB theory to avoid charge inversion and flow reversal effects. The analytical model shows normalization of the slip length (an interfacial property) with the Debye length determined by the ionic concentration, implying that the slip enhancement in EOFs is independent of the channel height. MD results are compared with the analytical solution using the apparent viscosity and slip lengths determined by force-driven flow simulations in charged silicon nanochannels. Onset of slip velocity within the electrical double layer and its effects on EOF are investigated as a function of the liquid–wall interaction strength. Good agreements between the analytical solutions and MD results validate PB-S equations in nanochannels as small as 3.5 nm. Results validate that slip enhancement in EOFs is independent of the channel height, which constitutes a theoretical basis for the slip-length measurements on hydrophobic dielectric surfaces using EOFs.

Chapter 4 - Single-Phase Electrokinetic Flow in Microchannels

Joule heating effect on electroosmotic flow and mass species transport in a microcapillary

In the present work, we realize a study about the influence of viscoelectric effect on the electroosmotic flow of Newtonian fluids in nanochannels formed by two parallel flat plates. In the problem, the channel walls have heterogeneous zeta potentials which follow a sinusoidal distribution; moreover, viscoelectric effects appear into the electric double layers when high zeta potentials are considered at the channel walls, modifying the fluid viscosity and the fluid velocity. To find the solution of flow field, the modified Poisson-Boltzmann, mass conservation and momentum governing equations, are solved numerically. In the results, combined effects from the zeta potential heterogeneities and viscosity changes yields different kind of flow recirculations controlled by the dephasing angle, amplitude and number of waves of the heterogeneities at the walls. The viscoelectric effect produces a decrease in the magnitude of velocity profiles and volumetric flow rate when the high zeta potentials are magnified. Additionally, the heterogeneous zeta potentials at the walls generate an induced pressure on the flow. This investigation extend the knowledge of electroosmotic flows under field effects for future mixing applications.

This study investigates characteristics of the mass transport for Maxwell fluids driven by a time‐periodic oscillatory electroosmotic flow (EOF) in annular microchannels under high zeta potential conditions. A finite difference method is employed to solve the nonlinear Poisson–Boltzmann equation, the Maxwell fluid momentum equation, the convection–diffusion equation, and the time‐ and space‐averaged mass transport rates are obtained by using the composite trapezoidal rules, and the reliability of the present numerical results for the low zeta potential is verified by comparing the analytical approximate results obtained by using the Debye–Hückel (D–H) linear approximation. The effects of key dimensionless parameters—including electrokinetic width, angular Reynolds number, wall potential ratio, relaxation time, and the inner‐to‐outer radius ratio—on flow velocity, solute concentration distribution, and average mass transport performance are systematically analyzed. The results show that: (1) a high zeta potential enhances velocity and concentration, while suppressing the spatio‐temporal average mass transport rate; (2) the elastic effects of Maxwell fluids, characterized by relaxation time, significantly modulate the structure of velocity and concentration fields under periodic electric forcing, thereby enhancing local mixing or enabling spatially selective separation; (3) at low Reynolds number, the flow remains relatively uniform, facilitating species separation, whereas at higher Reynolds number, amplified elastic responses near the walls lead to increased nonuniformity in velocity and concentration distributions, promoting mixing; (4) asymmetric zeta potentials induce elastic responses in the core region, further intensifying concentration nonuniformity and enabling species separation under specific parameter combinations; and (5) geometric factors such inner‐to‐outer radius ratio and electrokinetic width significantly affect radial gradient intensity, resulting in switching phenomena between fast‐ and slow‐diffusing species.

Electro-osmotic flow is the motion of fluid driven by an applied electric field, for which an electric double layer near a charged surface is deemed essential. Here, we find that electro-osmotic flow can occur in electrically neutral nanochannels in the absence of definable electric double layers through extensive molecular dynamics simulations. An applied electric field is shown to cause an intrinsic channel selectivity between cations and anions, by reorienting the hydration shells of these confined ions. The ion selectivity then results in a net charge density in the channel that induces the unconventional electro-osmotic flow. The flow direction is amenable to manipulation by the field strength and the channel size, which will inform ongoing efforts to develop highly integrated nanofluidic systems capable of complex flow control.

Purpose The characteristics of fluid motions in micro-channel are strong fluid-wall surface interactions, high surface to volume ratio, extremely low Reynolds number laminar flow, surface roughness and wall surface or zeta potential. Due to zeta potential, an electrical double layer (EDL) is formed in the vicinity of the wall surface, namely, the stern layer (layer of immobile ions) and diffuse layer (layer of mobile ions). Hence, its competent designs demand more efficient micro-scale mixing mechanisms. This paper aims to therefore carry out numerical investigations of electro osmotic flow and mixing in a constricted microchannel by modifying the existing immersed boundary method. Design/methodology/approach The numerical solution of electro-osmotic flow is obtained by linking Navier–Stokes equation with Poisson and Nernst–Planck equation for electric field and transportation of ion, respectively. Fluids with different concentrations enter the microchannel and its mixing along its way is simulated by solving the governing equation specified for the concentration field. Both the electro-osmotic effects and channel constriction constitute a hybrid mixing technique, a combination of passive and active methods. In microchannels, the chief factors affecting the mixing efficiency were studied efficiently from results obtained numerically. Findings The results indicate that the mixing efficiency is influenced with a change in zeta potential (ζ), number of triangular obstacles, EDL thickness (λ). Mixing efficiency decreases with an increment in external electric field strength (Ex), Peclet number (Pe) and Reynolds number (Re). Mixing efficiency is increased from 28.2 to 50.2% with an increase in the number of triangular obstacles from 1 to 5. As the value of Re and Pe is decreased, the overall percentage increase in the mixing efficiency is 56.4% for the case of a mixing micro-channel constricted with five triangular obstacles. It is also vivid that as the EDL overlaps in the micro-channel, the mixing efficiency is 52.7% for the given zeta potential, Re and Pe values. The findings of this study may be useful in biomedical, biotechnological, drug delivery applications, cooling of microchips and deoxyribonucleic acid hybridization. Originality/value The process of mixing in microchannels is widely studied due to its application in various microfluidic devices like micro electromechanical systems and lab-on-a-chip devices. Hence, its competent designs demand more efficient micro-scale mixing mechanisms. The present study carries out numerical investigations by modifying the existing immersed boundary method, on pressure-driven electro osmotic flow and mixing in a constricted microchannel using the varied number of triangular obstacles by using a modified immersed boundary method. In microchannels, the theory of EDL combined with pressure-driven flow elucidates the electro-osmotic flow.

Characterizing the mainly incompressible and laminar flows of aqueous electrolyte solutions through channels with an overall dimension of O(1–100 μm) is of interest in a variety of microfluidics applications. Solid surfaces such as the channel wall become (usually negatively) charged due to direct ionization or dissociation of surface groups, where the charge is typically characterized by the wall zeta-potential ζw. The surface in turn attracts mobile counterions from the fluid to form a (usually positively) charged screening, or electric double, layer (EDL). An external electric field can therefore be used to “pump” fluids through microfluidic Labs-on-a-Chip (LOC) by driving the charged fluid in the EDL. The resulting electroosmotic flow (EOF) is uniform outside the EDL, which has a thickness less than 50 nm in most cases. This uniform flow results in a more favorable scaling of the volume flowrate with channel diameter for microchannels, and also has less convective dispersion than shear flows. Electroosmotic flow is, however, very sensitive to changes in ζw. Various studies have shown, for example, that adding multivalent counterions to a monovalent electrolyte solution can greatly change ζw through both electrostatic and chemical interactions, even leading to “charge inversion” where the zeta-potential changes its sign. Evanescent-wave particle velocimetry, which tracks the motion of colloidal fluorescent tracer particles illuminated by evanescent waves within ∼400 nm of the wall, was therefore used to study the flow of various aqueous monovalent electrolyte solutions with small amounts of divalent cations such as Mg++ driven by an electric field through channels with a minimum dimension of ∼30 μm. The technique measures both the velocity components parallel to the wall and the steady-state distribution of these near-wall tracers. In these experiments, the tracers are convected parallel to the wall by both the EOF and directly by the applied electric field via electrophoresis because the surfaces of the particles also become negatively charged when suspended in the electrolyte solution. The electrophoretic contribution to the measured particle velocity was determined by measuring the particle zeta-potential with light scattering, and subtracted from the particle velocity to determine the actual EOF velocity.

A micron-resolution particle image velocimetry (PIV) system has been developed to spatially and temporally resolve electroosmotic flow fields within microfluidic bioanalytical devices. A second diagnostic technique, particle tracking velocimetry (PTV) has been used to determine the distribution of electrophoretic mobilities of seed particles and thereby make the PIV measurements quantitative. This second particle tracking technique has been used to determine probability distribution functions of the seed particles. Results from simulations of electric fields yield local electric field strengths in the geometries of interest. The measured mean mobility of the seed particles (obtained from PTV measurements) is then multiplied by the local electric field vector to obtain the electrophoretic velocity. The variance on the particle mobility measurement influences the errors introduced in the electroosmotic flow measurements. After total particle velocities are measured within a microfluidic system of interest, the seed particle electrophoretic velocities are subtracted from the PIV total velocity data to obtain electroosmotic flow field velocities. Ensemble-averaged velocity field measurements for electroosmotic flow at the intersection of a cross-channel are presented.

It is known that the interface current exists besides the bulk current in the channel of the electroosmotic flow (EOF). Interface current in electric double layer (EDL) is a main driving force of the EOF. However, due to its small size and the various geometrical constraint to access EDL, it is difficult to measure the interface current experimentally. In this study, a specially designed doughnut channel is utilized to measure the interface current. Two parallel doughnut-shaped glass plates were used for the doughnut channel. It is possible to adjust the height of doughnut channel continuously. Experimental studies were carried out on fully developed steady EOF in this channel. The characteristics of the interface current were examined. It is the first time that the interface current in a EOF was measured directly by experimental method. The structure of the EOF or EDL was considered in relation to the interface current.

Solid-state nanopores constitute a versatile platform for study of ion transport in nanoconfinement. The electrical double layer (EDL) plays a vital role in such nanoconfinements, but effects of induced surface charge on the EDL in the presence of an external transmembrane electric field are yet to be characterized. Here, the formation of induced charge on the nanopore sidewall surface and its effects, via modulation of the EDL and electroosmotic flow, on the ionic current are elucidated using a novel experimental setup with solid-state truncated-pyramidal nanopores. This study consists of three complementary approaches, i.e., an analytical model for induced surface charge, numerical simulation of induced surface charge, electroosmotic flow, and ionic current, and experimental validation with respect to the ionic current. The induced surface charge is generated by polarization in the dielectric membrane as a response to the applied electric field. This charge generation results in a nonuniform density of surface charge along the nanopore sidewall. It further causes ions in the electrolyte to redistribute, leading to a massive accumulation of single-polarity ions in the EDL and their counterions near the smaller opening of the nanopore. It also alters electrohydrodynamic properties in the nanopore, giving rise to the formation of electroosmotic vortexes in the vicinity of the smaller opening of the nanopore. Finally, the pattern of the electroosmotic flow can significantly influence the transport properties of the nanopore.

Thickness-averaged model for numerical simulation of electroosmotic flow in three-dimensional microfluidic chips

Electro-osmotically driven MHD flow and heat transfer in micro-channel

Flow behavior of time periodic electro-osmosis in a cylindrical microannulus is investigated based on a linearized Poisson–Boltzmann equation and Navier–Stokes equation. An analytical solution of electro-osmotic flow (EOF) velocity distribution as functions of radial distance, periodic time and relevant parameters is derived. By numerical computations, the influences of the electrokinetic width K denoting the characteristic scale of the microannulus to Debye length, the wall zeta potential ratio β denoting the inner cylinder to the outer cylinder, the ratio α denoting of the annular inner radius to outer radius and the periodical EOF electric oscillating Reynolds number Re on velocity profiles are presented. Results show that when electric oscillating Reynolds number is low and the electrokinetic width K is large, the electro-osmotic velocity amplitude shows a square pluglike profile. When the Reynolds number is high, the driving effect of the electric force decreases immediately away from the two cylindrical walls. The parameter β affects the dimension and direction of the EOF velocity profiles within the electric double layer near the two cylindrical walls in a microannulus. Two limiting cases are discussed, i.e., the time periodical EOF approximately in parallel plate microchannel and circular microtube. These results are agreed qualitatively with those obtained by previously related researches. Furthermore, the instantaneous EOF velocity profiles within a period of a time cycle for different applied electric frequency f, electrokinetic width K, and zeta potential ratio β are illustrated.

We perform a systematic study on the modulation of electroosmotic flow (EOF), tuning the selectivity using electrolyte ions and hydrodynamic dispersion of the solute band across the soft nanochannel. The supporting walls of the channel are considered to be hydrophobic and bear non-zero surface charge. For such a channel, the inner side of the supporting rigid walls of the channel are coated with a soft polyelectrolyte layer (PEL). The inhomogeneous distribution of monomers and accompanying volume charge within the PEL is modelled via soft-step function. The dielectric permittivity of the PEL and electrolyte solution are in general different, which in turn leads to the ion partitioning effect. The impact of ion steric effects due to finite sized ions is further accounted through the modified ion activity coefficient. To model the EOF modulation considering the combined impact of the ion steric and ion partitioning effects as well as inhomogeneous distribution of monomers across the PEL, we adopt the modified Poisson-Boltzmann equation as the governing equation for electrostatic potential. The Debye-Bueche model is adopted to study the flow field across the PEL and the Stokes equation governs the EOF outside the PEL. In order to study the impact of the modulated EOF field on the dispersion of uncharged solution, we adopt three different models, i.e., a general 2D convective-diffusion model as well as cross-sectional averaged dispersion models due to Gill and late-time Taylor and Aris. Going beyond the widely employed Debye-Hückel approximation and uniform distribution of the monomer as well as accompanying volume charge, we find the results for the electric double layer (EDL) potential, EOF field and averaged throughput, by tuning the ion selectivity, etc., which is sufficient to analyze the transport of ionized liquid across the channel. The numerical results are supplemented with analytical results for the EDL potential as well as the EOF field under various limiting situations. Besides, we have further shown the impact of the modulated EOF field on the solute dispersion process. We have presented results that highlight the impact of parameters related to EOF field modulation, on solute dispersion governed by a convective-diffusive process, as well as obtaining the results for an effective dispersion coefficient. The dispersion models under the modulated EOF field adopted in the present study can thus be applied to study the dispersion process in engineered microdevices.