Analysis of capillary filling in nanochannels with electroviscous effects

Capillary filling is the key phenomenon in planar chromatography techniques such as paper chromatography and thin layer chromatography. Recent advances in micro/nanotechnologies allow the fabrication of nanoscale structures that can replace the traditional stationary phases such as paper, silica gel, alumina, or cellulose. Thus, understanding capillary filling in a nanochannel helps to advance the development of planar chromatography based on fabricated nanochannels. This paper reports an analysis of the capillary filling process in a nanochannel with consideration of electroviscous effect. In larger scale channels, where the thickness of electrical double layer (EDL) is much smaller than the characteristic length, the formation of the EDL plays an insignificant role in fluid flow. However, in nanochannels, where the EDL thickness is comparable to the characteristic length, its formation contributes to the increase in apparent viscosity of the flow. The results show that the filling process follows the Washburn’s equation, where the filled column is proportional to the square root of time, but with a higher apparent viscosity. It is shown that the electroviscous effect is most significant if the ratio between the channel height (h) and the Debye length (κ ⁻¹) reaches an optimum value (i.e. κh ≈ 4). The apparent viscosity is higher with higher zeta potential and lower ion mobility.     

Molecular dynamics simulation of fluid containing gas in hydrophilic rough wall nanochannels

This study performed the molecular dynamic simulations to investigate the boundary behavior of liquid water with entrapped gas bubbles over various hydrophilic roughened substrates. A “liquid–gas–vapor coexistence setup” was employed to maintain a constant thermodynamic state during individual equilibrium simulations and corresponding non-equilibrium Poiseuille flow cases. The two roughened substrates (Si(100) and graphite) adopted in this study present similar contact angles and slip length with gas-free fluid. By considering the effects of argon molecules at the interface, we demonstrated that the boundary slip behavior differed dramatically between these two rough wall channels. This divergence can be attributed to differences in the morphology of argon bubble at the interface due to discrepancies in the atomic arrangement and wall–fluid interaction energy. Furthermore, the density of gas at the interface had a significant impact on the effective slip length of the roughened graphite substrate, whereas shear rate \(\dot{\gamma }\) presented no noticeable influence. On the roughened Si(100) surface, the morphology of the argon bubbles exhibited far higher meniscus curvature and unstable properties under hydrodynamic effects. Thus, this substrate exhibited no slip to slight negative slip and no remarkable influence from either the density of gas at the interface or shear rate. In the present study, we demonstrate that the morphology and behavior of interfacial gas bubbles are influenced by the parameters of wall–fluid interaction as well as the atomic arrangement of the substrate. Our results related to nanochannel flow reveal that different surfaces, such as Si(100) and graphite, may possess similar intrinsic wettability; however, properties of the interfacial gas bubbles can lead to noticeable changes in interfacial characteristics resulting in various degrees of boundary slippage.     

Capillary filling with the effect of pneumatic pressure of trapped air

This article presents an investigation into the effects of pneumatic pressure of trapped air on the dynamics of capillary filling. Controlled experiments were carried out in horizontal closed-end capillaries with diameters of 200–700 μm. Glycerol–DI water mixture solutions having viscosities ranging from 8 to 80 mPa s were used as the filling liquids. The pneumatic air backpressure is built up as a result of the air compressed at the closed end of the capillary. A model is presented based on the conventional theory of capillary filling (i.e., Washburn’s equation) with consideration of the effect of air backpressure force on the advancing meniscus. The molecular kinetics theory of Blake and De Coninck’s model (Adv Colloid Interface Sci 96:21–36, 2002) is also incorporated in the model to account for the dependence of dynamic contact angle on wetting velocity. The model predictions agree reasonably well with the experimental data. It is observed that due to the presence of air backpressure, the smaller the capillary diameter, the longer the length that the liquid fills the capillary, regardless of the liquid viscosity. It is also shown that the increased pneumatic air backpressure reduces the equilibrium contact angle (θ ⁰). A relation is then proposed among liquid penetration, capillary length and radius, and contact angle. In addition, a dimensionless analysis is performed on experimental data, and the power law dependence of dimensionless meniscus position on dimensionless time is obtained.     

Application of continuum mechanics to fluid flow in nanochannels

A fundamental understanding of the transport phenomena in nanofluidic channels is critical for systematic design and precise control of such miniaturized devices towards the integration and automation of Lab-on-a-chip devices. The goal of this study is to develop a theoretical model of electroosmotic flow in nano channels to gain a better understanding of transport phenomena in nanofluidic channels. 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 of an electrolyte solution in nano channels. Correct boundary conditions for the potential field at the center of the nanochannel and the concentration field at the wall of the channel are developed and applied to this model. It is found that the traditional plug-like velocity profile is distorted in the center of the channel due to the presence of net charges in this region opposite to that in the electrical double layer region. The developed model predicted a trend similar to that observed in experiments reported in the literature for the area-average velocity versus the ratio of Debye length to the channel height.     

Electrokinetic motion of single nanoparticles in single PDMS nanochannels

Electrokinetic motion of single nanoparticles in single nanochannels was studied systematically by image tracking method. A novel method to fabricate PDMS-glass micro/nanochannel chips with single nanochannels was presented. The effects of ionic concentration of the buffer solution, particle-to-channel size ratio and electric field on the electrokinetic velocity of fluorescent nanoparticles were studied. The experimental results show that the apparent velocity of nanoparticles in single nanochannels increases with the ionic concentration when the ionic concentration is low and decreases with the ionic concentration when the concentration is high. The apparent velocity decreases with the particle-to-channel size ratio (a/b). Under the condition of low electric fields, nanoparticles can hardly move in single nanochannels with a large particle-to-channel size ratio. Generally, the apparent velocity increases with the applied electric field linearly. The experimental study presented in this article is valuable for future research and applications of transport and manipulation of nanoparticles in nanofluidic devices, such as separation of charged nanoparticles and DNA molecules.     

Mesoscopic simulations of electroosmotic flow and electrophoresis in nanochannels

We review recent dissipative particle dynamics (DPD) simulations of electrolyte flow in nanochannels. A method is presented by which the slip length δB at the channel boundaries can be tuned systematically from negative to infinity by introducing suitably adjusted wall-fluid friction forces. Using this method, we study electroosmotic flow (EOF) in nanochannels for varying surface slip conditions and fluids of different ionic strength. Analytic expressions for the flow profiles are derived from the Stokes equation, which are in good agreement with the numerical results. Finally, we investigate the influence of EOF on the effective mobility of polyelectrolytes in nanochannels. The relevant quantity characterizing the effect of slippage is found to be the dimensionless quantity κδB, where 1/κ is an effective electrostatic screening length at the channel boundaries.     

Molecular dynamics-based prediction of boundary slip of fluids in nanochannels

Computational modeling and simulation can provide an effective predictive capability for flow properties of the confined fluids in micro/nanoscales. In this paper, considering the boundary slip at the fluid–solid interface, the motion property of fluids confined in parallel-plate nanochannels are investigated to couple the atomistic regime to continuum. The corrected second-order slip boundary condition is used to solve the Navier–Stokes equations for confined fluids. Molecular dynamics simulations for Poiseuille flows are performed to study the influences of the strength of the solid–fluid coupling, the fluid temperature, and the density of the solid wall on the velocity slip at the fluid boundary. For weak solid–fluid coupling strength, high temperature of the confined fluid and high density of the solid wall, the large velocity slip at the fluid boundary can be obviously observed. The effectiveness of the corrected second-order slip boundary condition is demonstrated by comparing the velocity profiles of Poiseuille flows from MD simulations with that from continuum.     

Fully explicit dissipative particle dynamics simulation of electroosmotic flow in nanochannels

A fully explicit mesoscale simulation of electroosmotic flow (EOF) in nanochannels is presented by an extended dissipative particle dynamics (DPD) method. To avoid formation of ionic pairs through interacting soft-core charges, a Slater-type smearing distribution borrowed from quantum mechanics is utilized to surround each soft DPD ion with a charge cloud. To account for reduced periodicity normal to the walls direction, a corrected version of 3D Ewald sum is implemented in which a dipole moment term is deducted from energy and force terms of non-frozen charges. Simulation box is then elongated normal to walls to dampen spurious interslab interactions by adding vacuum gaps between periodic images. These measures together with the established unit conversions guarantee perfect match to molecular dynamics results. The transition of EOF velocity profile from parabolic (equivalent to overlap of electric double layers) to plug-like shapes is studied across the changing electric field between 0.06 and 0.41 [V/nm], and varying salt concentration from 0.26 to 2.0 [M]. It is found that 1.25 [V] increase in the driving voltage can potentially enhance the electroosmotic flow rate by 8–11 times in the range of ionic concentrations studied. The range of surface zeta potential calculated as \( 27 < \zeta < 52 \) [mV] in the linear response regime, as identified to occur for 0.24 ≤ E [V/nm], agrees reasonably with numerical and experimental studies.     

Modeling of ferrofluid magnetic actuation with dynamic magnetic fields in small channels

One of the most important and promising research areas in biomedical and micropumping applications is magnetic actuation of ferrofluids with dynamic magnetic fields. For ensuring the use of ferrofluids in various applications in engineering fields, their flows generated by magnetic fields should be extensively investigated and simulated. In this study, simulations of ferrofluid actuation with dynamic magnetic fields were performed by modeling it using the COMSOL Multiphysics software, and iron oxide nanoparticle-based ferrofluids at different angles of rotating magnets were considered to provide insight into ferrofluid flow in small channels. Ferrofluid flows were modeled at different magnetic flux densities provided by rotating magnets, and velocity profiles inside the channel were analyzed. It was shown that ferrofluid actuation can be considered as a futuristic micropumping alternative, simulation results matched well with the experimental results of previous work, and the established model could serve as a tool to analyze ferrofluid flows generated by dynamic magnetic fields. The results of the model show that flow rates up to 100 µl/s can be reached at a rotation angle of 30° by using dynamic magnetic fields. Various applications including biomedical applications might be envisaged.     

Experimental study of the separation behavior of nanoparticles in micro- and nanochannels

In this article, we investigate the effects of pH, ionic strength, and channel height on the mobility and diffusivity of charged spherical particles within planar microfluidic channels. Specifically, we report results of a broad experimental study on the transport and separation behavior of 50 and 100 nm spherical carboxylated polystyrene nanoparticles, confined in 20 μm, 1 μm, and 250 nm deep fluidic channels. We find that pH, ionic strength, and channel height have coupled impacts on mobility changes. In particular, we show that, depending on pH, the dependence of particle mobility on channel size can have opposing behavior. In addition, we also show that at the nanoscale, at lower ionic strengths, there is a substantial increase in mobility, due to enhanced electric fields within the nanochannels. These effects are important to understand in order to avoid potential downfalls in terms of separation efficiency as well as design for better tuning of separation performance in micro- and nanochannels. Finally, we propose a method to estimate the effective zeta potential of spherical particles from measured electrophoretic mobility data. This could prove useful in characterizing a heterogeneous collection of particles having a distribution over a range of values of the zeta potential.     

Self-assembly and novel planetary motion of ferrofluid drops in a rotational magnetic field

We experimentally investigate the motion of a ferrodrop array in a rotating magnetic field. Magnetized and driven by the external field, the ferrodrops are stretched and self-aligned to form a drop array along the field orientation. An interesting planet-like dual rotation, including local self-spins of individual drops and a global revolution of the drop array, is newly identified. While the drops spin nearly synchronized with the external field, the revolution always lags behind the field and appears a forth and back movement. Prominence of the net revolutionary movement depends on the strength and uniformity of the overall field as well as the number of drops containing in the array. In general, more uniform and stronger rotating field leads to a more prominent global revolution. Phenomenon of such planetary motion can be applied to mix two fluids more effectively than self-spin drops.     

Hydrodynamic dispersion of neutral solutes in nanochannels: the effect of streaming potential

An analytical model is developed to account for the effect of streaming potential on the hydrodynamic dispersion of neutral solutes in pressure-driven flow. The pressure-driven flow and the resulting electroosmotic backflow exhibit coupled dispersion effects in nanoscale channels where the hydraulic diameter is on the order of the electrical double layer thickness. An effective diffusion coefficient for this regime is derived. The influence of streaming potential on hydrodynamic dispersion is found to be mainly dependent on an electrokinetic parameter, previously termed the “figure of merit”. Results indicate that streaming potential decreases the effective diffusion coefficient of the solute, while increasing the dispersion coefficient as traditionally defined. This discrepancy arises from the additional effect of streaming potential on average solute velocity, and discussed herein.     

Ion-enrichment and ion-depletion of nanochannels based on electrochemical potential in a micro-nanofluidic chip

In this paper, we present a new approach for ion-enrichment and ion-depletion effect (IEID) in micro-nanofluidic chips without external power source. The method utilizes different reducibility of various electrodes in the weak oxidizing solution to generate the electrochemical potential and then induce IEID at a micro-nano junction. The results show that the average gray values of the micro-nano junction based on Al–Pt, Fe–Pt, and Cu–Pt electrodes increase from 14.7 to 40.2, 27.1, 15.0 after 20 s, and electric currents for Al–Pt, Fe–Pt, and Cu–Pt electrodes are 5.0, 2.9 and 0 nA respectively. Metal cations generating from oxidation–reduction reaction and electroosmotic convection flow are evaluated and their influences to IEID can be neglected in this case. The IEID method based on the electrochemical potential is power-free and weak flow convective that will be beneficial to the integrity of micro-nanofluidic chips and stability of IEID.     

A method to generate pressure gradients for molecular simulation of pressure-driven flows in nanochannels

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.     

Analysis of the electroviscous effects on pressure-driven flow in nanochannels using effective ionic concentrations

The selection of proper boundary conditions is one of the most critical issues when predicting electroviscous effects. Despite numerous studies of the electroviscous effects in micro- and nanochannels with overlapped electric double layers, the boundary conditions for ionic concentrations remain controversial. In this study, the analytical model employing the effective ionic concentrations suitable for determining boundary conditions at the wall is proposed for better predictions of the electroviscous effects in an electrically charged channel with highly overlapped electric double layers. The introduction of the effective ionic concentration is validated using previous numerical results obtained from the lattice Poisson–Boltzmann method. Additionally, numerical results based on the proposed model for streaming conductance as a function of the KCl concentration (c ₀) are shown to be in close agreement with the experimental data. The proposed model is not only highly accurate compared with the existing analytical model, but also applicable to a wider range than the self-consistent NP model. Out of the numerical works in this study, a new parameter (ζ/ζ ₀)/(κH) ^a is introduced to quantify the effect of the electroviscosity, which is the dimensionless zeta potential divided by the dimensionless Debye–Hückel parameter, which was commonly employed in previous works. This study shows that the electroviscosity can be expressed as a function of (ζ/ζ ₀)/(κH) ^a only and the electroviscous effects can be safely neglected when (ζ/ζ ₀)/(κH)^1/4 is less than 20 in silica nanofluidic channels.     

Magnetic concentration of particles and cells in ferrofluid flow through a straight microchannel using attracting magnets

Concentrating particles to a detectable level is often necessary in many applications. Although magnetic force has long been used to enrich magnetic (or magnetically tagged) particles in suspensions, magnetic concentration of diamagnetic particles is relatively new and little reported. We demonstrate in this work a simple magnetic technique to concentrate polystyrene particles and live yeast cells in ferrofluid flow through a straight rectangular microchannel using negative magnetophoresis. The magnetic field gradient is created by two attracting permanent magnets that are placed on the top and bottom of the planar microfluidic device and held in position by their natural attractive force. The magnet–magnet distance is mainly controlled by the thickness of the device substrate and can be made small, allowing for the use of a dilute ferrofluid in the developed magnetic concentration technique. This advantage not only enables a magnetic/fluorescent label-free handling of diamagnetic particles, but also renders such handling biocompatible.