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.     

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

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

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

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

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.     

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.     

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.     

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。     

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.     

Infrared-based temperature measurements in capillary electrophoresis

In capillary electrophoresis (CE), the temperature inside the capillary is one of the most important parameters. In a concept for Analytical Instrument Qualification (AIQ) of CE systems, the temperature accuracy and stability have to be included. This fact requires an accurate look at the measurement of temperature which is generated by the applied electrical power. The generation of Joule heating is measured on the outside of the capillary using an infrared (IR) thermometer. The thermometer linearity is demonstrated over a wide range of various electrical field strength, buffer systems, and different capillary inner diameters. A slope of 6.3 °C m/W was found for the optimal thermometer capillary distance of 8 mm. Furthermore, the temperature measurements are highly precise, depending almost solely on the current variability. The proposed method is compared with three methods calculating the temperature from the conductance, the electroosmotic velocity, or the current. These indirect methods estimate slopes ranging from 7 to 10 °C m/W. In addition, the maximal suitable electrical power per unit length is estimated. Joule heating can often be tolerated up to 4 W/m. However, sensitive analytes can already be affected by using more than 1 W/m. In conclusion, the consideration of the temperature is essential for not only Analytical Instrument Qualification, but also certainly useful for method optimisation and method transfer.     

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.     

Variation of zeta-potential with temperature in fused-silica capillaries used for capillary electrophoresis

The temperature variation of electroosmotic mobility corrected for the effects of Joule heating (muEOF0) was employed to investigate the variation of the zeta-potential (zeta) with temperature in fused-silica capillaries. Experimentally determined values for zeta increased at 0.39% per degrees C, a rate that is about four to five times smaller than reported previously. Experimentally determined values of zeta were directly proportional to the absolute temperature although values were also influenced slightly by changes to the dielectric constant. It was found that the effective charge density at the inner surface of the capillary was independent of temperature.     

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 the ultimate minimum particle diameter of silica packings in capillary electrochromatography

Porous silica beads with an average particle diameter between 0.2 and 3 microm have been applied as packing material in capillary electrochromatography (CEC). The experiments were directed to investigate whether it is really feasible and as promising as expected to use such small particles. In CEC, plate heights of H approximately/= 1-2 d(p) can be achieved which is smaller than the plate heights usually attained in high-performance liquid chromatography. Using a capillary packed with 0.5 microm silica beads we achieved a plate height of H = 3 d(p) indicating the presence of dispersive effects like Joule heating. Calculations demonstrate that at a field strength of about 800 V cm(-1) one third of the plate height can be lost by Joule heating effects if the heat is not removed by a cooling system. Additionally, the H(u) curve is still descending at the maximum electroosmotic flow (EOF) velocity we generated with the modified capillary electrophoresis instrument. To fully exploit the potential of submicron size silicas higher field strengths, i.e., higher EOF velocities, must be attained. To study the influence of the kind of packing on the EOF porous as well as nonporous silicas have been applied. The experiments clearly indicate that the EOF of porous and nonporous silicas is the same. Since the EOF is more or less exclusively generated by the packing material the zeta potential of n-octyl bonded 0.5 microm silica has been determined. The dependence of the zeta potential on the pH is identical to the dependence of the EOF on the pH in a packed capillary. The point of zero charge of the silica is at pH 2-3.     

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.     

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.     

Joule heating monitoring in a microfluidic channel by observing the Brownian motion of an optically trapped microsphere

Electric fields offer a variety of functionalities to Lab‐on‐a‐Chip devices. The use of these fields often results in significant Joule heating, affecting the overall performance of the system. Precise knowledge of the temperature profile inside a microfluidic device is necessary to evaluate the implications of heat dissipation. This article demonstrates how an optically trapped microsphere can be used as a temperature probe to monitor Joule heating in these devices. The Brownian motion of the bead at room temperature is compared with the motion when power is dissipated in the system. This gives an estimate of the temperature increase at a specific location in a microfluidic channel. We demonstrate this method with solutions of different ionic strengths, and establish a precision of 0.9 K and an accuracy of 15%. Furthermore, it is demonstrated that transient heating processes can be monitored with this technique, albeit with a limited time resolution.     

Enhanced electrophoretic DNA separation in photonic crystal fiber

Joule heating generated by the electrical current in capillary electrophoresis leads to a temperature gradient along the separation channel and consequently affects the separation quality. We describe a method of reducing the Joule heating effect by incorporating photonic crystal fiber into a micro capillary electrophoresis chip. The photonic crystal fiber consists of a bundle of extremely narrow hollow channels, which ideally work as separation columns. Electrophoretic separation of DNA fragments was simultaneously but independently carried out in 54 narrow capillaries with a diameter of 3.7 μm each. The capillary bundle offers more efficient heat dissipation owing to the high surface-to-volume ratio. Under the same electrical field strength, notable improvement in resolution was obtained in the capillary bundle chip.     

Electrochromatography and micro high-performance liquid chromatography with 320 μm I.D. packed columns

Electrochromatography is a chromatographic method in which the mobile phase (liquid or supercritical fluid) is “pumped” through a stationary phase in a microbore or capillary column by electroosmosis using an electric field. The technique permits separation of charged and uncharged compounds with higher resolution and superior efficiency when compared with micro-HPLC with an identical column. It is desirable to work with packed capillary columns with wide diameter in electrochromatography in order to improve detectability and column loadability. This study shows that we have moved a step forward towards this goal in spite of problems and difficulties, due to Joule heating, frit making and column packing in using wide-diameter columns. The paper demonstrates that the pressure pump of micro-HPLC with a commercially available 320 μm I.D. column can be replaced by the electroosmotic “pump” of capillary zone electrophoresis. Experiments were carried out in a chromatographic system under both electroosmosis and pressure-driven flow with 320 and 50 μm I.D. columns packed with 3- and 5-μm ODS. The advantage of electrochromatography over conventional micro-HPLC is shown.