Field-Induced Hydration Shell Reorganization Enables Electro-osmotic Flow in Nanochannels.

Molecular simulations of electroosmotic flows in rough nanochannels

Effects of ion size, ion valence and pH of electrolyte solutions on EOF velocity in single nanochannels

Chapter 4 - Single-Phase Electrokinetic Flow in Microchannels

Hydrophobic surfaces with large slip lengths have the potential to enhance electro-osmotic flows. Existing theories of electroosmosis in hydrophobic channels postulate immobile surface charges and/or make a number of simplifying assumptions by considering mostly weakly charged surfaces and thin diffuse layers compared to channel dimension. In this paper, we extend prior models by focusing on planar and cylindrical nanochannels. Our theory accounts for a hydrodynamic slip and a mobility of surface charges, and is valid not only on the scale of the nanochannel with thin diffuse layers, but also on the scale of the overlapping diffuse layer. The model is simple enough to allow us to derive analytical approximations for the electro-osmotic velocities even when the surface potential and charge density are quite large. We also present numerical solutions to validate the analysis and illustrate the variation of electro-osmotic velocities in response to changes in the channel size, potential, surface charge and its mobility, hydrodynamic slip length, and salt concentration. Our results are directly relevant for carbon nanotubes, graphene nanochannels, and conventional nanoporous membranes.

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.

One of the difficulties in molecular simulation of pressure-driven fluid flow in nanochannels is to find an appropriate pressure control method. When periodic boundary conditions (PBCs) are applied, a gravity-like field has been widely used to replace actual pressure gradients. The gravity-fed method is not only artificial, but not adequate for studying properties of fluid systems which are essentially inhomogeneous in the flow direction. In this paper, a method is proposed which can generate any desired pressure difference to drive the fluid flow by attaching a “pump” to the nanofluidic system, while the model is still compatible with PBCs. The molecular dynamics model based on the proposed method is applied to incompressible flows in smooth nanochannels, and the predicted velocity profiles are identical to those by the gravity-fed method, as expected. For compressible flows, the proposed model successfully predicts the changes of fluid density and velocity profile in the flow direction, while the gravity-fed method can only predict constant fluid properties. For fluid flows in nanochannels with a variable cross-sectional area, the proposed model predicts higher mass flow rates as compared to the gravity-fed method and possible reasons for the difference are discussed.

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.

Development of nano-devices for various applications has drawn great attention recently driven by the need of miniaturizing the devices for the integration and automation of Biochips or Lab-on-a-Chip devices. Fundamental understanding of transport phenomena in nanofluidic channels is critical for systematic design and precise control of such devices. The goal of this study is to develop a theoretical model to study electroosmotic flow in nanochannels. Instead of using the Boltzmann distribution, the conservation condition of ion number and the Nernst equation are used in this new model to find the ionic concentration field in the nanochannels. A correct boundary condition for the concentration field at the wall of the channel is developed and the symmetry condition of the potential field at the center of the nanochannel is applied to this model. The ionic concentration field, electrical potential field and flow field are obtained by numerically solving this model. Comparisons of area-average velocity between the numerical simulations and experimental results reported in literature are provided.

This paper presents a theoretical model for the electro-osmotic flow (EOF) of semi-dilute polyelectrolyte (PE) solutions in nanochannels. We use mean-field theories to describe the properties of electric double layer and viscosity of PE solutions that are prerequisites for constructing the EOF model. The EOF model is validated via a good match to the existing experimental results. Based on the validated EOF model, we conduct a comprehensive analysis of EOF of semi-dilute PE solutions in nanochannels. First, we observe considerable EOF of PE solutions in the uncharged nanochannels, which is in stark contrast to EOF of simple electrolyte solutions. The analyses show that the EOF of PE solutions in uncharged nanochannels is triggered by the external electric field acting on the near-wall non-electroneutral regions resulting from the confinement-induced inhomogeneous distribution of PE monomers. Although the solutions are electroneutral as a whole, the presence of local non-electroneutral regions and the mismatch between non-electroneutral regions and high-viscosity regions lead to the net EOF in uncharged nanochannels. Furthermore, we reveal that the EOF mobility $\mu _{{eof}}$ in uncharged nanochannels exhibits a scaling law $\mu _{{eof}} \propto a^{-0.44}$ (wherein $a$ denotes monomer Kuhn length) and is inversely proportional to the PE chain length, while it decreases nonlinearly with the charge fraction of the PE chains. Moreover, the EOF mobility reaches its maximum at specific bulk monomer concentration, and increases with the nanochannel height before converging to that under no confinement. Second, we analyse the EOF of PE solutions in nanochannels with various wall effects, such as surface charge density, slip length and adsorption length. When the surface charge is absent, the adsorption length significantly influences the direction and magnitude of the EOF, whereas the slip length has no effect. When the wall becomes increasingly charged, the influence of adsorption length on EOF gradually diminishes, while the importance of the slip length progressively intensifies and the EOF is highly influenced by the co-action of various wall effects in a complicated manner. When the surface wall is oppositely charged to polymer monomers, the EOF mobility varies nonlinearly with the surface charge density, while a zero net flow of EOF followed by a direction reversal is discovered when the wall is likely charged to polymer monomers.

Electroosmotic Flow in a Capillary Annulus with High Zeta Potentials

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.

We are reporting electroosmotic flows in nanochannels having different surface roughness. Molecular dynamics simulation technique has been applied to understand microscopic or molecular aspects of solid-liquid interactions. The surface roughness in this study was modeled as a succession of expanding and contracting steps along the flow direction, determined by the electric field direction. Water and sodium ion density profiles for the smooth wall show strong layering of water molecules near the solid wall. For rough walls, the density profiles are very similar for all cases except where the steps are located. We observed that this disturbance grows with the amplitude of the roughness and decreases with the period of the roughness. To further investigate strong layering of the water molecules, the net electric dipole moment was computed for the smooth and rough walls. It shows ordering of water molecules near the wall. The rough wall result show water molecules are ordered more in the expanded region. The velocity profiles and the flow rate were calculated for all cases. From these, electric double layers are found to overlap. The maximum velocities and the flow rate decreased for the lower period and the higher amplitude of surface roughness.

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.

Manipulating water flow in nanochannels is crucial for advancing nanotechnology and nanofluidic. Using molecular dynamics simulation, we demonstrate that both the direction and rate of flow in a uniform nanochannel can be precisely tuned by varying the incident direction, field intensity, and irradiation range of a specific-frequency biased terahertz pulse stimulation, without requiring any external pressure gradients. The resonant coupling between the irradiated water molecules and terahertz pulses is revealed to create pressure gradients that determine the direction of water flow and control the flow rate. This effect is attributed to the asymmetric absorption of terahertz radiation by water molecules within the nanochannel, which generates a controllable energy flow. These insights provide a glorious inspiration for designing advanced nanofluidic devices that require facile and stable energy flow control, avoiding physical intrusion.

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.