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.     

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.     

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 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.     

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.     

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.     

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.     

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...     

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.     

Study of Joule heating effects on temperature gradient in diverging microchannels for isoelectric focusing applications

IEF is a high-resolution separation method taking place in a medium with continuous pH gradients, which can be set up by applying electrical field to the liquid in a diverging microchannel. The axial variation of the channel cross-sectional area will induce nonuniform Joule heating and set up temperature gradient, which will generate pH gradient when proper medium is used. In order to operationally control the thermally generated pH gradients, fundamental understanding of heat transfer phenomena in microfluidic chips with diverging microchannels must be improved. In this paper, two 3-D numerical models are presented to study heat transfer in diverging microchannels, with static and moving liquid, respectively. Through simulation, the temperature distribution for the entire chip has been revealed, including both liquid and solid regions. The model for the static liquid scenario has been compared with published results for validation. Parametric studies have showed that the channel geometry has significant effects on the peak temperature location, and the electrical conductivity of the medium and the wall boundary convection have effects on the generated temperature gradients and thus the generated pH gradients. The solution to the continuous flow model, where the medium convection is considered, shows that liquid convection has significant effects on temperature distribution and the peak temperature location.     

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.     

Joule heating effects on separation efficiency in capillary zone electrophoresis with an initial voltage ramp

An analytical model is developed to quantify the Joule heating effects on the separation efficiency in CZE with an initial voltage ramp. This model considers the temporal variations of nonuniform temperature and flow fields in the course of voltage ramping. The temperature dependence of electrical conductivity, dynamic viscosity, and mass density of the fluid is also taken into account. We demonstrate that the application of an initial voltage ramp delays the development of pressure-driven flows induced passively by the axial temperature gradients. The thermal dispersion is thus significantly reduced, resulting in a higher theoretical plate number in CZE. Such improvement in the separation efficiency is apparent in noncoated capillaries at high electric fields with an appropriate voltage ramp-up time. These predictions are consistent with previous observations in both aqueous and nonaqueous CZE that took place in uncoated capillaries. In coated capillaries where the EOF is suppressed, however, our model predicts a lower plate number in the presence of an initial voltage ramp.     

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.     

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.     

Role of Joule heating in dispersive mixing effects in electrophoretic cells: convective-diffusive transport aspects

This contribution addresses the problem of solute dispersion in a free convection electrophoretic cell for the batch mode of operation, caused by the Joule heating generation. The problem is analyzed by using the two-problem approach originally proposed by Bosse and Arce (Electrophoresis 2000, 21, 1018-1025). The approach identifies the carrier fluid problem and the solute problem. This contribution is focused on the latter. The strategy uses a sequential coupling between the energy, momentum and mass conservation equations and, based on geometrical and physical assumptions for the system, leads to the derivation of analytical temperature and velocity profiles inside the cell. These results are subsequently used in the derivation of the effective dispersion coefficient for the cell by using the method of area averaging. The result shows the first design equation that relates the Joule heating effect directly to the solute dispersion in the cell. Some illustrative results are presented and discussed and their implication to the operation and design of the device is addressed. Due to the assumptions made, the equation may be viewed as an upper boundary for applications such as free flow electrophoresis.     

Experimental study and numerical estimation of current changes in electroosmotically pumped microfluidic devices

Electroosmotic flow (EOF) was investigated in microfabricated fluidic devices using the current monitoring technique. Current changes ranging from 50 to 130 pA/s were detected. These observations indicate that in microfluidic devices with small reservoir volumes, electrolysis of water influences the fluid transport, giving rise to changes in pH and increase in concentration of ionic species in the fluidic system. As a result of the electrolysis and associated increment in ion concentration, the thickness of the Debye layer and surface potential vary, affecting the overall migration behavior of the solution. The magnitude of EOF and the electrophoretic properties of molecules can no longer be treated as constant/invariant. These temporal anomalies are undesirable during analytical separations and in fluid control applications. A numerical analysis of the impact of the continuous ionic strength increase on the EOF dynamics is presented using well-established conduction and EOF theories. The numerical results are found to be in good agreement with the observed current changes. These results indicate that to improve assay reproducibility, monitoring the electric current is an effective tool to determine whether electrolytic reactions are taking place. Our work also serves to test the numerical accuracy of EOF theories and models.     

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.     

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.