Rapid concentration of deoxyribonucleic acid via Joule heating induced temperature gradient focusing in poly-dimethylsiloxane microfluidic channel

This paper reports rapid microfluidic electrokinetic concentration of deoxyribonucleic acid (DNA) with the Joule heating induced temperature gradient focusing (TGF) by using our proposed combined AC and DC electric field technique. A peak of 480-fold concentration enhancement of DNA sample is achieved within 40 s in a simple poly-dimethylsiloxane (PDMS) microfluidic channel of a sudden expansion in cross-section. Compared to a sole DC field, the introduction of an AC field can reduce DC field induced back-pressure and produce sufficient Joule heating effects, resulting in higher concentration enhancement. Within such microfluidic channel structure, negative charged DNA analytes can be concentrated at a location where the DNA electrophoretic motion is balanced with the bulk flow driven by DC electroosmosis under an appropriate temperature gradient field. A numerical model accounting for a combined AC and DC field and back-pressure driven flow effects is developed to describe the complex Joule heating induced TGF processes. The experimental observation of DNA concentration phenomena can be explained by the numerical model.     

Numerical analysis of the thermal effect on electroosmotic flow and electrokinetic mass transport in microchannels

Joule heating is present in electrokinetically driven flow and mass transport in microfluidic systems. Nowadays, there is a trend of replacing costly glass-based microfluidic systems by the disposable, cheap polymer-based microfluidic systems. Due to poor thermal conductivity of polymer materials, the thermal management of the polymer-based microfluidic systems may become a problem. In this study, numerical analysis is presented for transient temperature development due to Joule heating and its effect on the electroosmotic flow (EOF) and mass species transport in microchannels. The proposed model includes the coupling Poisson-Boltzmann (P-B) equation, the modified Navier-Stokes (N-S) equations, the conjugate energy equation, and the mass species transport equation. The results show that the time development for both the electroosmotic flow field and the Joule heating induced temperature field are less than 1 s. The Joule heating induced temperature field is strongly dependent on channel size, electrolyte concentration, and applied electric field strength. The simulations reveal that the presence of the Joule heating can result in significantly different characteristics of the electroosmotic flow and electrokinetic mass transport in microchannels.     

Joule heating induced transient temperature field and its effects on electroosmosis in a microcapillary packed with microspheres

The Joule heating induced transient temperature field and its effect on the electroosmotic flow in a capillary packed with microspheres is analyzed numerically using the control-volume-based finite difference method. The model incorporates the coupled momentum equation for the electroosmotic velocity, the energy equations for the Joule heating induced temperature distributions in both the packed column and the capillary wall, and the mass and electric current continuity equations. The temperature-dependent physical properties of the electrolyte solution are taken into consideration. The characteristics of the Joule heating induced transient development of temperature and electroosmotic flow fields are studied. Specifically, the simulation shows that the presence of Joule heating causes a noticeable axial temperature gradient in the thermal entrance region and elevates a significant temperature increment inside the microcapillary. The temperature changes in turn greatly affect the electroosmotic velocity by means of the temperature-dependent fluid viscosity, dielectric constant, and local electric field strength. Furthermore, the model predicts an induced pressure gradient to counterbalance the axial variation of the electroosmotic velocity so as to maintain the fluid mass continuity. In addition, under specific conditions, the present model is validated by comparing with the existing analytical model and experimental data from the literature.     

Assessment of Joule heating and its effects on electroosmotic flow and electrophoretic transport of solutes in microfluidic channels

Joule heating is inevitable when an electric field is applied across a conducting medium. It would impose limitations on the performance of electrokinetic microfluidic devices. This article presents a 3-D mathematical model for Joule heating and its effects on the EOF and electrophoretic transport of solutes in microfluidic channels. The governing equations were numerically solved using the finite-volume method. Experiments were carried out to investigate the Joule heating associated phenomena and to verify the numerical models. A rhodamine B-based thermometry technique was employed to measure the solution temperature distributions in microfluidic channels. The microparticle image velocimetry technique was used to measure the velocity profiles of EOF under the influence of Joule heating. The numerical solutions were compared with experimental results, and reasonable agreement was found. It is found that with the presence of Joule heating, the EOF velocity deviates from its normal "plug-like" profile. The numerical simulations show that Joule heating not only accelerates the sample transport but also distorts the shape of the sample band.     

Electroosmotic flow with Joule heating effects

Electroosmotic flow with Joule heating effects was examined numerically and experimentally in this work. We used a fluorescence-based thermometry technique to measure the liquid temperature variation caused by Joule heating along a micro capillary. We used a caged-fluorescent dye-based microfluidic visualization technique to measure the electroosmotic velocity profile along the capillary. Sharp temperature drops close to the two ends and a high-temperature plateau in the middle of the capillary were observed. Correspondingly, concave-convex-concave velocity profiles were observed in the inlet-middle-outlet regions of a homogeneous capillary. These velocity perturbations were due to the induced pressure gradients resulting from axial variations of temperature. The measured liquid temperature distribution and the electroosmotic velocity profile along the capillary agree well with the predictions of a theoretical model developed in this paper.     

Numerical modeling of Joule heating-induced temperature gradient focusing in microfluidic channels

Temperature gradient focusing (TGF) is a recently developed technique for spatially focusing and separating ionic analytes in microchannels. The temperature gradient required for TGF can be generated either by an imposed temperature gradient or by Joule heating resulting from an applied electric field that also drives the flow. In this study, a comprehensive numerical model describing the Joule heating induced temperature development and TGF is developed. The model consists of a set of governing equations including the Poisson-Boltzmann equation, the Laplace equation, the Navier-Stokes equations, the energy equations and the mass transport equation. As the thermophysical and electrical properties including the liquid dielectric constant, viscosity, and electric conductivity are temperature-dependent, these governing equations are coupled, and therefore the coupled governing equations are solved numerically by using a CFD-based numerical method. The numerical simulations agree well with the experimental results, suggesting the valid mathematical model presented in this study.     

Influence of moderate Joule heating on electroosmotic flow velocity, retention, and efficiency in capillary electrochromatography

The influence of Joule heating on electroosmotic flow velocity, the retention factor of neutral analytes, and separation efficiency in capillary electrochromatography was investigated theoretically and experimentally. A plot of electrical current against the applied electrical field strength was used to evaluate the Joule heating effect. When the mobile phase concentration of Tris buffer exceeded 5.0 mM in the studied capillary electrochromatography systems using particulate and monolithic columns (with an accompanying power level of heat dissipation higher than 0.35 W/m), the Joule heating effect became clearly noticeable. Theoretical models for describing the variation of electroosmotic flow velocity with increasing applied field strength and the change of retention factors for neutral analytes with electrical field strength at higher Tris buffer concentrations were analyzed to explain consequences of Joule heating in capillary electrochromatography. Qualitative agreement between experimental data and implications of the theoretical model analysis was observed. The decrease of separation efficiency in capillary electrochromatography with macroporous octadecylsilica particles at high buffer concentration can be also attributed to Joule heating mainly via the increased axial diffusion of the analyte molecules and dispersion of solute bands by a nonuniform electroosmotic flow profile over the column cross-section. However, within a moderate temperature range, the contribution of the macroscopic velocity profile in the column arising from radial temperature gradients is insignificant.     

Continuous-Flow Nanoparticle Trapping Driven by Hybrid Electrokinetics in Microfluidics

We introduce herein an efficient microfluidic approach for continuous transport and localized collection of nanoparticles via hybrid electrokinetics, which delicately combines linear and nonlinear electrokinetics driven by a composite DC-biased AC voltage signal. The proposed technique utilizes a simple geometrical structure, in which one or a series of metal strips serving as floating electrode (FE) are attached to the substrate surface and arranged in parallel between a pair of coplanar driving electrodes (DE) in a straight microchannel. On application of a DC-biased AC electric field across the channel, nanoparticles can be transported continuously by DC bulk electroosmotic flow, and then trapped selectively onto the metal strips due to AC-field induced-charge electrokinetic (ICEK) phenomenon, which behaves as counter-rotating micro-vortices around the ideally polarizable surfaces of FE. Finite-element simulation is carried out by coupling the dual-frequency electric field, flow field and sample mass transfer in sequence, for guiding a practical design of the microfluidic nanoparticle concentrator. With the optimal device geometry, the actual performance of the technique is investigated with respect to DC bias, AC voltage amplitude, and field frequency by using both latex nanospheres (∼500 nm) and BSA molecules (∼10 nm). Our experimental observation indicates nanoparticles are always enriched into a narrow bright band on the surface of each FE, and a horizontal concentration gradient even emerges in the presence of multiple metal strips, which therefore permits localized analyte enrichment. The proposed trapping method is supposed to guide an elaborate design of flexible electrokinetic frameworks embedding FE for continuous-flow analyte manipulation in modern microfluidic systems.     

Analytical study of Joule heating effects on electrokinetic transportation in capillary electrophoresis

Electric fields are often used to transport fluids (by electroosmosis) and separate charged samples (by electrophoresis) in microfluidic devices. However, there exists inevitable Joule heating when electric currents are passing through electrolyte solutions. Joule heating not only increases the fluid temperature, but also produces temperature gradients in cross-stream and axial directions. These temperature effects make fluid properties non-uniform, and hence alter the applied electric potential field and the flow field. The mass species transport is also influenced. In this paper we develop an analytical model to study Joule heating effects on the transport of heat, electricity, momentum and mass species in capillary-based electrophoresis. Close-form formulae are derived for the temperature, applied electrical potential, velocity, and pressure fields at steady state, and the transient concentration field as well. Also available are the compact formulae for the electric current and the volume flow rate through the capillary. It is shown that, due to the thermal end effect, sharp temperature drops appear close to capillary ends, where sharp rises of electric field are required to meet the current continuity. In order to satisfy the mass continuity, pressure gradients have to be induced along the capillary. The resultant curved fluid velocity profile and the increase of molecular diffusion both contribute to the dispersion of samples. However, Joule heating effects enhance the sample transport velocity, reducing the analysis time in capillary electrophoretic separations.     

Temperature gradient focusing of bio-analyte in a microfluidic channel dealing with non-Newtonian electrolyte considering temperature-dependent zeta potential

Temperature gradient focusing (TGF) relies on establishing a precise balance between the electrophoretic motility of a target analyte and the advective flow of the background electrolyte (BGE) to locally concentrate the analyte in a microfluidic configuration. This paper presents a finite-element-based numerical analysis where the coupled electric field and the transport equations are solved to describe the effects of the shear-dependent apparent viscosity of a non-Newtonian BGE on the localized concentration buildup of a charged bio-sample inside a microchannel by TGF via Joule heating. Effects of the temperature-dependent nature of the wall zeta potential and the flow behavior index (n) of BGE on the flow, thermal, and species concentration profiles inside the microchannel have been investigated. Study using a fluorescein-Na analyte sample shows that the maximum normalized analyte concentration (C_max/C₀) reduces as the zeta potential increases linearly with temperature. The maximum concentration enhancement is achieved when the BGE displays the Newtonian rheology. For example, C_max/C₀ increases 134- to 280-fold when n is increased from 0.8 to 1 (pseudoplastic regime) and again reduces to 190-fold when n increases further from 1 to 1.2 (dilatant regime).     

Theoretical and numerical analysis of temperature gradient focusing via Joule heating

We present a detailed theoretical and numerical analysis of temperature gradient focusing (TGF) via Joule heating-an analytical species concentration and separation technique relying upon the dependence of an analyte's velocity on temperature due to the temperature dependence of a buffer's ionic strength and viscosity. The governing transport equations are presented, analyzed, and implemented into a quasi-1D numerical model to predict the resulting temperature, velocity, and concentration profiles along a microchannel of varying width under an applied electric field. Numerical results show good agreement with experimental trials presented in previous work. The model is used to analyze the effects of varying certain geometrical and experimental parameters on the focusing performance of the device. Simulations also help depict the separation capability of the device, as well as the effectiveness of different buffer systems used in the technique. The analysis provides rule-of-thumb methodology for implementation of TGF into analytical systems, as well as a fundamental model applicable to any lab-on-a-chip system in which Joule heating and temperature-dependent electrokinetic transport are to be analyzed.     

Electroosmotic flow in microchannels with arbitrary geometry and arbitrary distribution of wall charge

General solutions are developed for direct current (DC) and alternating current (AC) electroosmotic flows in microfluidic channels with arbitrary cross-sectional geometry and arbitrary distribution of wall charge (zeta potential). The applied AC electric field can also be of arbitrary waveform. By proposing a nondimensional time scale varpi defined as the ratio of the diffusion time of momentum across the electric double-layer thickness to the period of the applied electric field, we demonstrate analytically that the Helmholtz-Smoluchowski electroosmotic velocity is an appropriate slip condition for AC electroosmotic flows in typical microfluidic applications. With this slip condition approach, electroosmotic flows in rectangular and asymmetric trapezoidal microchannels with nonuniform wall charge, as examples, are investigated. The unknown constants in the proposed general solutions are numerically determined with a least-squares method through matching the boundary conditions. We find that the wall charge affects significantly the electroosmotic flow while the channel geometry does not. Moreover, the flow feature is characterized by another nondimensional time scale Omega defined as the ratio of the diffusion time of momentum across the channel hydraulic radius to the period of the applied electric field. The onset of phase shift between AC electroosmotic velocity and applied electric field is also examined analytically.     

Joule heating effects on electrokinetic flows with conductivity gradients

Instability occurs in the electrokinetic flow of fluids with conductivity and/or permittivity gradients if the applied electric field is beyond a critical value. Understanding such an electrokinetic instability is significant for both improved transport (via the suppressed instability) and enhanced mixing (via the promoted instability) of liquid samples in microfluidic applications. This work presents the first study of Joule heating effects on electrokinetic microchannel flows with conductivity gradients using a combined experimental and numerical method. The experimentally observed flow patterns and measured critical electric fields under Joule heating effects to different extents are reasonably predicted by a depth-averaged numerical model. It is found that Joule heating increases the critical electric field for the onset of electrokinetic instability because the induced fluid temperature rise and in turn the fluid property change (primarily the decreased permittivity) lead to a smaller electric Rayleigh number.     

Accumulation and trapping of hepatitis A virus particles by electrohydrodynamic flow and dielectrophoresis

Hepatitis A virus particles (d = 27 nm) were successfully accumulated and trapped in a microfluidic system by means of a combination of electrohydrodynamic flow and dielectrophoretic forces. Electric fields were generated in a field cage consisting of eight microelectrodes. In addition, high medium conductance (0.3 S/m) resulted in sufficient Joule heating and the corresponding spatial variation of temperature, density, and permittivity to induce electrohydrodynamic flow in the vicinity of the field cage. Flow vortices transport particles toward the center of the field cage, where dielectrophoretic forces cause permanent entrapment and particle aggregation. Spatial distribution of temperature, density, and permittivity as well as resulting flow patterns were modeled numerically and are in good agreement with experimental results. This accumulation scheme might be applicable to sample concentration enhancement in biosensor applications.     

Planar electrochromatography

Recent developments in planar electrochromatography (PEC) in both the normal-phase and the reversed-phase modes, and at both atmospheric and elevated pressure, are reviewed. Other forced-flow techniques in planar chromatography are also briefly covered. Mobile phase migration in PEC is primarily due to electroosmotic flow, which is controlled by the applied electric field. Capillary mediated flow is an important secondary contributor to migration, and occurs because the layer is unsaturated as a consequence of liquid evaporating from the layer due to Joule heating. The magnitude of the electric field and the concentration of ions in solution are important variables that control both electroosmotic flow and Joule heating. Separations are faster and more efficient than those obtained by conventional planar chromatography, provided appropriate experimental conditions are selected. With inappropriate conditions, either mobile phase accumulates on the surface of the sorbent layer, or Joule heating causes excessive evaporation. The former results in poor spot shape, and the latter can cause the layer to dry. Good separations are obtained when there is a balance between these two effects. The problems associated with mobile phase accumulating on the surface of the sorbent layer, and with excessive evaporation of mobile phase, do not occur with pressurized planar electrochromatography. This technique is performed at high pressure, under conditions that allow heat to be removed form the sorbent layer. This allows the use of a substantially higher electric field than in PEC, and results in a high mobile phase flow rate.     

Direct and indirect electroosmotic flow velocity measurements in microchannels

As microfluidic technologies mature, increasingly complex solutions are employed, and accurate methods for the measurement of electroosmotic flow rates are becoming increasingly important. The methodologies of both a direct method and an indirect method of flow rate measurement are presented here. The direct method involves flow visualization using trace amounts of a caged fluorescent dye. The indirect method is based on the change in current that occurs when one solution in the microchannel is replaced by another. The results of concurrent and independent measurements of electroosmotic velocities of Tris-acetate with EDTA (TAE) and Tris-borate with EDTA (TBE) at 1x concentration in fused silica capillaries are presented. Although these buffers are commonly used in biological chemistry, these mobilities have not previously been reported. Strong agreement among data collected with both methods establishes confidence in the electroosmotic mobility values obtained and indicates that the current-based method, which requires less infrastructure than the direct method, can provide accurate flow rate measurements under these conditions. Constant electroosmotic mobilities of 4.90 x 10(-8) m(2) V(-1) s(-1) for TAE and 3.10 x 10(-8) m(2) V(-1) s(-1) for TBE were determined by tests in a range of electrical field strengths from 5 to 20 kV/m. A linear flow rate increase with applied field strength indicated that constant mobility and negligible Joule heating effects were present. Applicability and limitations of both the measurement methods and these buffers are discussed in the context of microfluidic applications.     

Estimation of Joule heating effect on temperature and pressure distribution in electrokinetic-driven microchannel flows

In this study we present simple analytical models that predict the temperature and pressure variations in electrokinetic-driven microchannel flow under the Joule heating effect. For temperature prediction, a simple model shows that the temperature is related to the Joule heating parameter, autothermal Joule heating parameter, external cooling parameter, Peclet number, and the channel length to channel hydraulic diameter ratio. The simple model overpredicted the thermally developed temperature compared with the full numerical simulation, but in good agreement with the experimental measurements. The factors that affect the external cooling parameters, such as the heat transfer coefficient, channel configuration, and channel material are also examined based on this simple model. Based on the mass conservation, a simple model is developed that predicts the pressure variations, including the temperature effect. An adverse pressure gradient is required to satisfy the mass conservation requirement. The temperature effect on the pressure gradient is via the temperature-dependent fluid viscosity and electroosmotic velocity.     

Analytical and numerical study of Joule heating effects on electrokinetically pumped continuous flow PCR chips

Joule heating is an inevitable phenomenon for microfluidic chips involving electrokinetic pumping, and it becomes a more important issue when chips are made of polymeric materials because of their low thermal conductivities. Therefore, it is very important to develop methods for evaluating Joule heating effects in microfluidic chips in a relatively easy manner. To this end, two analytical models have been established and solved using the Green's function for evaluating Joule heating effects on the temperature distribution in a microfluidic-based PCR chip. The first simplified model focuses on the understanding of Joule heating effects by ignoring the influences of the boundary conditions. The second model aims to consider practical experimental conditions. The analytical solutions to the two models are particularly useful in providing guidance for microfluidic chip design and operation prior to expensive chip fabrication and characterization. To validate the analytical solutions, a 3-D numerical model has also been developed and the simultaneous solution to this model allows the temperature distribution in a microfluidic PCR chip to be obtained, which is used to compare with the analytical results. The developed numerical model has been applied for parametric studies of Joule heating effects on the temperature control of microfluidic chips.     

Numerical modeling of the Joule heating effect on electrokinetic flow focusing

In electrokinetically driven microfluidic systems, the driving voltage applied during operation tends to induce a Joule heating effect in the buffer solution. This heat source alters the solution's characteristics and changes both the electrical potential field and the velocity field during the transport process. This study performs a series of numerical simulations to investigate the Joule heating effect and analyzes its influence on the electrokinetic focusing performance. The results indicate that the Joule heating effect causes the diffusion coefficient of the sample to increase, the potential distribution to change, and the flow velocity field to adopt a nonuniform profile. These variations are particularly pronounced under tighter focusing conditions and at higher applied electrical intensities. In numerical investigations, it is found that the focused bandwidth broadens because thermal diffusion effect is enhanced by Joule heating. The variation in the potential distribution induces a nonuniform flow field and causes the focused bandwidth to tighten and broaden alternately as a result of the convex and concave velocity flow profiles, respectively. The present results confirm that the Joule heating effect exerts a considerable influence on the electrokinetic focusing ratio.     

Joule heating and heat transfer in poly(dimethylsiloxane) microfluidic systems

Joule heating is a significant problem in electrokinetically driven microfluidic chips, particularly polymeric systems where low thermal conductivities amplify the difficulty in rejecting this internally generated heat. In this work, a combined experimental (using a microscale thermometry technique) and numerical (using a 3D "whole-chip" finite element model) approach is used to examine Joule heating and heat transfer at a microchannel intersection in poly(dimethylsiloxane)(PDMS), and hybrid PDMS/Glass microfluidic systems. In general the numerical predictions and the experimental results agree quite well (typically within +/- 3 degree C), both showing dramatic temperature gradients at the intersection. At high potential field strengths a nearly five fold increase in the maximum buffer temperature was observed in the PDMS/PDMS chips over the PDMS/Glass systems. The detailed numerical analysis revealed that the vast majority of steady state heat rejection is through lower substrate of the chip, which was significantly impeded in the former case by the lower thermal conductivity PDMS substrate. The observed higher buffer temperature also lead to a number of significant secondary effects including a near doubling of the volume flow rate. Simple guidelines are proposed for improving polymeric chip design and thereby extend the capabilities of these microfluidic systems.