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.     

Solutal transport in rectangular nanochannels under pressure-driven flow conditions

In this article, we investigate the effect of channel sidewalls on the transport of neutral samples through rectangular conduits under pressure-driven flow and small zeta potential conditions. Our analyses show that while these structures can significantly reduce the streaming potential in small aspect ratio rectangular channels, they introduce a very minor variation in the sample velocity with the extent of Debye layer overlap in the system. Moreover, the increase in sample dispersion due to the channel side-regions has been shown to be nearly independent of the Debye layer thickness and very comparable to that reported under simple pressure-driven flow conditions. Interestingly however, a simple one-dimensional (1D) model that decouples band broadening arising due to diffusional limitations across the depth and width of the rectangular conduit has been shown to capture the predicted dependence of the Taylor–Aris dispersion coefficient on the channel aspect ratio under all operating conditions with less than 3% error.     

Surface wettability effects on flow in rough wall nanochannels

The effect of rough-wall/fluid interaction on flow in nanochannels is investigated by NEMD. Hydrophobic and hydrophilic surfaces are studied for walls with nearly atomic-size rectangular protrusions and cavities. Our NEMD simulations reveal that the number of liquid atoms temporarily trapped in the cavities is affected by the strength of the potential energy inside the cavities. Regions of low potential energy are possible trapping locations. Fluid atom localization is also affected by the hydrophilicity/hydrophobicity of the surface. Potential energy is greater between two successive hydrophilic protrusions, compared to hydrophobic ones. Moreover, groove size and wall wettability are factors that control effective slip length. Surface roughness and wall wettability have to be taken into account in the design of nanofluidic devices.     

Analysis and measurements of mixing in pressure-driven microchannel flow

The mixing phenomena for two fluid streams in pressure-driven rectangular microchannels are analyzed and directly compared with the measurements of mixing intensity for a wide range of aspect ratio (width/depth = 1–20). In the analysis, the three-dimensional transport equation for species mixing was solved using the spectral method in a dimensionless fashion covering a large regime of the normalized downstream distance. The analysis reveals the details of non-uniform mixing process, which originates from the top and bottom walls of the channel and stretches out toward the center of the channel, and its transition to uniformity. Employing different length scales for the non-uniform and uniform mixing regimes, the growth of mixing intensity can be expressed in a simple relationship for various aspect ratios in the large range. The mixing experiments were carried out on silicon- and poly(methyl methacrylate) (PMMA)-based T-type micromixers utilizing fluids of pH indicator (in silicon channel) and fluorescent dye (in PMMA channel) to evaluate the mixing intensity based on flow visualization images. Using conventional microscopes, the experiments demonstrate the mixing intensity as a power law of the stream velocity for all the microfluidic channels tested. The variations of measured mixing intensity with the normalized downstream distance are found in favorable agreement with the numerical simulations. The comparison between the experiments and simulations tells the capabilities and limitations on the use of conventional microscopes to measure the mixing performance.     

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 combined pressure-driven electroosmotic flow through square microchannels

In this paper three-dimensional single-phase liquid flow through microchannels with a square-shaped cross-section driven by simultaneous application of pressure gradient and electroosmotic pumping mechanism is studied. The governing system of equations consists of the electric potential field and flow field equations. The solution procedure involves three steps. First, the net charge distribution on the cross-section of the microchannel is computed by solving two-dimensional Poisson–Boltzmann equation using the finite element method. Then, using the computed fluid’s charge distribution, the magnitude of the resulting body force due to interaction of an external electric field with the charged fluid particles is calculated along the microchannel. In the third step, the flow equations are solved by considering three-dimensional Navier–Stokes equations with an electrokinetic body force. The computations reveal that the flow pattern in the microchannel is significantly different from the parabolic velocity profile of the laminar pressure-driven flow. The effect of the liquid bulk ionic concentration and the external electric field strength on flow patterns through the square-shaped microchannels is also investigated.     

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.     

Multi-scale study of liquid flow in micro/nanochannels: effects of surface wettability and topology

The paper reports parametric study, using a molecular dynamics–continuum hybrid simulation method, of liquid flow in micro/nanochannels with surface nanostructures. The effects of channel height, shape of roughening element, ratio of pitch to length of roughening element and liquid–solid bonding strengths (representing surface wettability) on the velocity and temperature boundary conditions are investigated. The velocity boundary condition is found to shift from significant slip to locking due to the blocking of the surface nanostructure. The blocking appears weak for small pitch ratio and weak liquid–solid bonding. Distorted streamlines, small random eddies and appreciable density oscillations are seen in the vicinity of the wall for small pitch ratio and strong liquid–solid bonding. On the other hand, smooth streamlines and weak density oscillations are seen for large pitch ratio and weak liquid–solid bonding. Results also reveals that: relative slip length, relative Kapitza length and minus pressure gradient vary with channel height and pitch ratio in functions of power law and approximately linear, respectively; relative slip and Kapitza lengths vary with liquid–solid bonding strength as approximately decreasing power functions (except for the strongest case), whereas minus pressure gradient varies with liquid–solid bonding strength as approximately a logarithm-like function. The effect of shape of roughening element is found to be much less significant compared with the other factors studied.     

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.     

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.     

Fabrication of 1D nanochannels on thermoplastic substrates using microchannel compression

We present a new method to fabricate one-dimensional (1D) nanochannels on a thermoplastic substrate. This method has two main steps. First, a mold with microscale features is used to replicate microchannels on a thermoplastic substrate. Second, the fabricated microchannel is compressed to a 1D nanochannel at a temperature above the glass transition temperature (T_g) of the themoplastics. The effects of compression temperature, compression pressure, retaining time and loading rate on microchannel compression have been studied. Results have shown that a 1D nanochannel of 1–30 μm wide and 200–300 nm deep can be readily fabricated by using this method.     

Prediction and analysis of flow behavior of a polymer melt through nanochannels using artificial neural network and statistical methods

A new methodology, namely, artificial neural network (ANN) approach was proposed for modeling and predicting flow behavior of the polyethylene melt through nanochannels of nanoporous alumina templates. Wetting length of the nanochannels was determined to be a function of time, temperature, diameter of nanochannels, and surface properties of the inner wall of the nanochannels. An ANN was designed to forecast the relationship between the length of wetting as output parameter and other aforementioned parameters as input variables. It was demonstrated that the ANN method is capable of modeling this phenomenon with high accuracy. The designed ANN was then employed to obtain the wetting length of the nanochannels for those cases, which were not reported by the wetting experiments. The results were then analyzed statistically to identify the effect of each independent variable, namely, time, temperature, diameter of nanochannels, and surface properties of the inner wall of nanochannels as well as their combinations on the wetting length of the nanochannels. Interesting results were attained and discussed.     

Cross-stream diffusion under pressure-driven flow in microchannels with arbitrary aspect ratios: a phase diagram study using a three-dimensional analytical model

This article presents a three-dimensional analytical model to investigate cross-stream diffusion transport in rectangular microchannels with arbitrary aspect ratios under pressure-driven flow. The Fourier series solution to the three-dimensional convection-diffusion equation is obtained using a double integral transformation method and associated eigensystem calculation. A phase diagram derived from the dimensional analysis is presented to thoroughly interrogate the characteristics in various transport regimes and examine the validity of the model. The analytical model is verified against both experimental and numerical models in terms of the concentration profile, diffusion scaling law, and mixing efficiency with excellent agreement (with <0.5% relative error). Quantitative comparison against other prior analytical models in extensive parameter space is also performed, which demonstrates that the present model accommodates much broader transport regimes with significantly enhanced applicability.     

Analysis of pressure-driven electrokinetic flows in hydrophobic microchannels with slip-dependent zeta potential

The present study is an analysis of pressure-driven electrokinetic flows in hydrophobic microchannels with emphasis on the slip effects under coupling of interfacial electric and fluid slippage phenomena. Commonly used linear model with slip-independent zeta potential and the nonlinear model at limiting (high-K) condition with slip-dependent zeta potential are solved analytically. Then, numerical solutions of the electrokinetic flow model with zeta potential varying with slip length are analyzed. Different from the general notion of “the more hydrophobic the channel wall, the higher the flowrate,” the results with slip-independent and slip-dependent zeta potentials both disclose that flowrate becomes insensitive to the wall hydrophobicity or fluid slippage at sufficiently large slip lengths. Boundary slip not only assists fluid motion but also enhances counter-ions transport in EDL and, thus, results in strong streaming potential as well as electrokinetic retardation. With slip-dependent zeta potential considered, flowrate varies non-monotonically with increasing slip length due to competition of the favorable and adverse effects with more complicated interactions. The influence of the slip on the electrokinetic flow is eventually nullified at large slip lengths for balance of the counter effects, and the flowrate becomes insensitive to further hydrophobicity of the microchannel. The occurrence of maximum, minimum, and insensitivity on the flowrate-slip curves can be premature at a higher zeta potential and/or larger electrokinetic separation distance.     

氯化钾溶液中离子水化的分子动力学模拟

使用Material Studio软件包中的COMPASS力场,采用分子动力学模拟的方法研究了温度为298.15 K时,浓度分别为1.065 mol/L、2.140 mol/L、3.129 mol/L的氯化钾溶液中离子水化的微观结构和动力学性质.发现浓度对离子近程水化的结构有一定的影响,随着溶液浓度的增加O-O径向分布...     

Effect of channel geometry on solute dispersion in pressure-driven microfluidic systems

Pressure-driven transport of fluid and solute samples is often desirable in microfluidic devices, particularly where sufficient electroosmotic flow rates cannot be realized or the use of an electric field is restricted. Unfortunately, this mode of actuation also leads to hydrodynamic dispersion due to the inherent fluid shear in the system. While such dispersivity is known to scale with the square of the Peclet number based on the narrower dimension of the conduit (often the channel depth), the proportionality constant can vary significantly depending on its actual cross section. In this article, we review previous studies to understand the effect of commonly microfabricated channel cross sections on the Taylor–Aris dispersion of solute slugs in simple pressure-driven flow systems. We also analyze some recently proposed optimum designs which can reduce the contribution to this band broadening arising from the presence of the channel sidewalls. Finally, new simulation results have been presented in the last section of this paper which describe solutal spreading due to bowing of microchannels that can occur from stresses developed during their fabrication or operation under high-pressure conditions.     

The effects of wall roughness on the methane flow in nano-channels using non-equilibrium multiscale molecular dynamics simulation

This paper presents a non-equilibrium multiscale molecular dynamics simulation method to investigate the effects of periodic wall surface roughness on the structure and mass transfer of methane fluid through the silicon nano-channels. In order to accurately capture the trajectories and microstructure of methane nano-fluidics, the present modification of OPLS fully atomic model is employed. Meanwhile, we introduce the corresponding coarse-grained model to solve the problem of wall–fluid interaction for methane Poiseuille flow within silicon atomic walls using the classical Lorentz–Berthelot mixing rules. The geometries of the upper wall roughness are modeled by rectangular waves with different amplitudes and wavelengths. The three-dimensional number densities of C (H) atom and kinetic energy distribution plots give a clear observation of the impacts of surface roughness on the localization micro-information of methane fluid. Moreover, the slip length of fluid over rough surface decreases with the increase in amplitude. The diffusion coefficients appear anisotropic, and the radial distribution functions decrease with the increase in the amplitude. These properties should be taken into account in the design of energy-saving emission reduction nano-fluidic devices. All numerical results also indicate that the presented method not only can well solve the issue of wall–fluid interactions, but also could accurately predict the micro-information and dynamic properties of methane Poiseuille flow.