Research Papers

Thermal Effect on Microchannel Electro-osmotic Flow With Consideration of Thermodiffusion

[+] Author and Article Information
Yi Zhou, Yee Cheong Lam

School of Mechanical and
Aerospace Engineering,
Nanyang Technological University,
50 Nanyang Avenue,
Singapore 639798

Yongqi Xie

School of Aeronautics Science
and Engineering,
Beihang University,
Beijing 100191, China

Chun Yang

School of Mechanical and
Aerospace Engineering,
Nanyang Technological University,
50 Nanyang Avenue,
Singapore 639798
e-mail: mcyang@ntu.edu.sg

1Corresponding author.

Manuscript received May 18, 2014; final manuscript received February 8, 2015; published online May 14, 2015. Assoc. Editor: L. Q. Wang.

J. Heat Transfer 137(9), 091023 (Sep 01, 2015) (10 pages) Paper No: HT-14-1317; doi: 10.1115/1.4030240 History: Received May 18, 2014; Revised February 08, 2015; Online May 14, 2015

Electro-osmotic flow (EOF) is widely used in microfluidic systems. Here, we report an analysis of the thermal effect on EOF under an imposed temperature difference. Our model not only considers the temperature-dependent thermophysical and electrical properties but also includes ion thermodiffusion. The inclusion of ion thermodiffusion affects ionic distribution, local electrical potential, as well as free charge density, and thus has effect on EOF. In particular, we formulate an analytical model for the thermal effect on a steady, fully developed EOF in slit microchannel. Using the regular perturbation method, we solve the model analytically to allow for decoupling several physical mechanisms contributing to the thermal effect on EOF. The parametric studies show that the presence of imposed temperature difference/gradient causes a deviation of the ionic concentration, electrical potential, and electro-osmotic velocity profiles from their isothermal counterparts, thereby giving rise to faster EOF. It is the thermodiffusion induced free charge density that plays a key role in the thermodiffusion induced electro-osmotic velocity.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Piruska, A., Gong, M., Sweedler, J. V., and Bohn, P. W., 2010, “Nanofluidics in Chemical Analysis,” Chem. Soc. Rev., 39(3), pp. 1060–1072. [CrossRef] [PubMed]
Livak-Dahl, E., Sinn, I., and Burns, M., 2011, “Microfluidic Chemical Analysis Systems,” Annu. Rev. Chem. Biomol. Eng., 2, pp. 325–353. [CrossRef] [PubMed]
Erickson, D., and Li, D., 2004, “Integrated Microfluidic Devices,” Anal. Chim. Acta, 507(1), pp. 11–26. [CrossRef]
Marcos, Chun, Y., Tiow, O. K., and Neng, W. T., 2005, Elementary Electrokinetic Flow, Prentice-Hall, Singapore.
Laser, D. J., and Santiago, J. G., 2004, “A Review of Micropumps,” J. Micromech. Microeng., 14(6), pp. R35–R64. [CrossRef]
Burgreen, D., and Nakache, F. R., 1964, “Electrokinetic Flow in Ultrafine Capillary Slits,” J. Phys. Chem., 68(5), pp. 1084–1091. [CrossRef]
Rice, C. L., and Whitehead, R., 1965, “Electrokinetic Flow in a Narrow Cylindrical Capillary,” J. Phys. Chem., 69(11), pp. 4017–4024. [CrossRef]
Kang, Y., Yang, C., and Huang, X., 2002, “Electroosmotic Flow in a Capillary Annulus With High Zeta Potentials,” J. Colloid Interface Sci., 253(2), pp. 285–294. [CrossRef] [PubMed]
Ghosal, S., 2002, “Lubrication Theory for Electro-osmotic Flow in a Microfluidic Channel of Slowly Varying Cross-Section and Wall Charge,” J. Fluid Mech., 459(1), pp. 103–128. [CrossRef]
Marcos, Kang, Y. J., Ooi, K. T., Yang, C., and Wong, T. N., 2005, “Frequency Dependent Velocity and Vorticity Fields of Electroosmotic Flow in a Closed-End Cylindrical Microchannel,” J. Micromech. Microeng., 15(2), pp. 301–312. [CrossRef]
Xuan, X., and Dongqing, L., 2005, “Electroosmotic Flow in Microchannels With Arbitrary Geometry and Arbitrary Distribution of Wall Charge,” J. Colloid Interface Sci., 289(1), pp. 291–303. [CrossRef] [PubMed]
Patankar, N. A., and Hu, H. H., 1998, “Numerical Simulation of Electroosmotic Flow,” Anal. Chem., 70(9), pp. 1870–1881. [CrossRef] [PubMed]
Ermakov, S. V., Jacobson, S. C., and Ramse, J. M., 1998, “Computer Simulations of Electrokinetic Transport in Microfabricated Channel Structures,” Anal. Chem., 70(21), pp. 4494–4504. [CrossRef] [PubMed]
Xuan, X., and Li, D., 2004, “Analysis of Electrokinetic Flow in Microfluidic Networks,” J. Micromech. Microeng., 14(2), pp. 290–298. [CrossRef]
Ajdari, A., 1995, “Electro-Osmosis on Inhomogeneously Charged Surfaces,” Phys. Rev. Lett., 75(4), pp. 755–758. [CrossRef] [PubMed]
Stroock, A. D., Weck, M., Chiu, D. T., Huck, W. T. S., Kenis, P. J. A., Ismagilov, R. F., and Whitesides, G. M., 2000, “Patterning Electro-osmotic Flow With Patterned Surface Charge,” Phys. Rev. Lett., 84(15), pp. 3314–3317. [CrossRef] [PubMed]
Fu, L.-M., Lin, J.-Y., and Yang, R.-J., 2003, “Analysis of Electroosmotic Flow With Step Change in Zeta Potential,” J. Colloid Interface Sci., 258(2), pp. 266–275. [CrossRef] [PubMed]
Wang, M., and Kang, Q., 2009, “Electrokinetic Transport in Microchannels With Random Roughness,” Anal. Chem., 81(8), pp. 2953–2961. [CrossRef] [PubMed]
Ng, C.-O., and Zhou, Q., 2012, “Dispersion Due to Electroosmotic Flow in a Circular Microchannel With Slowly Varying Wall Potential and Hydrodynamic Slippage,” Phys. Fluids, 24(11), p. 112002. [CrossRef]
Chu, H. C. W., and Ng, C.-O., 2012, “Electroosmotic Flow Through a Circular Tube With Slip–Stick Striped Wall,” ASME J. Fluids Eng., 134(11), p. 111201. [CrossRef]
Santiago, J. G., 2001, “Electroosmotic Flows in Microchannels With Finite Inertial and Pressure Forces,” Anal. Chem., 73(10), pp. 2353–2365. [CrossRef] [PubMed]
Huang, X., Gordon, M. J., and Zare, R. N., 1988, “Current-Monitoring Method for Measuring the Electroosmotic Flow Rate in Capillary Zone Electrophoresis,” Anal. Chem., 60(17), pp. 1837–1838. [CrossRef]
Ren, L., Escobedo-Canseco, C., and Li, D., 2002, “A New Method of Evaluating the Average Electro-osmotic Velocity in Microchannels,” J. Colloid Interface Sci., 250(1), pp. 238–242. [CrossRef] [PubMed]
Wang, C., Wong, T. N., Yang, C., and Ooi, K. T., 2007, “Characterization of Electroosmotic Flow in Rectangular Microchannels,” Int. J. Heat Mass Transfer,50(15–16), pp. 3115–3121. [CrossRef]
Paul, P. H., Garguilo, M. G., and Rakestraw, D. J., 1998, “Imaging of Pressure- and Electrokinetically Driven Flows Through Open Capillaries,” Anal. Chem., 70(13), pp. 2459–2467. [CrossRef] [PubMed]
Ross, D., Johnson, T. J., and Locascio, L. E., 2001, “Imaging of Electroosmotic Flow in Plastic Microchannels,” Anal. Chem., 73(11), pp. 2509–2515. [CrossRef] [PubMed]
Kim, M. J., Beskok, A., and Kihm, K. D., 2002, “Electro-osmotic-Driven Micro-Channel Flows: A Comparative Study of Microscopic Particle Image Velocimetry Measurements and Numerical Simulations,” Exp. Fluids, 33(1), pp. 170–180. [CrossRef]
Devasenathipathy, S., and Santiago, J. G., 2002, “Particle Tracking Techniques for Electrokinetic Microchannel Flows,” Anal. Chem., 74(15), pp. 3704–3713. [CrossRef] [PubMed]
Sinton, D., and Li, D., 2003, “Electroosmotic Velocity Profiles in Microchannels,” Colloids Surf. A., 222(1–3), pp. 273–283. [CrossRef]
Sinton, D., 2004, “Microscale Flow Visualization,” Microfluid. Nanofluid., 1(1), pp. 2–21. [CrossRef]
Yan, D. G., Yang, C., and Huang, X. Y., 2007, “Effect of Finite Reservoir Size on Electroosmotic Flow in Microchannels,” Microfluid. Nanofluid., 3(3), pp. 333–340. [CrossRef]
Yan, D., Nguyen, N.-T., Yang, C., and Huang, X., 2006, “Visualizing the Transient Electroosmotic Flow and Measuring the Zeta Potential of Microchannels With a Micro-PIV Technique,” J. Chem. Phys., 124(2), p. 021103. [CrossRef] [PubMed]
Yan, D., Yang, C., Nguyen, N.-T., and Huang, X., 2007, “Diagnosis of Transient Electrokinetic Flow in Microfluidic Channels,” Phys. Fluids, 19(1), p. 017114. [CrossRef]
Wang, G., Sas, I., Jiang, H., Janzen, W. P., and Hodge, C. N., 2008, “Photobleaching-Based Flow Measurement in a Commercial Capillary Electrophoresis Chip Instrument,” Electrophoresis, 29(6), pp. 1253–1263. [CrossRef] [PubMed]
Kuang, C., Yang, F., Zhao, W., and Wang, G., 2009, “Study of the Rise Time in Electroosmotic Flow Within a Microcapillary,” Anal. Chem., 81(16), pp. 6590–6595. [CrossRef] [PubMed]
Kuang, C., Qiao, R., and Wang, G., 2011, “Ultrafast Measurement of Transient Electroosmotic Flow in Microfluidics,” Microfluid. Nanofluid., 11(3), pp. 353–358. [CrossRef]
Knox, J. H., and McCormack, K. A., 1994, “Temperature Effects in Capillary Electrophoresis. 1: Internal Capillary Temperature and Effect Upon Performance,” Chromatographia,38(3–4), pp. 207–214. [CrossRef]
Swinney, K., and Bornhop, D. J., 2002, “Quantification and Evaluation of Joule Heating in On-Chip Capillary Electrophoresis,” Electrophoresis, 23(4), pp. 613–620. [CrossRef] [PubMed]
Tang, G. Y., Yang, C., Chai, C. J., and Gong, H. Q., 2003, “Modeling of Electroosmotic Flow and Capillary Electrophoresis With the Joule Heating Effect: The Nernst–Planck Equation Versus the Boltzmann Distribution,” Langmuir, 19(2), pp. 10975–10984. [CrossRef]
Tang, G. Y., Yang, C., Chai, J. C., and Gong, H. Q., 2004, “Joule Heating Effect on Electroosmotic Flow and Mass Species Transport in a Microcapillary,” Int. J. Heat Mass Transfer, 47(2), pp. 215–227. [CrossRef]
Xuan, X., Sinton, D., and Li, D., 2004, “Thermal End Effects on Electroosmotic Flow in a Capillary,” Int. J. Heat Mass Transfer,47(14–16), pp. 3145–3157. [CrossRef]
Xuan, X., Xu, B., Sinton, D., and Li, D., 2004, “Electroosmotic Flow With Joule Heating Effects,” Lab Chip, 4(3), pp. 230–236. [CrossRef] [PubMed]
Tang, G. Y., Yang, C., Gong, H. Q., Chai, C. J., and Lam, Y. C., 2005, “On Electrokinetic Mass Transport in a Microchannel With Joule Heating Effect,” ASME J. Heat Transfer, 127(6), pp. 660–663. [CrossRef]
Kang, Y., Yang, C., and Huang, X., 2005, “Joule Heating Induced Transient Temperature Field and Its Effects on Electroosmosis in a Microcapillary Packed With Microspheres,” Langmuir, 21(16), pp. 7598–7607. [CrossRef] [PubMed]
Tang, G., Yan, D., Yang, C., Gong, H., Chai, J. C., and Lam, Y. C., 2006, “Assessment of Joule Heating and Its Effects on Electroosmotic Flow and Electrophoretic Transport of Solutes in Microfluidic Channels,” Electrophoresis, 27(3), pp. 628–639. [CrossRef] [PubMed]
Xuan, X., 2008, “Joule Heating in Electrokinetic Flow,” Electrophoresis, 29(1), pp. 33–43. [CrossRef] [PubMed]
Yang, C., Li, D., and Masliyah, J. H., 1998, “Modeling Forced Liquid Convection in Rectangular Microchannels With Electrokinetic Effects,” Int. J. Heat Mass Transfer, 41(24), pp. 4229–4249. [CrossRef]
Maynes, D., and Webb, B. W., 2003, “Fully-Developed Thermal Transport in Combined Pressure and Electro-osmotically Driven Flow in Microchannels,” ASME J. Heat Transfer, 125(5), pp. 889–895. [CrossRef]
Horiuchi, K., and Dutta, P., 2004, “Joule Heating Effects in Electroosmotically Driven Microchannel Flows,” Int. J. Heat Mass Transfer,47(14–16), pp. 3085–3095. [CrossRef]
Liechty, B. C., Webb, B. W., and Maynes, R. D., 2005, “Convective Heat Transfer Characteristics of Electro-osmotically Generated Flow in Microtubes at High Wall Potential,” Int. J. Heat Mass Transfer, 48(12), pp. 2360–2371. [CrossRef]
Chakraborty, S., 2006, “Analytical Solutions of Nusselt Number for Thermally Fully Developed Flow in Microtubes Under a Combined Action of Electroosmotic Forces and Imposed Pressure Gradients,” Int. J. Heat Mass Transfer,49(3–4), pp. 810–813. [CrossRef]
Zade, A. Q., Manzari, M. T., and Hannani, S. K., 2007, “An Analytical Solution for Thermally Fully Developed Combined Pressure—Electroosmotically Driven Flow in Microchannels,” Int. J. Heat Mass Transfer,50(5–6), pp. 1087–1096. [CrossRef]
Sanchez, S., Mendez, F., Martinez-Suastegui, L., and Bautista, O., 2012, “Asymptotic Analysis for the Conjugate Heat Transfer Problem in an Electro-osmotic Flow With Temperature-Dependent Properties in a Capillary,” Int. J. Heat Mass Transfer,55(25–26), pp. 8163–8171. [CrossRef]
Hawkins, B. G., and Kirby, B. J., 2010, “Electrothermal Flow Effects in Insulating (Electrodeless) Dielectrophoresis Systems,” Eletrophoresis, 31(22), pp. 3622–3633. [CrossRef]
Sridharan, S., Zhu, J., Hu, G., and Xuan, X., 2011, “Joule Heating Effects on Electroosmotic Flow in Insulator-Based Dielectrophoresis,” Electrophoresis, 32(17), pp. 2274–2281. [CrossRef] [PubMed]
Gagnon, Z. R., and Chang, H.-C., 2009, “Electrothermal AC Eletro-osmosis,” Appl. Phys. Lett., 94(2), p. 024101. [CrossRef]
Wu, J., Lian, M., and Yang, K., 2007, “Micropumping of Biofluids by Alternating Current Electrothermal Effects,” Appl. Phys. Lett., 90(23), p. 234103. [CrossRef]
Ross, D., and Locascio, L. E., 2002, “Microfluidic Temperature Gradient Focusing,” Anal. Chem., 74(11), pp. 2556–2564. [CrossRef] [PubMed]
Sommer, G. J., Kim, S. M., Littrell, R. J., and Hasselbrink, E. F., 2007, “Theoretical and Numerical Analysis of Temperature Gradient Focusing Via Joule Heating,” Lab Chip, 7(7), pp. 898–907. [CrossRef] [PubMed]
Tang, G., and Yang, C., 2008, “Numerical Modeling of Joule Heating Induced Temperature Gradient Focusing in Microfluidic Channels,” Electrophoresis, 29(5), pp. 1006–1012. [CrossRef] [PubMed]
Ge, Z., and Yang, C., 2010, “Concentration Enhancement of Sample Solutes in a Sudden Expansion Microchannel With Joule Heating,” Int. J. Heat Mass Transfer,53(13–14), pp. 2722–2731. [CrossRef]
Ge, Z., Wang, W., and Yang, C., 2011, “Towards High Concentration Enhancement of Microfluidic Temperature Gradient Focusing of Sample Solutes Using Combined AC and DC Field Induced Joule Heating,” Lab Chip, 11(7), pp. 1396–1402. [CrossRef] [PubMed]
Bar-Cohen, A., 2013, “Gen-3 Thermal Management Technology: Role of Microchannels and Nanostructures in an Embedded Cooling Paradigm,” ASME J. Nanotechnol. Eng. Med., 4(2), p. 020907. [CrossRef]
Agar, J. N., and Turner, J. C. R., 1960, “Thermal Diffusion in Solutions of Electrolytes,” Proc. R. Soc. London A, 255(1282), pp. 307–330. [CrossRef]
Agar, J. N., Mou, C. Y., and Lin, J., 1989, “Single-Ion Heat of Transport in Electrolyte Solutions. A Hydrodynamic Theory,” J. Phys. Chem., 93(5), pp. 2079–2082. [CrossRef]
Würger, A., 2008, “Transport in Charged Colloids Driven by Thermoelectricity,” Phys. Rev. Lett., 101(10), p. 108302. [CrossRef] [PubMed]
Ghonge, T., Chakraborty, J., Dey, R., and Chakraborty, S., 2013, “Electrohydrodynamics Within the Electrical Double Layer in the Presence of Finite Temperature Gradients,” Phys. Rev. E, 88(5), p. 053020. [CrossRef]
Masliyah, J. H., and Bhattacharjee, S., 2006, Electrokinetic and Colloid Transport Phenomena, Wiley, Hoboken, NJ. [CrossRef]


Grahic Jump Location
Fig. 1

Schematic diagram of a negatively charged slit microchannel of L in length and 2 h in height with a Cartesian coordinate system. Under an applied axial electrical field Ea, EOF of an electrolyte solution is generated. The top and bottom walls of the channel are maintained at constant temperatures Th and Tc with Th > Tc. The presence of such temperature gradient not only drives ions to accumulate on the cold side but also alters thermophysical and electrical properties of the liquid solution, giving rise to a thermal effect on EOF.

Grahic Jump Location
Fig. 2

Transverse distributions of the dimensionless ionic concentration (given by Eq. (19)) for three different values of nondimensional electrokinetic height κrefh = 5,50,and 500 and a constant negative zeta potential ζ* = -0.5: (a) cations c1* and (b) anions c2*. The dashed lines denote the cases without imposed temperature difference (gradient). The solids lines depict the cases of thermal effect with γT = 0.04 (the normalized temperature difference γT = ΔTref/Tc) and ETD* = -0.1 (the nondimensional ion thermodiffusion induced electric field ETD*= (((ST1*-ST2*)/2)γT(dΘ/dy*))/ζ*). The dimensionless cationic and anionic Soret coefficients are ST1* = 2.7 and ST2* = 0.2, respectively, indicating both cations and anions migrate to the cold region due to ion thermodiffusion. The reference temperature is Tc = 298.15K.

Grahic Jump Location
Fig. 3

Transverse profiles of the dimensionless ion thermodiffusion induced free charge density ρe*|TDexpressed by Eq. (23) for a thin EDL case of κrefh = 500 and a constant negative zeta potential ζ* = -0.5. The square symbols denote no ion thermodiffusion effect, γT = 0.04 and ETD* = 0. The thermal effects on free charge density are shown by the dashed line for the case of γT = 0.04 and ETD* = -0.1 and by the solid line for the case of γT = 0.04 and ETD* = 0.1.

Grahic Jump Location
Fig. 4

Transverse distributions of the dimensionless electro-osmotic velocity normalized by the slip velocity us for three different values of nondimensional electrokinetic height κrefh = 5,50,and 500 and a constant of negative zeta potential ζ* = -0.5. The dashed lines denote the dimensionless electro-osmotic velocity without thermal effect u*|no_th expressed by Eq. (33). The solids lines depict the dimensionless electro-osmotic velocity with thermal effect u/us expressed by Eq. (32) when γT = 0.04 and ETD* = -0.1.

Grahic Jump Location
Fig. 5

Thermal effect on transverse profile of dimensionless electro-osmotic velocity normalized by the slip velocity us for a thin EDL case of κrefh = 500 and a constant negative zeta potential ζ* = -0.5. The thermal effect is specified as γT = 0.04 for both cases of ETD* = -0.1 and ETD* = 0.1. The solid lines denote the thermal effect induced dimensionless electro-osmotic velocity u*|th expressed by Eq. (34). The dashed lines depict the ion thermodiffusion induced dimensionless electro-osmotic velocity u*|TD expressed by Eq. (35). The dotted dashed line represents the temperature-dependent permittivity and viscosity induced dimensionless electro-osmotic velocity u*|T expressed by Eq. (40).

Grahic Jump Location
Fig. 6

Transverse profiles of the ion thermodiffusion induced dimensionless electro-osmotic velocity u*|TD given by Eq. (35), the thermoelectricity effect induced dimensionless velocity u*|TE given by Eq. (36), the dimensionless velocity accounting for ion thermodiffusion induced electrical potential and temperature-dependent permittivity u*|Cɛ_Ψ*| TD given by Eq. (37), the dimensionless velocity accounting for ion thermodiffusion induced electrical potential and temperature-dependent viscosity u*|Cμ_Ψ*| TD given by Eq. (38), and the dimensionless velocity due to the free charge density induced by the electrical potential under the ion thermodiffusion effect u*|Ψ*|TD given by Eq. (39). Other parameters used in computing the figure are: γT = 0.04, ETD* = -0.1, κrefh = 500, and ζ* = -0.5.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In