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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.

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Figures

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.

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