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

• Published in: Journal of fluid mechanics 2013-05, Vol.722, p.496-532
• Main Authors: Bautista, O., Sánchez, S., Arcos, J. C., Méndez, F.
• Format: Article
• Language: English
• Subjects: Applied fluid mechanics; Asymptotic properties; Boundary conditions; Computational fluid dynamics; Electric potential; Exact sciences and technology; Flow velocity; Fluid dynamics; Fluid flow; Fluid mechanics; Fluidics; Fluids; Fundamental areas of phenomenology (including applications); Heating; Mathematical analysis; Mathematical models; Microchannels; Non-newtonian fluid flows; Numerical analysis; Physics; Rheology; Temperature gradients; Thermal conductivity; Thermal energy
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2013.107

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.