Electroosmotic flows in an electric double layer overlapped channel with rectangle-waved surface roughness

To further understand the wall-roughness effect, the present study has performed numerical simulations, by employing the Poisson–Nernst–Planck model, on the two-dimensional electroosmotic flow in a plane channel with dielectric walls of rectangle-waved surface roughness where the two electric double layers (EDLs) are overlapped. Results show that the steady electroosmotic flow and ionic-species transport depend significantly on the shape of the surface roughness such as the amplitude and periodic length of wall wave, but their characteristics are basically different from those in the case where the EDLs are not overlapped at all (Kang and Suh in Microfluid Nanofluid, doi:, 2008). It is found that the fluid flows over the waved wall (or wall roughness) with involving a separation or recirculation of flow in the cavity, which resembles much the traditional pressure-driven flow. In addition, the flow characteristics are determined chiefly by the level of the electric-charge density in the bulk region above the waved wall. As a result, with increasing wall-wave amplitude (0.01 ≤ h/H ≤ 0.2), the flow rate increases due to the enhanced amount of electric charges released from the enlarged wet surface at low amplitudes and then decreases due to the reduced flow-passage area at high amplitudes above a certain critical value. With increasing periodic length (0.2 ≤ L/H ≤ 1.2), on the other hand, the flow rate decreases in a hyperbolic fashion due to the reduced amount of electric charges.     

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.     

Broadening of neutral analyte band in electroosmotic flow through slit channel with different zeta potentials of the walls

The study is concerned with addressing hydrodynamic dispersion of an electroneutral non-adsorbed solute being transported by electroosmotic flow through a slit channel formed by walls with different zeta potentials. The analysis is conducted in terms of the plate height which, using the Van Deemter equation, can be expressed through the cross-sectional mean flow velocity, the solute molecular diffusion coefficient and a length scale parameter having meaning of the minimum achievable plate height and depending on the velocity distribution within the channel cross-section. The minimum plate height is determined by substituting distribution of electroosmotic velocity into the preliminary derived integral expression that is valid for any given velocity distribution within a slit channel cross-section. The electroosmotic velocity distribution within the slit channel cross-section is obtained by solving one-dimensional version of the Stokes equation accounting for electric force exerted on the local equilibrium electric space charge. The major obtained result is an analytical expression which represents the minimum plate height normalized by half of channel width as a function of two dimensionless parameters, namely, half of channel width normalized by the Debye length, and the ratio of the wall zeta potentials. The obtained result reveals a substantial increase in the minimum plate height compared with the case of equal wall zeta potentials. Different limiting cases of the obtained relationships are analyzed and possible applications are discussed.     

Peristaltic transport of a third order fluid under the effect of a magnetic field

The peristaltic transport of a third order fluid in a planar channel is considered. The fluid is electrically conducting by a transverse magnetic field. The perturbation solution is obtained using small Deborah number. Expressions of stream function, longitudinal velocity and pressure gradient valid for long wavelength are developed. Numerical integration is performed to analyze the effect of Hartman number on the pressure rise and frictional force. It is noted that both Hartman and Deborah numbers suppress the flow.     

Numerical analysis on electroosmotic flows in a microchannel with rectangle-waved surface roughness using the Poisson–Nernst–Planck model

The present study has numerically investigated two-dimensional electroosmotic flows in a microchannel with dielectric walls of rectangle-waved surface roughness to understand the roughness effect. For the study, numerical simulations are performed by employing the Nernst–Planck equation for the ionic species and the Poisson equation for the electric potential, together with the traditional Navier–Stokes equation. Results show that the steady electroosmotic flow and ionic-species transport in a microscale channel are well predicted by the Poisson–Nernst–Planck model and depend significantly on the shape of surface roughness such as the amplitude and periodic length of wall wave. It is found that the fluid flows along the surface of waved wall without involving any flow separation because of the very strong normal component of EDL (electric double layer) electric field. The flow rate decreases exponentially with the amplitude of wall wave, whereas it increases linearly with the periodic length. It is mainly due to the fact that the external electric-potential distribution plays a crucial role in driving the electroosmotic flow through a microscale channel with surface roughness. Finally, the present results using the Poisson–Nernst–Planck model are compared with those using the traditional Poisson–Boltzmann model which may be valid in these scales.     

Simulation of a pad slider flying on a wavy surface

This paper describes following-up characteristic of a pad slider to a wavy surface. The pad slider comprises a leading pad and a trailing pad. We use a sine wave to replace an actual wavy surface. The response of the pad slider due to the sine wave is analyzed by computer simulation. The response of the pad slider is evaluated from variation in slider flying height (FH). A variation gain that is a ratio of FH fluctuation and wave amplitude is defined to explain the following-up characteristic of slider. To analyze the following-up characteristic, different wavelengths are used as parameter to calculate the variation gain. Because pads on the air-bearing surface of the slider are able to occur at two pressure peaks on the leading edge and trailing edge that enable a pitching motion of the slider, the slider can follow the disk waviness with a wavelength that is shorter than the slider length. The variation gain is 0.33 for the wavelength that is equal to the slider length. However, the slider cannot follow the disk waviness with a wavelength that is shorter than the pad length. The variation gain is greater than 1 for the wavelength 0.2 mm. To study the relationship between the variation gain and the dynamics of slider, a transient response simulation is carried out in order to investigate a natural frequency of slider. We set a projection on a plane surface. When the slider is flying over the projection, we can obtain a flying height response curve and a pitch response curve. The natural frequency of flying height and pitch angle can be known by FFT. The transient response of slider in pitch mode is compared with the variation gain. The simulation results make clear the fact that the following-up characteristic has correlation with the dynamics of the pitch model and the phase difference between a locus of head and a wave of disk surface.     

Modulation of electroosmotic flow by electric field-responsive polyelectrolyte brushes: a molecular dynamics study

Molecular dynamics simulations were done to study the electroosmotic flow (EOF) transport in a nanochannel grafted with polyelectrolytes under the control of an electric field normal to the channel wall. This study first addresses some problems on the interplay between complex EOF and non-equilibrium conformational behavior of polyelectrolyte brushes at a molecular level. We demonstrated that changing the normal electric field has a significant impact on the conformational transition of polyelectrolytes and ion distributions, further leading to some new flow phenomena. The coupling mechanisms of polyelectrolyte chain dynamics and electrohydrodynamics were discussed. A remarkable result obtained is that fluid flux depends nonmonotonically on the normal electric field. Our work provides fundamental understanding of the EOF modulation using polyelectrolyte brushes and guidance for the design of smart nanofluidic channels.     

Forced convection in electro-osmotic/Poiseuille micro-channel flows of viscoelastic fluids: fully developed flow with imposed wall heat flux

The analytical solution for heat transfer in a dynamic and thermally fully developed channel flow of the simplified Phan-Thien–Tanner fluid induced by combined electro-osmosis and pressure gradient was obtained assuming that material properties are independent of temperature. The flow forcing was quantified by an appropriate dimensionless parameter and its effect and that of all other relevant dimensionless numbers is presented and discussed. Specifically, the forced convection occurs under conditions of constant wall heat flux and the solution includes the effects of Weissenberg number, electric double layer (EDL) thickness, forcing ratio parameter, viscous dissipation as well as of Joule heating due to the electric currents and was obtained under the simplifying Debye–Hückel approximation. Generally speaking, the Joule effect is stronger than the viscous dissipation except in very narrow channels, but these fall outside the validity of the Debye–Hückel conditions. For pure electro-osmosis, viscous dissipation is restricted to the near-wall region and virtually nonexistent elsewhere, so it is irrelevant for thin electric double layers and Joule heating is more relevant. As the EDL thickens and/or the pressure gradient contribution increases, the role of viscous dissipation grows and shear-thinning effects also appear more clearly on the Nusselt number. Generally speaking, an increase in internal heating results in lower Nusselt numbers and this effect is stronger than the effect of shear-thinning, which is responsible for a slight increase in the Nusselt number.     

Microfluidic mixing using pulsating flows

Mixing of biological species in microfluidic channels is challenging since the mixing process is limited by the small mass diffusion coefficient of the species and by the dominance of viscous effects, captured by the low value of Reynolds number characteristic of laminar liquid flow in microchannels. This paper investigates the use of pulsating flows to enhance mixing in microflows. The dependence of the degree of mixing on various dimensionless groups is investigated. These dimensionless numbers are Strouhal number, pulse amplitude divided by base velocity, Reynolds number, location along the mixing channel normalized by the channel width, channel cross section aspect ratio, and phase difference between the inlet streams. The degree of mixing, observed to experience both spatial fluctuations down the mixing channel and temporal fluctuations over a pulsation cycle at the quasi-stationary state, is shown to be most sensitive to changes in pulsation amplitude and frequency. For a fixed pulsation amplitude and Reynolds number, the degree of mixing has a peak value for a certain Strouhal number above and below which the degree of mixing decreases. Increasing the pulsation amplitude improves mixing with the behavior becoming asymptotic at large pulsation amplitudes. The temporal fluctuations in the degree of mixing over a cycle at the quasi-stationary state decrease and the average degree of mixing increases downstream the mixing channel. The fluctuations are also smaller at higher values of the Strouhal number and are generally larger for larger pulsation amplitudes. This study also takes into account the rate of work input required to overcome viscous effects. While this power input is independent of the pulsation frequency, it exhibits a parabolic dependence on the pulsation amplitude. Finally, considering the dependence of the degree of mixing (mean and standard deviation), mixing length, and energy consumption on these dimensionless groups, examples of the trade-off that has to be made in choosing the operating conditions based on different constraints are presented.     

Acoustically generated flows in microchannel flexural plate wave sensors: Effects of compressibility

Acoustically generated flowfields in flexural plate wave sensors filled with a Newtonian liquid (water) are considered. A computational model based on compressible flow is developed for the sensor with a moving wall for pumping and mixing applications in microchannels. For the compressible flow formulation, an isothermal equation of state for water is employed. The velocity and pressure profiles for different parameters including flexural wall frequency, channel height, amplitude of the wave and wave length are investigated for four microchannel height/length geometries. It is found that the flowfield becomes pseudo-steady after sufficient number of flexural cycles. Both instantaneous and time averaged results show that an evanescent wave is generated in the microchannel. The predicted flows generated by the FPWs are compared with results available in the literature. The proposed device can be exploited to integrate micropumps with complex microfluidic chips improving the portability of micro-total-analysis systems.     

Spatial-temporal scales of Green Island wake due to passing of the Kuroshio current

The Kuroshio current-induced island wake downstream of Green Island, Taiwan, is studied using satellite imagery and a depth-averaged shallow-water model. Spatial–temporal scales, such as aspect ratio, dimensionless width, and Strouhal number, as well as propagation speed of the vortices, are quantified for Reynolds numbers 100, 200, and 500, respectively. It is found that the aspect ratio is between 1.76 and 2.72 obtained from satellite images and between 3.50 and 3.72 from numerical simulations. The dimensionless width is in the range of 1.84 to 1.92 from satellite images, and 1.29 to 1.33 from numerical modelling. The Strouhal number is between 0.17 and 0.20 from numerical simulations. Computed results are compared with theory, available satellite imagery, and in situ measurements, and show reasonable agreement. The magnitude of the propagation speed of the vortices is found to be of the same order as that of the Kuroshio, implying non-linearity as well as interactions of vortices, and the Kuroshio is strong. The Coriolis force affects the free-surface distribution, but its effect on vortices and flow field is insignificant.     

降膜蒸发过程的数值模拟和传热传质分析

利用CFD软件对逆流降膜蒸发过程进行了实验模拟研究,研究了速度边界层、热边界层和浓度边界层的变化对降膜蒸发传热传质特性的影响规律;通过建立一维逆流降膜蒸发的数学方程编程求解出了对流传热传质的Nu数和Sh数,利用Fluent软件模拟出的实验结果采用回归分析得出了气液流量比Raw、流道的长宽比αL、空气进口无量纲温度θai以及空气进口Re数与Nu数、Sh数之间的无量纲关系式,可为降膜蒸发换热器的设计提供参考。     

Peristaltic transport of fractional Maxwell fluids in uniform tubes: Applications in endoscopy

This paper presents the effect of endoscope on peristaltic transport of fractional Maxwell fluids through the gap between two concentric uniform tubes under the assumptions of large wavelength and low Reynolds number. The inner tube is an endoscope and the outer tube has a sinusoidal wave traveling down its wall, i.e. the inner tube is rigid and outer tube is flexible. Solutions for the problem are obtained by two numerical methods named as homotopy perturbation method and variational iteration method. The impacts of endoscope, relaxation time and fractional parameters on pressure per wavelength and friction force (on inner and outer tubes) per wavelength are discussed with the help of computational results which are presented in graphical form. On the basis of the present study, it is revealed that pressure diminishes with increase in the magnitude of first fractional parameter, ratio of tube radii and relaxation time whereas it enhances with increasing the magnitude of second fractional parameter and amplitude ratio. The study further reveals the important fact that the effects of all pertinent parameters (except ratio of tube radii) on friction force at inner tube are similar in magnitude but opposite in direction to that of pressure and the effects of same parameters on friction force at outer tube are similar in magnitude but opposite in direction to that of pressure.     

Numerical simulation of three-dimensional turbulent separated and reattaching flows using a modified turbulence model

A modified version of k-ε model is proposed through modification of the damping function of eddy viscosity that incorporates the effect of wall proximity in the near the wall region and the effect of non-equilibrium away from the wall together with the simple model functions in the ε equation. The proposed turbulence model is validated with the available experimental data of reattachment length, mean streamwise velocity distribution, turbulence intensity profile, and wall static pressure coefficient in the turbulent backward-facing step flows. The predicted results with the present model are in good agreement with the experiments. Computed results reveal that the reattachment length (recirculation zone) and the wall static pressure are decreased with increasing inlet velocity. And the asymmetric distributions of the reattachment point, cross-section view of velocity vector, streamwise skin friction coefficient, and turbulent kinetic energy demonstrate the important three-dimensional side-wall effect in an insufficient aspect ratio channel flow.     

Effect of the wavy leading edge on hydrodynamic characteristics for flow around low aspect ratio wing

The present study numerically investigates the effect of the wavy leading edge on hydrodynamic characteristics for the flow of rectangular wings with the low aspect ratio of 1.5 at one Reynolds number of 10⁶ based on free stream velocity and the chord length C. The waviness ratio R_w is defined by the span length of wing to the spanwise length covered by the waviness. Five different waviness ratios of 0.2, 0.4, 0.6, 0.8 and 1.0 at fixed wavelength of 0.2C and wavy amplitude of 0.025C have been considered. The smooth wing and R_w = 0.2 revealed the similar variation of lift coefficient C_L according to the angle of attack α, resulting in the same stall angle of 20°, where the maximum lift appears. The case of R_w = 0.6 presented the earliest occurrence of the stall at α = 12°. The cases of R_w = 1.0, 0.8 and 0.4 produced the same stall angle of α = 16°. In the post-stall region, C_L for R_w = 0.4, 0.6, 0.8 and 1.0 recovered and became larger than those of the smooth wing and R_w = 0.2. A spiral formation of the limiting streamlines occurred in the wavy troughs, which derive relatively low pressure along the leading edge.     

Effects of applied electric field and microchannel wetted perimeter on electroosmotic velocity

Parameters which affect electroosmotic flow (EOF) behavior need to be determined for characterizing flow in miniature biological and chemical experimental processes. Several parameters like buffer pH, ionic concentration, applied electric field and channel dimensions influence the magnitude of the electroosmotic flow. We conducted numerical and experimental investigations to determine the impact of electric field strength and wetted microchannel perimeter on EOF in straight microchannels of rectangular cross-section. Deviation from theoretical behavior was also investigated. In the numerical model, we solved the continuity and Navier–Stokes equations for the fluid flow and the Gauss law equation for the electric field. Computational results were validated against experimental data for PDMS-glass channels of different wetted perimeters over a range of applied electric fields. Results show that increasing the applied electric field at constant wetted perimeter caused the electroosmotic mobility, the ratio of electroosmotic velocity to applied electric field, to increase nonlinearly. It was also found that increasing the wetted perimeter at constant applied electric field decreased the electroosmotic flow. These findings will be useful in determining the optimum value of the electric field required to produce a desired electroosmotic flow rate in a channel of a particular dimension. Alternately, these will also be useful in determining the optimum channel dimensions to provide a desired electroosmotic flow rate at a specified value of the electric field.     

Friction model of fingertip sliding over wavy surface for friction-variable tactile feedback panel

A friction-variable touch panel is capable of presenting virtual bumps and holes on its flat surface through the control of the surface friction when a fingertip slides over it. To improve the presentation, we developed a friction model of a fingertip sliding over a sinusoidal surface with an amplitude of 0.5–2.5 mm and a spatial wavelength of 20–50 mm. When a metal ball rolls over a wavy surface with a low friction and contact area, the ratio of the horizontal force to the normal force is equal to the gradient of the surface (this is referred to as the ball bearing model) and is hardly affected by the normal load and rolling speed. In contrast, the profile of the force ratio of a sliding finger is substantially skewed and affected by the sliding direction and normal force exerted by the finger. To model this skewed force ratio, we formulated the asymmetric pressure distribution in the finger-surface contact area and used the effects of the adhesion friction to model the dependency of the force ratio on the normal force and sliding direction. The developed model of a bare finger with these features was found to sufficiently simulate the experimentally observed force ratios. The model can be easily applied to friction-variable touch panels and enables the achievement of a wide variety of haptic contents with macroscopically concave or convex surfaces.     

Scale effects in nano-channel liquid flows

Force-driven liquid argon flows both in nanoscale periodic domains and in gold nano-channels are simulated using non-equilibrium molecular dynamics to investigate the scale and wall force field effects. We examined variations in liquid density, viscosity, velocity profile, slip length, shear stress and mass flow rate in different sized periodic domains and nano-channels at a fixed thermodynamic state. In the absence of walls, liquid argon obeys Newton’s law of viscosity with the desired absolute viscosity in domains as small as 4 molecular diameters in height. Results prove that deviations from continuum solution are solely due to wall effects. Simulations in nano-channels with heights varying from 3.26 to 36 nm exhibit parabolic velocity profiles with constant slip length modeled by Navier-type slip boundary condition. Both channel averaged density and “apparent viscosity” decrease with reduced channel height, which has competing effects in determination of the mass flow rate. Density layering and wall force field induce deviations from Newton’s law of viscosity in the near-wall region, while constant “apparent viscosity” with the deformation rate from a parabolic velocity profile successfully predicts shear stress in the bulk flow region.     

Application of a Spectral Element Method to Two-Dimensional Forward-Facing Step Flow

In the present study, we investigate the two-dimensional laminar flow through a one-sided constriction of a plane channel with a ratio of h:H=1:4 (where h is the step height and H is the channel height). The computational approach employed is based on a mixed implicit/explicit time discretization scheme together with a highly accurate spatial discretization using a P _N –P _N–2 spectral-element method. It is well known that this so-called forward-facing step (FFS) flow exhibits a singularity in the pressure and the velocity derivatives at the corner point. We account for this singularity by a geometric mesh refinement strategy that was proposed in a hp-FEM context. A detailed numerical study of the FFS flow reveals that length and height of the recirculation zone in front of the step are almost constant for creeping flow. In the limit of high Reynolds numbers the length and height of the recirculation zone increase proportional to Re ^0.6 and Re ^0.2, respectively.     

Improvement of capillary electrophoresis property for microchannels fabricated by deep X-ray lithography

We fabricated the electrophoresis microchips using the UV polymerization technique. We employed plastic substrates that were suitable for rapid prototyping instead of glass and quartz. A thick UV negative photo resist was used to form molds and poly-dimethylsilozane (PDMS) was polymerized by a thermal curing process on the mold to obtain replica microchips. Electroosmotic flow (EOF) was measured to evaluate the surface. Characteristic differences between UV-fabricated and SR-fabricated microchips were evaluated by electro osmotic flow (EOF) measurement. It was observed that microchannels fabricated by SR lithography show constant peak heights and FWHMs. We also investigated the effect of the change of the channel width along the EOF direction. It is demonstrated that broadening width channel significantly restricts the sample diffusion towards the EOF direction and leads to the high resolusion separation on the PDMS microchips. Thus the advantage of the application of SR lithography to the mold fabrication is also demonstrated.