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.     

Band-broadening in capillary zone electrophoresis with axial temperature gradients

It is widely accepted that Joule heating effects yield radial temperature gradients in capillary zone electrophoresis (CZE). The resultant parabolic profile of electrophoretic velocity of analyte molecules is believed to increase the band-broadening via Taylor-Aris dispersion. This typically insignificant contribution, however, cannot explain the decrease in separation efficiency at high electric fields. We show that the additional band-broadening due to axial temperature gradients may provide the answer. These axial temperature variations result from the change of heat transfer condition along the capillary, which is often present in CZE with thermostating. In this case, the electric field becomes nonuniform due to the temperature dependence of fluid conductivity, and hence the induced pressure gradient is brought about to meet the mass continuity. This modification of the electroosmotic flow pattern can cause significant band-broadening. An analytical model is developed to predict the band-broadening in CZE with axial temperature gradients in terms of the theoretical plate height. We find that the resultant thermal plate height can be very high and even comparable to that due to molecular diffusion. This thermal plate height is much higher than that due to radial temperature gradients alone. The analytical model explains successfully the phenomena observed in previous experiments.     

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.     

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.     

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.     

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 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.     

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 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.     

Sample transport and electrokinetic injection in a microchip device for chemical cytometry

Sample transport and electrokinetic injection bias are well characterized in capillary electrophoresis and simple microchips, but a thorough understanding of sample transport on devices combining electroosmosis, electrophoresis, and pressure-driven flow is lacking. In this work, we evaluate the effects of electric fields from 0 to 300 V/cm, electrophoretic mobilities from 10(-4) to 10(-6) cm(2)/Vs, and pressure-driven fluid velocities from 50 to 250 μm/s on sample injection in a microfluidic chemical cytometry device. By studying a continuous sample stream, we find that increasing electric field strength and electrophoretic mobility result in improved injection and that COMSOL simulations accurately predict sample transport. The effects of pressure-driven fluid velocity on injection are complex, and relative concentration values lie on a surface defined by pressure-driven flow rates. For high-mobility analytes, this surface is flat, and sample injection is robust despite fluctuations in flow rate. For lower mobility analytes, the surface becomes steeper, and injection depends strongly on pressure-driven flow. These results indicate generally that device design must account for analyte characteristics and specifically that this device is suited to high-mobility analytes. We demonstrate that for a suitable pair of peptides fluctuations in injection volume are correlated; electrokinetic injection bias is minimized; and electrophoretic separation is achieved.     

In-line application of electric field in capillary separation systems: Joule heating, pH and conductivity

This study concerns the technique electric field-assisted capillary liquid chromatography. In this technique, an electric field is applied over the separation capillary in order to provide an additional selectivity. In this technique, the electric field is applied in-line in the separation capillary and here the electric current is the factor limiting the magnitude of applied electric field. The influence of Joule heating and other factors on the current in such systems has been investigated. The temperature in the capillary was first measured within a standard CE set-up, as function of effect per unit of length. Then the same cooling system was applied to an in-line set-up, to replicate the conditions between the two systems, and thus the temperature. Thus Joule heating effects could then be calculated within the in-line system. It was found that for systems applying an electric field in line, the direct influence from Joule heating was only relatively small. The pH in the capillary was measured in the in-line set-up using cresol red/TRIS solutions as pH probe. Significant changes in pH were observed and the results suggested that electrolysis of water is the dominant electrode reaction in the in-line system. In summary, the observed conductivity change in in-line systems was found to be mainly due to the pH change by hydrolysis of water, but primarily not due the temperature change in the capillary column.     

Effect of Joule heating on efficiency and performance for microchip-based and capillary-based electrophoretic separation systems: a closer look

An attempt is made to revisit the main theoretical considerations concerning temperature effects ("Joule heating") in electro-driven separation systems, in particular lab-on-a-chip systems. Measurements of efficiencies in microfabricated devices under different Joule heating conditions are evaluated and compared to both theoretical models and measurements performed on conventional capillary systems. The widely accepted notion that planar microdevices are less susceptible to Joule heating effects is largely confirmed. The heat dissipation from a nonthermostatically controlled glass microdevice was found to be comparable to that from a liquid-cooled-fused silica capillary. Using typically dimensioned glass and glass/silicon microdevices, the experimental results indicate that 5-10 times higher electric field strengths can be applied than on conventional capillaries, before detrimental effects on the separation efficiency occur. The main influence of Joule heating on efficiency is via the establishment of a radial temperature profile across the lumen of the capillary or channel. An overall temperature increase of the buffer solution has only little influence on the quality of the separation. Still, active temperature control (cooling, thermostatting) can help prevent boiling of the buffer and increase the reproducibility of the results.     

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.     

Joule heating-enabled electrothermal enrichment of nanoparticles in insulator-based dielectrophoretic microdevices

Insulator-based dielectrophoresis (iDEP) exploits the electric field gradients formed around insulating structures to manipulate particles for diverse microfluidic applications. Compared to the traditional electrode-based dielectrophoresis, iDEP microdevices have the advantages of easy fabrication, free of water electrolysis, and robust structure, etc. However, the presence of in-channel insulators may cause thermal effects because of the locally amplified Joule heating of the fluid. The resulting electrothermal flow circulations are exploited in this work to trap and concentrate nanoscale particles (of 100 nm diameter and less) in a ratchet-based iDEP microdevice. Such Joule heating-enabled electrothermal enrichment of nanoparticles are found to grow with the increase of alternating current or direct current electric field. It also becomes more effective for larger particles and in a microchannel with symmetric ratchets. Moreover, a depth-averaged numerical model is developed to understand and simulate the various parametric effects, which is found to predict the experimental observations with a good agreement.     

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.     

A simple method for assessment and minimization of errors in determination of electrophoretic or electroosmotic mobilities and velocities associated with the axial electric field distortion

It is commonly accepted that the modern CE instruments equipped with efficient cooling system enable accurate determination of electrophoretic or electroosmotic mobilities. It is also often assumed that velocity of migration in a given buffer is constant throughout the capillary length. It is simultaneously neglected that the noncooled parts of capillary produce extensive Joule heating leading to an axial electric field distortion, which contributes to a difference between the effective and nominal electric field potentials and between velocities in the cooled and noncooled parts of capillary. This simplification introduces systematic errors, which so far were however not investigated experimentally. There was also no method proposed for their elimination. We show a simple and fast method allowing for estimation and elimination of these errors that is based on combination of a long‐end and short‐end injections. We use it to study the effects caused by variation of temperature, electric field, capillary length, and pH.     

Electrokinetic transport through the nanopores in cell membrane during electroporation

In electroporation, applied electric field creates hydrophilic nanopores in a cell membrane that can serve as a pathway for inserting biological samples to the cell. It is highly desirable to understand the ionic transfer and fluid flow through the nanopores in order to control and improve the cell transfection. Because of submicron dimensions, conventional theories of electrokinetics may lose their applicability in such nanopores. In the current study, the Poisson-Nernst-Planck equations along with modified Navier-Stokes equations and the continuity equation are solved in order to find electric potential, fluid flow, and ionic concentration through the nanopores. The results show that the electric potential, velocity field, and ionic concentration vary with the size of the nanopores and are different through the nanopores located at the front and backside of the cell membrane. However, on a given side of the cell membrane, angular position of nanopores has fewer influences on liquid flow and ionic transfer. By increasing the radius of the nanopores, the averaged velocity and ionic concentration through the nanopores are increased. It is also shown that, in the presence of electric pulse, electrokinetic effects (electroosmosis and electrophoresis) have significant influences on ionic mass transfer through the nanopores, while the effect of diffusion on ionic mass flux is negligible in comparison with electrokinetics. Increasing the radius of the nanopores intensifies the effect of convection (electroosmosis) in comparison with electrophoresis on ionic flux.     

Free-flow zone electrophoresis: a novel approach and scale-up for preparative protein separation

Different continuously working free-flow zone electrophoresis (FFZE) chambers have already been developed [1, 2]. All of them deal with the problem of distinctive Joule heating. The resulting temperature gradients cause an unstable density field which leads to thermal convection and thus to an intermixing of the different fractions within the chamber. The most promising and simple approach to stabilize the flow is to build chambers with one very small dimension (e.g., h = 0.5 mm) to assure efficient heat withdrawal. This in turn presents substantial disadvantages, namely limited throughput and restricted scale-up potential. The novel approach combines a simplified design and assembly with the possibility of straightforward scale-up. It still operates with one small dimension (d = 1-2 mm) to handle the Joule heating. Here, however, not the dimension perpendicular to the electric field but the dimension parallel to the electric field (separation distance) is chosen as the smallest dimension. The efficiency of the new device is shown by the separation of bovine serum albumin (BSA) and cytochrome c with an overall protein throughput of up to 1.1 g/h, using a cell with a separation volume of less than 20 mL.     

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.