Influence of combined electromagnetohydrodynamics on microchannel flow with electrokinetic effect and interfacial slip

We investigate analytically the combined consequences of electromagnetohydrodynamic forces and interfacial slip on streaming potential mediated pressure-driven flow in a microchannel. Going beyond traditional Debye–Hückel limit, we first derive a closed-form analytical solution for velocity field by considering nonlinear electrical potential distribution, wall slip effects, externally imposed transverse magnetic field, and laterally applied electric field in the plane of flow. The effects of electrical double-layer (EDL) formation and the consequent interfacial phenomena are critically examined under such situations. An expression for induced streaming potential in the microchannel is deduced considering EDL formation and the consequences of finite conductance of the immobilized Stern layer. This simplified analytical expression is later on critically assessed against three-dimensional simulation paradigm of streaming potential mediated flows, which is a first effort of this kind. We demonstrate that flow rate increases progressively with increasing surface potential and eventually approaches to a limiting value. Combination of electromagnetohydrodynamic effect with liquid slip is shown to amplify the flow rate, even at lower values of surface potential. Our study brings out the possibility of achieving an optimum flow rate by judicious application of combined electromagnetohydrodynamics. The present analysis has significant consequence in the design of advanced microfluidic devices with improved efficiency and functionality.     

Pressure-driven electrokinetic slip flows of viscoelastic fluids in hydrophobic microchannels

This work investigates the steady-state slip flow of viscoelastic fluids in hydrophobic two-dimensional microchannels under the combined influence of electro-osmotic and pressure gradient forcings with symmetric or asymmetric zeta potentials at the walls. The Debye–Hückel approximation for weak potential is assumed, and the simplified Phan-Thien-Tanner model was used for the constitutive equation. Due to the different hydrophobic characteristics of the microchannel walls, we study the influence of the Navier slip boundary condition on the fluid flow, by considering different slip coefficients at both walls and varying the electrical double-layer thickness, the ratio between the applied streamwise gradients of electric potential and pressure, and the ratio of the zeta potentials. For the symmetric case, the effect of the nonlinear Navier slip model on the fluid flow is also investigated.     

Electrokinetic and aspect ratio effects on secondary flow of viscoelastic fluids in rectangular microchannels

The secondary flow of PTT fluids in rectangular cross-sectional plane of microchannels under combined effects of electroosmotic and pressure driving forces is the subject of the present study. Employing second-order central finite difference method in a very refined grid network, we investigate the effect of electrokinetic and geometric parameters on the pattern, strength and the average of the secondary flow. In this regard, we try to illustrate the deformations of recirculating vortices due to change in the dimensionless Debye–Hückel and zeta potential parameters as well as channel aspect ratio. We demonstrate that, in the presence of thick electric double layers, significant alteration occurs in the secondary flow pattern by transition from favorable to adverse pressure gradients. Moreover, it is found that for polymer-electrolyte solutions with large Debye lengths, the secondary flow pattern and the shape of vortices are generally dependent upon the width-to-height ratio of the channel cross section. Also, the inspections of strength and average of secondary flow reveal that the sensitivity of these quantities with respect to the electrokinetic, geometric and rheological parameters increases by increasing the absolute value of velocity scale ratio. In this regard, utilizing the curve fitting of the results, several empirical expressions are presented for the strength and average of the secondary flow under various parametric conditions. The obtained relations with the other predictions for secondary flow are of high practical importance when dealing with the design of microfluidic devices that manipulate viscoelastic fluids.     

A new model for predicting the thermodynamic phase behavior of electrolyte in aqueous solutions

In the present study, the phase behavior of aqueous electrolyte solutions has been correlated with a new three-parameter model based on the Debye–Hückel model. The new model was evaluated by the estimation of the osmotic and mean ionic activity coefficients of 123 electrolytes in aqueous solutions. The adjustable parameters of the new model were obtained by using non-linear regression between the experimental data and the results of the new model. Using adjustable parameters, the osmotic coefficients of the aqueous solutions were calculated. The results of the standard deviations of the osmotic and mean ionic activity coefficients were in a good agreement.     

A nonlinear study on the interfacial instabilities in electro-osmotic flows based on the Debye–Hückel approximation

Interfacial instabilities in an electro-osmotic micro-film flow are studied by deriving an evolution equation for the local film thickness and subsequent numerical integrations. The free-surface electro-osmotic flow has an inherent instability of the long-wave type, which generates corrugations on the film surface. These corrugations may critically affect the transport characteristics of the flow, and deserve a nonlinear analysis based on conservation laws. It is shown that the electro-osmotic instability can cause severe local depression of the film even in the absence of the van der Waals attraction between the film surface and the substrate. The electrical double layer (EDL) then may be penetrated by the film surface, and film rupture can occur, resulting in loss of the electro-osmotic driving force. Since the Debye–Hückel approximation used becomes inadequate as the film thins locally to a nano-scale, quantitative analysis of the incipient rupture reported would require a fully coupled system for fluid flow, ionic concentration, and electric field.     

Effect of the skimming layer on electro-osmotic��Poiseuille flows of viscoelastic fluids

An analytical solution is derived for the micro-channel flow of viscoelastic fluids by combined electro-osmosis and pressure gradient forcing. The viscoelastic fluid is described by the Phan-Thien–Tanner model with due account for the near-wall layer depleted of macromolecules. This skimming layer is wider than the electric double layer (EDL) and leads to an enhanced flow rate relative to that of the corresponding uniform concentration flow case. The derived solution allows a detailed investigation of the flow characteristics due to the combined effects of fluid rheology, forcing strengths ratio, skimming layer thickness and relative rheology of the two fluids. In particular, when the EDL is much thinner than the skimming layer and simultaneously the viscosity of the Newtonian fluid inside this layer is much lower than that of the fluid outside, the flow is dominated by the characteristics of the Newtonian fluid. Outside these conditions, proper account of the various fluid layers and their properties must be considered for an accurate prediction of the flow characteristics. The analytical solution remains valid for the flow driven by a pressure gradient and its streaming potential, which is determined in the appendix.     

Approach to analytic solutions for electroosmotic flow in micro-ducts by eigenfunctions of the Helmholtz equation

In the literature, a limited number of analytical solutions for electroosmotic (EO) flow in micro-ducts were obtained. In this study, we present a general formulation using eigenfunctions of the Helmholtz equation to obtain analytic solutions for steady and unsteady EO flow in micro-ducts under Debye–Hückel approximation. The key observation is that the differential operator associated with the equation for the EO flow is strictly positive definite. Examples that add to analytic solutions for EO flow include exact series and closed-form solutions to the steady flow, and the starting flow and the oscillatory flow in three triangular ducts are found. It is easy to deduce some salient features of flow physics, such as the flow rate, transient time and phase lag as well as the velocity profile from the general solution, and they are given quantitative values in the individual examples.     

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.     

Fully developed thermal transport in combined pressure and electroosmotically driven flow of nanofluid in a microchannel under the effect of a magnetic field

This paper critically analyzes, for the first time, the effect of nanofluid on thermally fully developed magnetohydrodynamic flows through microchannel, by considering combined effects of externally applied pressure gradient and electroosmosis. The classical boundary condition of uniform wall heat flux is considered, and the effects of viscous dissipation as well as Joule heating have been taken into account. Closed-form analytical expressions for the pertinent velocity and temperature distributions and the Nusselt number variations are obtained, in order to examine the role of nanofluids in influencing the fully developed thermal transport in electroosmotic microflows under the effect of magnetic field. Fundamental considerations are invoked to ascertain the consequences of particle agglomeration on the thermophysical properties of the nanofluid. The present theoretical formalism addresses the details of the interparticle interaction kinetics in tune with the pertinent variations in the effective particulate dimensions, volume fractions of the nanoparticles, as well as the aggregate structure of the particulate system. It is revealed that the inclusion of nanofluid changes the transport characteristics and system irreversibility to a considerable extent and can have significant consequences in the design of electroosmotically actuated microfluidic systems.     

Long-wave interfacial instabilities in a thin electrolyte film undergoing coupled electrokinetic flows: a nonlinear analysis

Spatiotemporal deformations of the free charged surface of a thin electrolyte film undergoing a coupled electrokinetic flow composed of an electroosmotic flow (EOF) on a charged solid substrate and an electrophoretic flow (EPF) at its free surface are explored through linear stability analysis and the long-wave nonlinear simulations. The nonlinear evolution equation for the deforming surface is derived by considering both the Maxwell’s stresses and the hydrodynamic stresses. The electric potential across the film is obtained from the Poisson–Boltzmann equation under the Debye–Hückel approximation. The simulations show that at the charged electrolyte–air interface, the applied electric field generates an EPF similar to that of a large charged particle. The EOF near the solid–electrolyte interface and the EPF at the electrolyte–air interface are in the same (or opposite) directions when the zeta potentials at the two interfaces are of the opposite (or same) signs. The linear and nonlinear analyses of the evolution equation predict the presence of travelling waves, which is strongly modulated by the applied electric field and the magnitude/sign of the interface zeta potentials. The time and length scales of the unstable modes reduce as the sign of zeta potential at the two interfaces is varied from being opposite to same and also with the increasing applied electric field. The increased destabilization is caused by a reverse EPF near the free surface when the interfaces bear the same sign of zeta potentials. Flow reversal by EPF at the free surface occurs at smaller zeta potential of the free surface when the film is thicker because of less influence of the EOF arising at the solid–electrolyte boundary. The amplitude of the surface waves is found to be smaller when the unstable waves travel at a faster speed. The films can undergo pseudo-dewetting when the free surface is almost stationary under the combined influences of EPF and EOF. The free surface instability of the coupled EOF and EPF has some interesting implications in the development of micro/nano fluidic devices involving a free surface.     

Maxwell stress generated long wave instabilities in a thin aqueous film under time-dependent electro-osmotic flow

In this study the dynamics and stability of thin and electrically conductive aqueous films under the influence of a time-periodic electric field are explored. With the help of analytical linear stability analysis for long wavelength disturbances, the stability threshold of the system as a function of various electrochemical parameters and transport coefficients is presented. The contributions of parameters like surface tension, disjoining pressure, electric double layer (Debye length and interfacial zeta potential), and unsteady Maxwell and viscous stresses are highlighted with the help of appropriate dimensionless groups. The physical mechanisms affecting the stability of thin films are detailed with the above-mentioned forces and parametric dependence of stability trends is discussed.     

Thermally developing electroosmotic transport of nanofluids in microchannels

A theoretical analysis is presented in this work to assess the influence of nanofluids on thermally developing and hydrodynamically developed electroosmotic transport in parallel plate microchannels (Graetz problem). The hydraulic diameters of the microchannels are assumed to be beyond a certain threshold limit, so that the electric double layers formed adjacent to the plates do not overlap with each other. The volumetric heating arising from the conduction currents in the flow is modeled using Ohm’s law. The viscous generation terms in the energy equation are neglected, based on the earlier findings that the consequent effects are negligible as compared to the Joule heating effects in electroosmotically driven microchannel flows. Closed form expressions for the pertinent temperature distributions and the Nusselt number variations are obtained by employing the method of separation of variables in conjunction with an eigen value formulation, in order to assess the influence of volume fraction of the dispersed nano-particles on the overall rates of convective transport. It is revealed that the effects of nano-particles in the fluid turn out to be significant in the thermal entrance region only, especially for higher Peclet number values. The implications of the incorporation of nanofluids are demonstrated to be somewhat non-trivial in nature, and are strongly determined by the effective Peclet number values obtained on the basis of the phase-integral values of the thermo-physical properties and the pertinent flow parameters.     

Direct measurement of electric double layer in a nanochannel by electrical impedance spectroscopy

The ion distribution and physical behavior induced by applying an electric field to a nano-interfacial space are very important for investigating electric double layers (EDLs) in very confined spaces. We perform direct measurements of an EDL in a nanochannel by electrical impedance spectroscopy to experimentally evaluate the EDL thickness dependence on the ion density and the channel width. To this end, we developed a nanofluidic device consisting of a pair of sensing electrodes with a nanochannel between them. The measurement electrodes are completely embedded in a substrate to generate a uniform electric field and to provide a flat surface that can easily be used to seal the nanochannel. Using this device, we found that the EDL on one electrode expands with decreasing ion concentration and eventually merges with the EDL on the opposite electrode so that the nanochannel becomes completely filled with the EDL. The trend observed for the EDL width agrees well with that predicted by theory for the Debye length. These results provide valuable insight into the physical ionic structure in nanochannels, which will improve impedance-based electrical sensing and electrokinetic applications.     

Assessment of thermal expansion coefficient for pure metals

In this paper, thermal expansion coefficients of 42 pure metallic elements were evaluated on the basis of empirical and theoretical methods and the adjusted Debye–Grüneisen model. In Debye–Grüneisen model, Debye temperature was regarded as an undetermined constant. Parameters in the model were determined via the nonlinear least square fit method through MATLAB program. Besides, for pure metallic elements with phase transition, segment fitting can be realized and the computational results fit experimental data well; meanwhile, reliable forecast for high-temperature or low-temperature thermal expansion can be provided, and a set of average Debye temperatures based on thermal expansion coefficients have been obtained.     

Improving the separation efficiency of DNA biosamples in capillary electrophoresis microchips using high-voltage pulsed DC electric fields

This paper proposes a simple method for enhancing the separation efficiency of DNA biosamples in a capillary electrophoresis (CE) microchip by using high-voltage pulsed DC electric fields. A high-voltage amplifier is used to establish electric fields of up to 1 kHz to carry out CE separation; electrophoresis and electroosmotic effects are then pulsely induced. The experimental and numerical investigations commence by separating a mixed sample comprising two fluoresceins with virtually identical physical properties, namely Rhodamine B and Rhodamine 6G. It is found that the level of separation is approximately 2.1 times higher than that achieved using a conventional DC electric field of the same intensity. The performance of the proposed method is further evaluated by separating a DNA sample of HaeIII digested ΦX-174 ladder. The experimental results indicate that the separation level of the neighboring peaks 5a and 5b in the DNA marker is approximately 1.2, which is significantly higher than the value of 0.8 obtained using a CE scheme with a conventional DC electric field. The improved separation performance of the proposed pulsed DC electric field approach is attributed to a lower Joule heating effect as a result of a lower average power input and the opportunity for heat dissipation during the zero-voltage stage of the pulse cycle. Overall, the results demonstrate that the method proposed in this study provides a simple, low-cost technique for achieving a high separation performance in CE microchips.     

Dielectrophoresis in aqueous suspension: impact of electrode configuration

Dielectrophoresis (DEP) allows to moving neutral or charged particles in liquids by supplying a non-uniform electric field. When using alternating current and insulated electrodes, this is possible in conducting media such as aqueous solutions. However, relatively high field strength is required that is discussed to induce also an undesired Joule heating effect. In this paper, we demonstrate boundary conditions for avoiding this side effect and suggest a novel design of an interdigitated electrode (IDE) configuration to reduce the power consumption. Numerical simulation using OpenFOAM demonstrated that, when replacing conventional plate IDE by cylindrical micro-IDE in microchannel systems, the dielectrophoretic force field, i.e., the electric field gradient squared, becomes stronger and more homogeneously distributed along the electrodes array. Also the resulting particle DEP velocities were highest for the cylindrical IDE. The simulations were experimentally confirmed by measuring velocity of resin particle located at the subsurface of demineralized water. Surprisingly the fluid flow induced by electrothermal effect turned out to be negligible in microchannels when compared to the DEP effect and becomes dominant only for distances between particle and IDE larger than 6,000 μm. The well-agreed experimental and simulation results allow for predicting particle motion. This can be expected to pave the way for designing DEP microchannel separators with high throughput and low energy consumption.     

Approximating thermo-viscoelastic heating of largely strained solid rubber components

Mechanically induced viscoelastic dissipation is difficult to compute when the constitutive model is defined by history integrals. The computation of the viscous energy dissipated is in the form of a double convolution integral. In this study, we present a method to approximate the dissipation for constitutive models in history integral form that represent Maxwell-like materials. The dissipation is obtained without directly computing the double convolution integral. The approximation requires that the total stress can be separated into elastic and viscous components, and that the relaxation form of the constitutive law is defined with a Prony series. A numerical approach often taken to approximate a history integral involves interpolating the history integral’s kernel across a time step. Integration then yields finite difference equations for the evolution of the viscous stresses in time. In the case when the material is modeled with a Prony series, the form of these finite difference equations is similar to the form of the finite difference equations for a Maxwell solid. Since the dissipation rate in a Maxwell solid can be easily computed from knowledge of its viscous stress and the Prony series constants (spring-dashpot constants), we computationally investigated employing a Maxwell solid’s dissipation function to couple thermal and large strain history integral based finite element models of solid rubber components. Numerical data is provided to support this analogy and to help understand its limitations. A rubber cylinder with an imbedded steel disk is dynamically loaded, and the non-uniform heating within the cylinder is computed.     

Effect of solvent polarization on electroosmotic transport in a nanofluidic channel

In this paper, we develop a theory based on the Langevin–Bikerman approach to study the electroosmotic (EOS) transport in a nanofluidic channel in the presence of finite solvent polarization effect (SPE). At the outset, we conduct an analysis based on practically achievable parameters to highlight the consequence of SPE in the variation in the electric double-layer (EDL) electrostatics. We witness that SPE invariably increases the effective EDL thickness; our numerical results are justified through a scaling analysis. More importantly, we unravel that the EOS transport, most remarkably, shows negligible influence on the qualitative variation in the EDL electrostatic potential; rather, it is dictated by the ratio of the effective to the actual EDL thicknesses. This finding, supported by scaling analysis, ensures that for the chosen set of parameters, SPE invariably enhances the EOS transport. Apart from shedding light on this extremely non-intuitive nanoscopic electroosmotic flow phenomenon, we anticipate that the present study will embolden us to better control the nanofluidic transport for a plethora of biological and industrial applications.     

Effects of heat source/sink,radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a stretching sheet

This paper presents a study of the flow and heat transfer of an incompressible homogeneous second-grade fluid over a non-isothermal stretching sheet. The governing partial differential equations are converted into ordinary differential equations by a similarity transformation. The effects of viscous dissipation, work due to deformation, internal heat generation/absorption and thermal radiation are considered in the energy equation, and the variations of dimensionless surface temperature and dimensionless surface temperature gradient as well as the heat transfer characteristics with various physical parameters are graphed and tabulated. Two cases are studied, namely, (i) a sheet with prescribed surface temperature (PST case) and (ii) a sheet with prescribed heat flux (PHF case).     

Experimental evaluation of a pyroelectric detector linearity used for pulsed laser energy absolute measurement

The linearity of a pyroelectric detector used for pulsed laser energy absolute measurement has been studied using an experimental evaluation. Two different methods were used to evaluate the detector linearity: by comparison to a calorimeter and using the inverse square distance law. Different detection substrates were used and tested. A heating material in the form of a thin film was integrated into the substrate. This material is not only absorbent to transform laser energy into heat but also electrically resistive to transform the electric energy delivered by a current pulses generator into heat by Joule effect. An original approach based upon an electric substitution method has been used to measure the pulses energy given by the laser system and not the pulses mean power as it is commonly used. The measurement method is then based upon the comparison of the maximum voltage responses which are proportional to the pulse energy.