Lubrication theory for electro-osmotic flow in a slit microchannel with the Phan-Thien and Tanner model

O. Bautista, S. Sánchez, J. C. Arcos, F. Méndez

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

In this work the purely electro-osmotic flow of a viscoelastic liquid, which obeys the simplified Phan-Thien-Tanner (sPTT) constitutive equation, is solved numerically and asymptotically by using the lubrication approximation. The analysis includes Joule heating effects caused by an imposed electric field, where the viscosity function, relaxation time and electrical conductivity of the liquid are assumed to be temperature-dependent. Owing to Joule heating effects, temperature gradients in the liquid make the fluid properties change within the microchannel, altering the electric potential and flow fields. A consequence of the above is the appearance of an induced pressure gradient along the microchannel, which in turn modifies the normal plug-like electro-osmotic velocity profiles. In addition, it is pointed out that, depending on the fluid rheology and the used values of the dimensionless parameters, the velocity, temperature and pressure profiles in the fluid are substantially modified. Also, the finite thermal conductivity of the microchannel wall was considered in the analysis. The dimensionless temperature profiles in the fluid and the microchannel wall are obtained as function of the dimensionless parameters involved in the analysis, and the interactions between the coupled momentum, thermal energy and potential electric equations are examined in detail. A comparison between the numerical predictions and the asymptotic solutions was made, and reasonable agreement was found. © 2013 Cambridge University Press.
Original languageAmerican English
Pages (from-to)496-532
Number of pages37
JournalJournal of Fluid Mechanics
DOIs
StatePublished - 1 May 2013

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lubrication
microchannels
Microchannels
Lubrication
slits
Joule heating
Fluids
fluids
temperature profiles
Liquids
liquids
velocity distribution
constitutive equations
Electric potential
electric potential
potential fields
plugs
Thermal energy
Constitutive equations
Pressure gradient

Cite this

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title = "Lubrication theory for electro-osmotic flow in a slit microchannel with the Phan-Thien and Tanner model",
abstract = "In this work the purely electro-osmotic flow of a viscoelastic liquid, which obeys the simplified Phan-Thien-Tanner (sPTT) constitutive equation, is solved numerically and asymptotically by using the lubrication approximation. The analysis includes Joule heating effects caused by an imposed electric field, where the viscosity function, relaxation time and electrical conductivity of the liquid are assumed to be temperature-dependent. Owing to Joule heating effects, temperature gradients in the liquid make the fluid properties change within the microchannel, altering the electric potential and flow fields. A consequence of the above is the appearance of an induced pressure gradient along the microchannel, which in turn modifies the normal plug-like electro-osmotic velocity profiles. In addition, it is pointed out that, depending on the fluid rheology and the used values of the dimensionless parameters, the velocity, temperature and pressure profiles in the fluid are substantially modified. Also, the finite thermal conductivity of the microchannel wall was considered in the analysis. The dimensionless temperature profiles in the fluid and the microchannel wall are obtained as function of the dimensionless parameters involved in the analysis, and the interactions between the coupled momentum, thermal energy and potential electric equations are examined in detail. A comparison between the numerical predictions and the asymptotic solutions was made, and reasonable agreement was found. {\circledC} 2013 Cambridge University Press.",
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Lubrication theory for electro-osmotic flow in a slit microchannel with the Phan-Thien and Tanner model. / Bautista, O.; Sánchez, S.; Arcos, J. C.; Méndez, F.

In: Journal of Fluid Mechanics, 01.05.2013, p. 496-532.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Lubrication theory for electro-osmotic flow in a slit microchannel with the Phan-Thien and Tanner model

AU - Bautista, O.

AU - Sánchez, S.

AU - Arcos, J. C.

AU - Méndez, F.

PY - 2013/5/1

Y1 - 2013/5/1

N2 - In this work the purely electro-osmotic flow of a viscoelastic liquid, which obeys the simplified Phan-Thien-Tanner (sPTT) constitutive equation, is solved numerically and asymptotically by using the lubrication approximation. The analysis includes Joule heating effects caused by an imposed electric field, where the viscosity function, relaxation time and electrical conductivity of the liquid are assumed to be temperature-dependent. Owing to Joule heating effects, temperature gradients in the liquid make the fluid properties change within the microchannel, altering the electric potential and flow fields. A consequence of the above is the appearance of an induced pressure gradient along the microchannel, which in turn modifies the normal plug-like electro-osmotic velocity profiles. In addition, it is pointed out that, depending on the fluid rheology and the used values of the dimensionless parameters, the velocity, temperature and pressure profiles in the fluid are substantially modified. Also, the finite thermal conductivity of the microchannel wall was considered in the analysis. The dimensionless temperature profiles in the fluid and the microchannel wall are obtained as function of the dimensionless parameters involved in the analysis, and the interactions between the coupled momentum, thermal energy and potential electric equations are examined in detail. A comparison between the numerical predictions and the asymptotic solutions was made, and reasonable agreement was found. © 2013 Cambridge University Press.

AB - In this work the purely electro-osmotic flow of a viscoelastic liquid, which obeys the simplified Phan-Thien-Tanner (sPTT) constitutive equation, is solved numerically and asymptotically by using the lubrication approximation. The analysis includes Joule heating effects caused by an imposed electric field, where the viscosity function, relaxation time and electrical conductivity of the liquid are assumed to be temperature-dependent. Owing to Joule heating effects, temperature gradients in the liquid make the fluid properties change within the microchannel, altering the electric potential and flow fields. A consequence of the above is the appearance of an induced pressure gradient along the microchannel, which in turn modifies the normal plug-like electro-osmotic velocity profiles. In addition, it is pointed out that, depending on the fluid rheology and the used values of the dimensionless parameters, the velocity, temperature and pressure profiles in the fluid are substantially modified. Also, the finite thermal conductivity of the microchannel wall was considered in the analysis. The dimensionless temperature profiles in the fluid and the microchannel wall are obtained as function of the dimensionless parameters involved in the analysis, and the interactions between the coupled momentum, thermal energy and potential electric equations are examined in detail. A comparison between the numerical predictions and the asymptotic solutions was made, and reasonable agreement was found. © 2013 Cambridge University Press.

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