A Particle Method for the KdV Equation

We extend the dispersion-velocity particle method that we recently introduced to advection models in which the velocity does not depend linearly on the solution or its derivatives. An example is the Korteweg de Vries (KdV) equation for which we derive a particle method and demonstrate numerically how it captures soliton–soliton interactions.     

Electrophoresis of a finite rod along the axis of a long cylindrical microchannel filled with Carreau fluids

The boundary effect on the electrophoretic behavior of a particle in a non-Newtonian fluid is studied by considering the electrophoresis of a finite rod along the axis of a cylindrical microchannel filled with shear-thinning Carreau fluids, which include both Newtonian and power-law fluids as special cases. Under the conditions of low surface potential and weak applied electric field, the influences of the radius of the microchannel, the aspect ratio of the rod, the thickness of double layer, and the nature of the Carreau fluid on the mobility of the rod are investigated. We show that due to the shear-thinning effect, the mobility of the rod in the present case can be significantly larger than that in the corresponding Newtonian case; the former is more sensitive to the variation in the thickness of double layer than the latter, and the difference between the two increases with decreasing thickness of double layer. The shear-thinning effect is important under the following conditions: the double layer is thin, the boundary effect is important, and/or the aspect ratio is large. We show that increasing the aspect ratio can either raise or lessen its mobility, which is not found previously, and can play an important role in electrophoresis measurement.     

Experiment and simulation of mixed flows in a trapezoidal microchannel

This paper presents experimental and numerical results of mixed electroosmotic and pressure driven flows in a trapezoidal shaped microchannel. A micro particle image velocimetry (μPIV) technique is utilized to acquire velocity profiles across the microchannel for pressure, electroosmotic and mixed electroosmotic-pressure driven flows. In mixed flow studies, both favorable and adverse pressure gradient cases are considered. Flow results obtained from the μPIV technique are compared with 3D numerical predictions, and an excellent agreement is obtained between them. In the numerical technique, the electric double layer is not resolved to avoid expensive computation, rather a slip velocity is assigned at the channel surface based on the electric field and electroosmotic mobility. This study shows that a trapezoidal microchannel provides a tapered-cosine velocity profile if there is any pressure gradient in the flow direction. This result is significantly different from that observed in rectangular microchannels. Our experimental results verify that velocity distribution in mixed flow can be decomposed into pressure and electroosmotic driven components.     

Scaling law for cross-stream diffusion in microchannels under combined electroosmotic and pressure driven flow

This paper presents an analytical study of the cross-stream diffusion of an analyte in a rectangular microchannel under combined electroosmotic flow (EOF) and pressure driven flow to investigate the heterogeneous transport behavior and spatially dependent diffusion scaling law. An analytical model capable of accurately describing 3D steady-state convection–diffusion in microchannels with arbitrary aspect ratios is developed based on the assumption of the thin electric double layer. The model is verified against high-fidelity numerical simulation in terms of flow velocity and analyte concentration profiles with excellent agreement (<0.5 % relative error). An extensive parametric analysis is then undertaken to interrogate the effect of the combined flow velocity field on the transport behavior in both the positive pressure gradient (PPG) and negative pressure gradient cases. For the first time, the evolution from the spindle-shaped concentration profile in the PPG case, via the stripe-shaped profile (pure EOF), and finally to the butterfly shaped profile in the PPG case is obtained using the analytical model along with a quantitative depiction of the spatially dependent diffusion layer thickness and scaling law across a wide range of the parameter space.     

Neuro-fuzzy based constitutive modeling of undrained response of Leighton Buzzard Sand mixtures

This study aims to develop neuro-fuzzy (NF) based constitutive model for Leighton Buzzard Sand fraction B and Leighton Buzzard Sand fraction E mixtures using experimental data. The experimental database used for NF modeling is based on a laboratory study of saturated mixtures with various mix ratios under a 100 kPa effective stress. Emphasis was placed on assessing the role of fines content in mixture and strain level on the deviatoric stress and pore water pressure generation in a 100 mm diameter triaxial testing apparatus. The input variables in the developed rule based NF models are the Leighton Buzzard Sand fraction E content, and strain, and the outputs are deviatoric stress, pore water pressure generation and undrained Young’s modulus. Experimental results show that Leighton Buzzard Sand fraction B and Leighton Buzzard Sand fraction E mixtures exhibits clay-like behavior due to particle–particle effects with the increase in Leighton Buzzard Sand fraction E content. It is also shown that the performance of capacities of proposed NF models are quite satisfactory.     

Diffusioosmosis of electrolyte solutions in fibrous porous media

An analytical study is presented for the diffusioosmotic flow of an electrolyte solution in the fibrous medium constructed by an ordered array of parallel charged circular cylinders at the steady state. The prescribed electrolyte concentration gradient is constant but can be oriented arbitrarily with respect to the axes of the cylinders. The electric double layer surrounding each cylinder may have an arbitrary thickness relative to the radius of the cylinder. A unit cell model which allows for the overlap of the double layers of adjacent cylinders is employed to account for the effect of fibers on each other. The electrostatic potential distribution in the fluid phase of a cell is obtained by solving the linearized Poisson–Boltzmann equation, which applies to the case of low surface potential of the cylinders. The macroscopic electric field induced by the imposed electrolyte concentration gradient through the fluid phase in a cell is determined as a function of the radial position. A closed-form formula for the fluid velocity profile of the electrolyte solution due to the combination of electroosmotic and chemiosmotic contributions as a function of the porosity of the array of cylinders correct to the second order of their surface charge density or zeta potential is derived as the solution of a modified Navier–Stokes equation. The diffusioosmotic velocity can have more than one reversal in direction over a small range of the zeta potential. For a given electrolyte concentration gradient in a cell, the fluid flow rate does not necessarily increase with an increase in the electrokinetic radius of the cylinder, which is the cylinder radius divided by the Debye screening length. The effect of the radial distribution of the induced axial electric field in the double layer on the diffusioosmotic flow is found to be of dominant significance in most practical situations.     

Controlling electroosmotic flow by polymer coating: a dissipative particle dynamics study

We have performed dissipative particle dynamics (DPDs) simulations of electroosmotic flow (EOF) through a polymer-grafted nanopore. In this model, charged particles including salt ions and counterions are not included explicitly, and EOF is created using an effective boundary condition. The screening effect of polymer layer on EOF is investigated in detail under different solvent qualities and boundary electroosmotic velocities. Results show that the solvent quality has a significant effect on the conformational properties of polymer chains and the flow characteristics of the solvent. The polymer layer undergoes a collapsed transition when decreasing the solvent quality from good to poor. Under different solvent qualities, enhancing the EOF leads to a different variation tendency of the layer thickness. The solvent-induced permeability change is inconsistent with the steady velocity away from the surface. The minimum value of the solvent permeability occurs at an intermediate solvent quality. However, the layer thickness drops gradually to a smallest value (corresponding to the largest effective pore radius) in the poor solvent condition. It is also found that the polymer inclination and stretching length exhibit a complex behavior under the combined effect of solvent quality and electroosmosis-induced shear.     

Piezoelectric linear motor with unimorph structure by co-extrusion process

A new piezoelectric linear motor was developed using a ring-shaped, unimorph stator composed of a piezoelectric active layer (0.3PZN–0.7PZT/Mn) and a conductive passive layer (0.3PZN–0.7PZT/Mn/Ag). The stator was prepared by co-extrusion followed by the thermoplastic green machining (TGM) process. After co-extruding the piezoelectrically active and passive layers together, they were machined into a ring shape and then sintered at 930 °C for 4 h. The stator was poled in the thickness direction and operated in radial vibration mode. A glass rod was used as the moving shaft. When a saw-tooth electric field was applied, the shaft moved linearly as a result of the stator's bending motion. When an inverted saw-tooth electric potential was applied, the shaft moved linearly in the opposite direction. The velocity of the piezoelectric linear motor was about 4 mm/s at an applied voltage of 80 V_p–p and a resonance frequency of 36.5 kHz.     

Computational characterization on the thermoacoustic thermophone effects induced by micro/nano-heating elements

A thermoacoustic thermophone is a classical device wherein an alternating current passes through a thin heating element to emit sound. The newly emerging micro- and nanotechnology has not only greatly improved such a device’s performance, but also expended its new potential functions such as serving as directional ultrasound sources, phased arrays, or even in some audible sound applications. So far, most investigations on thermoacoustic thermophones are on experimental parts. Besides, the existing theoretic analysis generally adopted a fundamental equation for characterizing the surrounding gas which unfortunately could only consider the heat conduction effect. However, the transient volume and pressure change in an ideal gas caused by the periodic heating would definitely trigger the flow process, which in fact contributed to most of the phenomena occurring in small scale. Here, to disclose the actual working process of the thermoacoustic thermophone and the mechanisms thus involved, we developed a computational model to systematically describe both the gas flow dynamics and heat transfer behavior for the first time. Some important physical parameter variations initiated by the alternating voltage and the corresponding double frequency heat flux, such as pressure, velocity, temperature, etc., were successfully revealed. Discoveries on such variations paved the way for the identification of critical factors that affected the sound pressure, which as a result would serve as a valuable reference for designing a thermoacoustic thermophone in the near future.     

Wall polymer depletion effects on electrokinetic diffusioosmosis of power-law liquids in cylindrical capillaries

We investigate electrokinetic diffusioosmotic flows of power-law liquids including the effects of a polymer-depleted Newtonian liquid layer near the wall boundaries in circular cylindrical capillaries. Semi-analytical solutions to the flow velocity distribution and volume flow rate are obtained for conditions involving finite double layer effects on the induced electric field of the electrokinetic diffusioosmosis. Results show that the flow behavior and responses of the electrokinetic diffusioosmotic flow depend not only on the wall zeta potential, diffusivity difference parameter, and flow behavior index, but also on the depletion layer thickness to Debye thickness ratio, the ratio of the flow consistency parameter of the power-law liquid core to the viscosity of the Newtonian depletion layer, as well as the exact numeric values of the flow consistency parameter and the Newtonian viscosity. Including the Newtonian depletion layer gives rise to wiggled-shaped zero flow rate border curves on the zeta potential versus diffusivity difference parameter map when the depletion layer thickness to Debye thickness ratio and the ratio of the flow consistency parameter of the power-law liquid core to the viscosity of the Newtonian depletion layer are close to one. These results are not identified in previous Newtonian or non-Newtonian electrokinetic diffusioosmosis literature and may likely open new possibilities and suggest new ideas in the analysis and design of diffusiophoretic separation and diffusioosmotic flow operations.     

Modeling of high-affinity binding of the novel atrial anti-arrhythmic agent, vernakalant, to Kv1.5 channels

Vernakalant (RSD1235) is an investigational drug that converts atrial fibrillation rapidly and safely in patients intravenously [Roy et al., J. Am. Coll. Cardiol. 44 (2004) 2355–2361; Roy et al., Circulation 117 (2008) 1518–1525] and maintains sinus rhythm when given orally [Savelieva et al., Europace 10 (2008) 647–665]. Here, modeling using AutoDock4 allowed exploration of potential binding modes of vernakalant to the open-state of the Kv1.5 channel structure. Point mutations were made in the channel model based on earlier patch-clamp studies [Eldstrom et al., Mol. Pharmacol. 72 (2007) 1522–1534] and the docking simulations re-run to evaluate the ability of the docking software to predict changes in drug–channel interactions. Each AutoDock run predicted a binding conformation with an associated value for free energy of binding (FEB) in kcal/mol and an estimated inhibitory concentration (K_i). The most favored conformation had a FEB of −7.12 kcal/mol and a predicted K_i of 6.08 μM (the IC50 for vernakalant is 13.8 μM; [Eldstrom et al., Mol. Pharmacol. 72 (2007) 1522–1534]). This conformation makes contact with all four T480 residues and appears to be clearly positioned to block the channel pore.     

Characterization of the electrophoretic mobility of gold nanoparticles with different sizes using the nanoporous alumina membrane system

This work presents a new analytical system to study the electrophoretic mobility of gold nanoparticles with different sizes, in which the platinum-coated alumina membranes are used as the separator due to the high pore densities, rigid support structure, chemical and thermal stability. It is shown that the electrophoretic mobility of gold nanoparticles is dependent on the nature of mobile phase and interfacial properties of alumina channels. The transport performance of nanoparticles are improved with the addition of sodium dodecyl sulfate (SDS) into the mobile phase, because SDS not only decreases the physical adsorption of gold nanoparticles on the nano-channel wall of alumina membrane, but also reduces the thickness of the electric double layer (decreasing the apparent size of particles). When the alumina membranes were modified with 6-aminohexanoic acid, it was further confirmed that the physical adsorption played a key role for the electrophoretic mobility of gold nanoparticles. Under optimized conditions, the mobility of gold nanoparticles had a fairly linear dependence on particle size (R² > 0.99), reiterating that our membrane system was also capable of characterizing gold nanoparticles in nanometer-size regimes.     

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.     

Turbulent boundary layer structure of flow over a smooth-curved ramp

The effects of a convex-curved wall followed by a recovery over a flat surface on a turbulent boundary layer structure are addressed via large-eddy simulation (LES). The curved wall constitutes a smooth ramp formed by a portion of circular arc. The statistically two-dimensional upstream boundary layer flow is realistically fed by an injected inflow boundary condition. The inflow is extracted from a simultaneously simulated flat-plate boundary layer which is computed based on a compressible rescaling method. After flowing over the curved surface the flow is allowed to recover its realistic condition by passing over a downstream flat surface. The Reynolds number introduced at the inlet section of the computational domain which starts 4 times the ramp length (L_r) upstream of the curved surface is Re_δo=U_∞δ_o/ν=9907. The Reynolds number is based on the inflow boundary layer thickness δ_o, the free-stream velocity U_∞ and the kinematic viscosity ν.Mean flow predictions obtained using the present LES with the rescaling–recycling inflow condition agree well with the available experimental data from literature. The Reynolds stress components match the experimental one. However, small deviation occurs due to the smaller-domain height used in the present simulation. The experiments showed that there is a generated pressure gradient on the upper wall and this in return affects the turbulence energy on the other wall. The numerical data as well as the experiments show an enhancement of the turbulent stresses in the adverse pressure gradient region. The increased level of turbulent stresses is accompanied with large peaks aligned with the inflection point of the velocity profiles. The high stress levels are nearly unchanged by reattachment process, decaying only after the mean velocity recovered and the high production of turbulence near the outer layer drops. The recovery of the outer layer is due to the turbulent eddies generated by the separation region. Numerical visualizations show strong elongation and lifting of eddies in the region of the adverse pressure gradient generated by the curved wall. Computations of two-point correlations are also performed to represent the formation and deformation of the turbulent eddies before, over and after the curved wall. Different effects on the eddy size and its structure angle are presented.     

A 3D finite element model for free-surface flows

The present work deals with the validation of 3D finite element model for free-surface flows. The model uses the non-hydrostatic pressure and the eddy viscosities from the conventional linear turbulence model are modified to account for the secondary effects generated by strong channel curvature in the natural rivers with meandering open channels. The unsteady Reynolds-averaged Navier–Stokes equations are solved on the unstructured grid using the Raviart–Thomas finite element for the horizontal velocity components, and the common P1 linear finite element in the vertical direction. To provide the accurate resolution at the bed and the free-surface, the governing equations are solved in the multi-layers system (the vertical plane of the domain is subdivided into fixed thickness layers). The up-to-date k–ε turbulence solver is implemented for computing eddy coefficients, the Eulerian–Lagrangian–Galerkin (ELG) temporal scheme is performed for enhancing numerical time integration to guarantee high degree of mass conservation while the CFL restriction is eliminated. The present paper reports on successful validation of the numerical model through available benchmark tests with increasing complexity, using the high quality and high spatial resolution three-dimensional data set collected from experiments.     

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.     

Pressure field evaluation in microchannel junction flows through μPIV measurement

An experimental method for evaluating pressure fields in a microchannel flow was studied using μPIV measurement in conjunction with the pressure Poisson equation. The pressure error due to the influence of numbers of measurement planes, computational grids for solving pressure Poisson equation, and an experimental error in μPIV measurement was evaluated with respect to the exact solution of Navier–Stokes equation for straight microchannel flow. The mean velocity field in microchannel junction flows with bifurcation and confluence was measured by a μPIV system, which consists of a CCD camera and a microscope with an in-line illumination of white light from stroboscopes. The planar velocity fields at various cross-sections of the microchannel flow were measured by traversing the focal plane within a depth of focus of the microscope. The pressure contour in the microchannel flow was evaluated by solving the pressure Poisson equation with the experimental velocity data. The results indicate that the pressure field in the microchannel junction flow agrees closely with the numerical simulation of laminar channel flow, which suggests the validity of the present method.     

Numerical simulation of emergence of a water droplet from a pore into a microchannel gas stream

A numerical investigation on the dynamic behavior of liquid water entering a microchannel through a lateral opening (pore) in the wall is reported in this paper. The channel dimensions, flow conditions and transport properties are chosen to simulate those in the gas channel of a typical proton exchange membrane fuel cell (PEMFC). Two-dimensional transient simulations employing the volume of fluid method are used to explicitly track the liquid–gas interface, and to gain understanding into the dynamics of a water droplet subjected to airflow in the bulk of the microchannel. A series of parametric studies, including the effects of static contact angle, dimensions of the pore, air-inlet velocity, and water-inlet velocity are performed with a particular focus on the effect of hydrophobicity. The simulations show that the wettability of the microchannel surface has a major impact on the dynamics of the water droplet. Flow patterns are presented and analyzed showing the splitting of a droplet for a hydrophobic surface, and the tendency for spreading and film flow formation for a hydrophilic surface. The time evolution of the advancing and receding contact angles of the droplet are found to be sensitive to the wettability when the gas diffusion layer surface is hydrophilic, but independent of wettability when the surface is hydrophobic. The critical air velocity at which a droplet detaches is found to decrease with increasing hydrophobicity and with increasing initial dimension of the droplet. The critical air velocity found in the present study by taking into account the water transport and evolution of the droplet from a pore are found to differ significantly from previous works which consider a stagnant droplet sitting on the surface.     

Electrophoresis of an axisymmetric particle along its axis of revolution perpendicular to two parallel plane walls

The axisymmetric electrophoretic motion of a dielectric particle of revolution situated at an arbitrary position in a slit microchannel is studied theoretically at the quasisteady state. The applied electric field is uniform, along the axis of symmetry of the particle, and perpendicular to the two plane walls of the slit. The electric double layer at the particle surface is assumed to be thin relative to the particle size and to the particle–wall gap widths. A method of distribution of a set of spherical singularities along the axis of symmetry within a prolate particle or on the fundamental plane within an oblate particle is used to find the general solutions for the electric potential distribution and fluid velocity field. The apparent slip condition on the particle surface is satisfied by applying a boundary collocation technique to these general solutions. Numerical results for the electrophoretic velocity of a prolate or oblate spheroid along its axis of revolution and perpendicular to two plane walls are obtained with good convergence behavior for various cases. The effect of the confining walls is to reduce the velocity of the particle, irrespective of its aspect ratio or the relative particle–wall separation distances. For fixed separation parameters, the normalized velocity of the spheroid decreases with a decrease in its axial-to-radial aspect ratio, and the boundary effect on electrophoresis of an oblate spheroid can be very significant. When a spheroid with a specified aspect ratio is located near a first plane wall, the approach of a second wall far from the particle can first increase the electrophoretic mobility to a maximum, then reduce this mobility when the second wall is close to the particle, and finally lead to a minimum mobility when it reaches to the same distance from the particle as the first wall. For a given separation between the two plane walls relative to the axial size of the spheroid, the electrophoretic mobility has a maximum when the spheroid is located midway between the walls and decreases as it approaches either of the walls.     

LSI channel routing algorithms

A new method is proposed and an algorithm is developed for two-wire channel routing in a two-layer board, with horizontal interconnections made in one layer and vertical interconnections in the other layer.Translated from Kibernetika, No. 3, pp. 32–35, May–June, 1991.