Effect of the Joule heating and of the material voids on free-convective transport in porous or fibrous media with applied electrical fields

The effect of the geometry of the soil in electrokinetic application has been studied by using capillary models of annular geometry. The Joule heating generation has been included as a primary effect of temperature development leading to buoyancy flows. The heat transfer model has been formulated for conduction-dominated regime. The results of this model have been coupled with the motion equation to obtain the analytical hydrodynamic velocity profile. Numerical illustrations, demonstrating the effect of the cross-sectional area of the annular region on the velocity field, have been included. It is observed that a substantial effect on the magnitude of such velocity field for different parameters of the system. The results are useful to obtain better understanding of the role of the soil geometry in potential soil cleaning field operations.     

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 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.     

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.     

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.     

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.     

The role of Joule heating in dispersive mixing effects in electrophoretic cells: hydrodynamic considerations

The analysis described in this contribution is focused on the effect of Joule heating generation on the hydrodynamics of batch electrophoretic cells (i.e., cells that do not display a forced convective term in the motion equation). The hydrodynamics of these cells is controlled by the viscous forces and by the buoyancy force caused by the temperature gradients due to the Joule heating generation. The analysis is based on differential models that lead to analytical and/or asymptotic solutions for the temperature and velocity profiles of the cell. The results are useful in determining the characteristics of the temperature and velocity profiles inside the cell. Furthermore, the results are excellent tools to be used in the analysis of the dispersive-mixing of solute when Joule heating generation must be accounted for. The analysis is performed by identifying two sequentially coupled problems. Thus, the "carrier fluid problem" and the "solute problem" are outlined. The former is associated with all the factors affecting the velocity profile and the latter is related to the convective-diffusion aspects that control the spreading of the solute inside the cell. The analysis of this contribution is centered on the discussion of the "carrier fluid problem" only. For the boundary conditions selected in the contribution, the study leads to the derivation of an analytical temperature and a "universal" velocity profile that feature the Joule heating number. The Grashof number is a scaling factor of the actual velocity profile. Several characteristics of these profiles are studied and some numerical illustrations have been included.     

Towards high concentration enhancement of microfluidic temperature gradient focusing of sample solutes using combined AC and DC field induced Joule heating

It is challenging to continuously concentrate sample solutes in microfluidic channels. We present an improved electrokinetic technique for enhancing microfluidic temperature gradient focusing (TGF) of sample solutes using combined AC and DC field induced Joule heating effects. The introduction of an AC electric field component services dual functions: one is to produce Joule heat for generating temperature gradient; the other is to suppress electroosmotic flow. Consequently the required DC voltages for achieving sample concentration by Joule heating induced TGF are reduced, thereby leading to smaller electroosmotic flow (EOF) and thus backpressure effects. As a demonstration, the proposed technique can lead to concentration enhancement of sample solutes of more than 2500-fold, which is much higher than the existing literature reported microfluidic concentration enhancement by utilizing the Joule heating induced TGF technique.     

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.     

A new zwitterionic electrochromatographic stationary phase based on poly(3‐chloro‐2‐hydroxypropyl methacrylate‐co‐ethylene dimethacrylate) reactive monolith

A new reactive monolith, poly(3‐chloro‐2‐hydroxypropyl methacrylate‐co‐ethylene dimethacrylate), poly(HPMA‐Cl‐co‐EDMA) was synthesized and post‐functionalized by taurine (2‐aminoethane sulfonic acid) to obtain a zwitterionic stationary phase for capillary electrochromatography. The new stationary phase contained charged groups such as secondary amine providing anodic electroosmotic flow and sulfonic acid groups providing cathodic electroosmotic flow. Hence, the capillary electrochromatography separations with the new zwitterionic monolith were performed with either anodic or cathodic electroosmotic flow. The electrochromatographic separation of alkylbenzenes and phenols was successfully performed. The zwitterionic monolith also allowed the separation of nucleosides using only electrokinetic mode. Theoretical plate numbers up to ~10⁵ plates/m were achieved. Our study is the first report based on poly(HPMA‐Cl‐co‐EDMA) reactive monolith post‐functionalized with a zwitterionic ligand allowing to operate in both anodic and cathodic electroosmotic flow modes. Copyright © 2014 John Wiley & Sons, Ltd.     

Stepwise gradient of buffer concentration for capillary electrochromatography of peptides on sulfonated naphthalimido-modified silyl silica gel

The advantage of using a stepwise gradient of buffer concentration in CEC was demonstrated with the mixed-mode stationary phase, 3-(4-sulfo-1,8-naphthalimido)propyl-modified silyl silica gel (SNAIP). Before the application of a stepwise gradient, the effect of buffer concentration on the separations of six peptides and tryptic digests was investigated. Bubble formation caused by Joule heating at currents up to 95 microA was successfully suppressed by using SNAIP column even without pressurization, which contributed to a stepwise gradient of buffer concentration. Utilizing the stepwise gradient improved and shortened the separation of six peptides as compared to the separation under an isocratic elution.     

Investigation into the Formation of Bubbles in Capillary Electrochromatography

The formation of bubbles in capillary electrochromatography (CEC) is well documented: possible origins include Joule heating and variations in EOF velocity on passing from the stationary phase through the frit and into the open tube. Methods for the prevention of bubble formation are discussed which are confirmed by experimental results. Using frit lengths varying from 1 mm to 6 mm it is shown how frit length is directly related to the likelihood of bubble formation and how this is affected by applied voltage. It is shown that the change in applied voltage across a capillary affects the formation of bubbles and also that rebonding octadecylsilane (ODS) onto the silica frit after formation of the frit can minimize the formation of bubbles and how this effects the chromatography. A method is also described for increasing the robustness of silica capillaries using a column coupler along with modifications made to conventional capillary electrophoresis equipment to cater for CEC.     

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.     

电色谱塔板高度方程的推导

比较了电色谱与高效液相色谱在动力学过程方面的异同。从热传导方程出发导出在有源无限长均匀圆柱体内温度场分布函数及组分移动速度径向分布函数,进而导出了温度场导致谱带弥散的弥散系数Ｄ热。提出了较全面地反映电色谱动力学过程的塔板高度方程,从而为改进柱型、选择电色谱分离条件提供了理论参考。     

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 in electrokinetic flow

Electrokinetic flow is an efficient means to manipulate liquids and samples in lab-on-a-chip devices. It has a number of significant advantages over conventional pressure-driven flow. However, there exists inevitable Joule heating in electrokinetic flow, which is known to cause temperature variations in liquids and draw disturbances to electric, flow and concentration fields via temperature-dependent material properties. Therefore, both the throughput and the resolution of analytic studies performed in microfluidic devices are affected. This article reviews the recent progress on the topic of Joule heating and its effect in electrokinetic flow, particularly the theoretical and experimental accomplishments from the aspects of fluid mechanics and heat/mass transfer. The primary focus is placed on the temperature-induced flow variations and the accompanying phenomena at the whole channel or chip level.     

毛细管反相电色谱法分离行为的研究

对乙睛-水-磷酸二氢销体系毛细管反相电色谱分离行为进行了研究。采用柱上紫外检测,在75μmi.d.×30cm的毛细管ODS（3μm）填充柱上获得了小于2.0的折合培板高度。同时还研究了乙睛的比例、电解质的浓度和电场强度等因素对电渗流和往效的影响。     

Joule heating in packed capillaries used in capillary electrochromatography

Effective heat dissipation is critical for reproducible and efficient separations in electrically driven separation systems. Flow rate, retention kinetics, and analyte diffusion rates are some of the characteristics that are affected by variation in the temperature of the mobile phase inside the column. In this study, we examine the issue of Joule heating in packed capillary columns used in capillary electrochromatography (CEC). As almost all commonly used CEC packings are poor thermal conductors, it is assumed that the packing particles do not conduct heat and heat transfer is solely through the mobile phase flowing through the system. The electrical conductivity of various mobile phases was measured at different temperatures by a conductivity meter and the temperature coefficient for each mobile phase was calculated. This was followed by measurement of the electrical current at several applied voltages to calculate the conductivity of the solution within the column as a function of the applied voltage. An overall increase in the conductivity is attributed to Joule heating within the column, while a constant conductivity means good heat dissipation. A plot of conductivity versus applied voltage was used as the indicator of poor heat dissipation. Using theories that have been proposed earlier for modeling of Joule heating effects in capillary electrophoresis (CE), we estimated the temperature within CEC columns. Under mobile and stationary phase conditions typically used in CEC, heat dissipation was found to be not always efficient. Elevated temperatures within the columns in excess of 23 degrees C above ambient temperature were calculated for packed columns, and about 35 degrees C for an open column, under a given set of conditions. The results agree with recently published experimental findings with nuclear magnetic resonance (NMR) thermometry, and Raman spectroscopic measurements.     

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.     

Harnessing Joule heating in microfluidic thermal gel electrophoresis to create reversible barriers for cell enrichment

Gel electrophoresis is a ubiquitous bioanalytical technique used to characterize the components of cell lysates. However, analyses of bulk lysates sacrifice detection sensitivity because intracellular biomolecules become diluted, and the liberation of proteases and nucleases can degrade target analytes. This report describes a method to enrich cells directly within a microfluidic gel as a first step toward online measurement of trace intracellular biomolecules with minimal dilution and degradation. Thermal gels were employed as the gel matrix because they can be reversibly converted between liquid and solid phases as a function of temperature. Rather than fabricate costly heating elements into devices to control temperature—and thus the phase of the gel—Joule heating was used instead. Adjoining regions of liquid-phase and solid-phase gel were formed within microfluidic channels by selectively inducing localized Joule heat. Cells migrated through the liquid gel but could not enter the solid gel—accumulating at the liquid–solid gel boundary—whereas small molecule contaminants passed through to waste. Barriers were then liquified on-demand by removing Joule heat to collect the purified, non-lysed cells for downstream analyses. Using voltage-controlled Joule heating to regulate the phase of thermal gels is an innovative approach to facilitate in-gel cell enrichment in low-cost microfluidic devices.