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.     

Effect of Joule heating on electrokinetic transport

The Joule heating (JH) is a ubiquitous phenomenon in electrokinetic flow due to the presence of electrical potential gradient and electrical current. JH may become pronounced for applications with high electrical potential gradients or with high ionic concentration buffer solutions. In this review, an in-depth look at the effect of JH on electrokinetic processes is provided. Theoretical modeling of EOF and electrophoresis (EP) with the presence of JH is presented and the important findings from the previous studies are examined. A numerical study of a fused-silica capillary PCR reactor powered by JH is also presented to extend the discussion of favorable usage of JH.     

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.     

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.     

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.     

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.     

An entropy approach of Williamson nanofluid flow with Joule heating and zero nanoparticle mass flux

Journal of Thermal Analysis and Calorimetry - The important focus of this research is to investigate the features of MHD radiative Williamson nanofluid flow caused by a stretchable surface...     

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.     

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.     

Quantification and evaluation of Joule heating in on-chip capillary electrophoresis

We present the use of a novel, picoliter volume interferometer to measure, for the first time, the extent of Joule heating in chip-scale capillary electrophoresis (CE). The simple optical configuration for the on-chip interferometric backscatter detector (OCIBD) consists of an unfocused laser, an unaltered silica chip with a half-cylinder channel and a photodetector. Using OCIBD for millidegree-level noninvasive thermometry, temperature changes associated with Joule heating (2.81 degrees C above ambient) in on-chip CE have been observed in 90 microm wide and 40 microm deep separation channels. The temporal response of Joule heating in isotropically etched channels was exponential, with it taking an excess of 2.7 s to reach equilibrium. Buffer viscosity changes have also been derived from empirical on-chip thermometry data, allowing for the determination of diffusion coefficients for solutes when separated in heated buffers. In addition, OCIBD has allowed the reduction in separation efficiency to be estimated in the absence of laminar flow and due to increased molecular diffusion and lower buffer viscosity. A 7% reduction in separation efficiency was determined for a high current drawing buffer such as Tris-boric acid under an applied field of just 400 V/cm. Results indicate that heating effects in on-chip CE have been underestimated and there is a need to readdress the theoretical model.     

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.     

Reliable electrophoretic mobilities free from Joule heating effects using CE

Ionic electrophoretic mobilities determined by means of CE experiments are sometimes different when compared to generally accepted values based on limiting ionic conductance measurements. While the effect of ionic strength on electrophoretic mobility has been long understood, the increase in the mobility that results from Joule heating (the resistive heating that occurs when a current passes through an electrolyte) has been largely overlooked. In this work, a simple method for obtaining reliable and reproducible values of electrophoretic mobility is described. The electrophoretic mobility is measured over a range of driving powers and the extrapolation to zero power dissipation is employed to eliminate the effect of Joule heating. These extrapolated values of electrophoretic mobility can then be used to calculate limiting ionic mobilities by making a correction for ionic strength; this somewhat complicated calculation is conveniently performed by using the freeware program PeakMaster 5. These straightforward procedures improve the agreement between experimentally determined and literature values of limiting ionic mobility by at least one order of magnitude. Using Tris-chromate BGE with a value of conductivity 0.34 S/m and ionic strength 59 mM at a modest dissipated power per unit length of 2.0 W/m, values of mobility for inorganic anions were increased by an average of 12.6% relative to their values free from the effects of Joule heating. These increases were accompanied by a reduction in mobilities due to the ionic strength effect, which was 11% for univalent and 28% for divalent inorganic ions compared to their limiting ionic mobilities. Additionally, it was possible to determine the limiting ionic mobility for a number of aromatic anions by using PeakMaster 5 to perform an ionic strength correction. A major significance of this work is in being able to use CE to obtain reliable and accurate values of electrophoretic mobilities with all its benefits, including understanding and interpretation of physicochemical phenomena and the ability to model and simulate such phenomena accurately.     

Accessing DNA by low voltage alternating current Joule effect heating

A DNA release sample preparation method based on the use of low voltage alternating currents (LVACs) to generate Joule effect heating (JEH) is reported. This is a simple cell disruption strategy that offers internal, homogenous, rapid and low power consumption heating for the access of analytical grade DNA in seconds.A 100 μL JEH microreactor with a parallel and symmetric two electrode arrangement for uniform field generation was fabricated by machining and used to characterise JEH and DNA release from human epithelia, yeast (Saccharomyces cerevisiae) and Gram-positive bacteria (Enterococcus faecium) cell types. A 1 kHz sinusoidal low voltage (e.g. 10 Vrms) alternating current was used to reduce electrode:sample interactions. Following 96 °C JEH treatment, effective DNA release was identified by PicoGreen^® quantification for all three cell types. The JEH treated sample material was further successfully used, without purification, as a PCR template. Exposure to JEH-mediated 96 °C temperatures for a 1 s duration was used to provide PCR-grade DNA template material from S. cerevisiae and E. faecium cells, and a 10 s duration was used for human epithelia cells. However, prolonged (>1 min) exposure to 96 °C JEH-mediated temperatures resulted in diminished DNA returns and the production of components that interfered with the PCR reaction.Further miniaturisation of the LVAC JEH cell by microfabrication was considered, and a JEH microreactor designs were evaluated by FLOTHERM v3.2 thermal modelling. Thermal isolation, using a free-standing cavity structure was identified as an excellent means to enable rapid heating (220 °C s⁻¹) with low power consumption (0.2 W).     

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.     

Revisit of Joule heating in CE: the contribution of surface conductance

We present in this short communication the true form of Joule heating in CE which considers the contribution of surface conductance. This increased conductivity of electrolyte solution within electrical double layer has never been discussed in previous studies. The resultant intensive heat generation near the capillary wall is demonstrated using numerical simulation to produce not a locally strong temperature rise, but an additional temperature elevation in the whole solution compared to the model neglecting surface conductance. The latter effect is, however, negligible in typical CE while it might become significant in very small channels.     

Precise temperature control in microfluidic devices using Joule heating of ionic liquids

Microfluidic devices for spatially localised heating of microchannel environments were designed, fabricated and tested. The devices are simple to implement, do not require complex manufacturing steps and enable intra-channel temperature control to within +/-0.2 degrees C. Ionic liquids held in co-running channels are Joule heated with an a.c. current. The nature of the devices means that the internal temperature can be directly assessed in a facile manner.     

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.     

Joule heating and determination of temperature in capillary electrophoresis and capillary electrochromatography columns

This article reviews the progress that has taken place in the past decade on the topic of estimation of Joule heating and temperature inside an open or packed capillary in electro-driven separation techniques of capillary electrophoresis (CE) and capillary electrochromatography (CEC), respectively. Developments in theoretical modeling of the heat transfer in the capillary systems have focused on attempts to apply the existing models on newer techniques such as CEC and chip-based CE. However, the advent of novel analytical tools such as pulsed magnetic field gradient nuclear magnetic resonance (NMR), NMR thermometry, and Raman spectroscopy, have led to a revolution in the area of experimental estimation of Joule heating and temperature inside the capillary via the various noninvasive techniques. This review attempts to capture the major findings that have been reported in the past decade.     

A dynamic molecular probe to investigate catalytic effects and Joule heating in enantioselective MEKC

Enantiomerization of ferroin [tris(1,10-phenanthroline)-iron(II)-complex] was investigated by enantioselective dynamic micellar EKC. The enantiomer separation was performed in an aqueous 50 mM sodium borate/sodium dihydrogenphosphate buffer at pH 8.0 in the presence of the chiral surfactant sodium cholate. The unified equation of dynamic chromatography was employed to determine reaction rate constants from the electropherograms featured with distinct plateau formation. Activation parameters DeltaH( not equal) = 124.0 +/- 0.5 kJ/mol and DeltaS( not equal) = 121 +/- 1 J.K(-1)mol(-1) were calculated from temperature-dependent measurements between 10.0 and 27.5 degrees C in 2.5 K steps. Considering the data obtained by polarimetry of enantiomeric pure ferroin in water, it was found that enantiomerization rate in the micelle is accelerated by a factor of 12. Because of the highly positive activation entropy DeltaS( not equal), ferroin was used as a temperature-sensitive dynamic molecular probe to determine temperature deviations caused by Joule heating.