Abstract
The flow of viscoelastic fluids between parallel plates under the combined influence of electro-osmotic and pressure gradient forcings with asymmetric boundary conditions, by considering different zeta potentials at the walls, is investigated. The fluids are z–z symmetric electrolytes. The analytic solutions of the electrical potential, velocity distributions and streaming potential are based on the Debye–Hückel approximation for weak potential. The viscoelastic fluids used are modelled by the simplified Phan-Thien–Tanner constitutive equation, with linear kernel for the stress coefficient function, and the Finitely Extensible Nonlinear Elastic dumbbells model with a Peterlin approximation for the average spring force. The combined effects of fluid rheology, electrical double-layer thickness, ratio of the wall zeta potentials and ratio between the applied streamwise gradients of electrostatic potential and pressure on the fluid velocity and stress distributions are discussed.
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References
Soong CY, Wang SH (2003) Theoretical analysis of electrokinetic flow and heat transfer in a microchannel under asymmetric boundary conditions. J Colloid Interface Sci 265: 202–213
Nguyen N-T, Wereley ST (2006) Fundamentals and applications of microfluidics, chap 3: fabrication techniques in microfluidics, 2nd edn. Artech House, Boston, USA
Kuo A-T, Chang C-H, Wei H-H (2008) Transient currents in electrolyte displacement by asymmetric electro-osmosis and determination of surface zeta potentials of composite microchannels. Appl Phys Lett 92: 244102
Islam N, Wu J (2006) Microfluidic transport by AC electroosmosis. J Phys Conf Ser 34: 356–361
Mansuripur TS, Pascall AJ, Squires TM (2009) Asymmetric flows over symmetric surfaces: capacitive coupling in induced-charge electro-osmosis. New J Phys 11: 075030
Afonso AM, Alves MA, Pinho FT (2009) Analytical solution of mixed electro-osmotic/pressure driven flows of viscoelastic fluids in microchannels. J Non-Newtonian Fluid Mech 159: 50–63
Phan-Thien N, Tanner RI (1977) New constitutive equation derived from network theory. J Non-Newtonian Fluid Mech 2: 353–365
Phan-Thien N (1978) A non-linear network viscoelastic model. J Rheol 22: 259–283
Bird RB, Dotson PJ, Johnson NL (1980) Polymer solution rheology based on a finitely extensible bead-spring chain model. J Non-Newtonian Fluid Mech 7: 213–235
Dhinakaran S, Afonso AM, Alves MA, Pinho FT (2010) Steady viscoelastic fluid flow between parallel plates under electro-osmotic forces: Phan-Thien Tanner model. J Colloid Interface Sci 344: 513–520
Park HM, Lee WM (2008) Helmholtz–Smoluchowski velocity for viscoelastic electroosmotic flows. J Colloid Interface Sci 317: 631–636
Sousa JJ, Afonso AM, Pinho FT, Alves MA (2010) Effect of the skimming-layer on electro-osmotic—Poiseuille flows of viscoelastic fluids. Microfluid Nanofluid. doi:10.1007/s10404-010-0651-y
Sousa PC, Pinho FT, Oliveira MSN, Alves MA (2010) Efficient microfluidic rectifiers for viscoelastic fluid flow. J Non-Newtonian Fluid Mech 165: 652–671
Bruus H (2008) Theoretical microfluidics, Oxford master series in Condensed matter physics. Oxford University Press, Oxford, UK
Oliveira PJ, Pinho FT (1999) Analytical solution for fully developed channel and pipe flow of Phan-Thien–Tanner fluids. J Non-Newtonian Fluid Mech 387: 271–280
Oliveira PJ (2002) An exact solution for tube and slit flow of a FENE-P fluid. Acta Mech 158: 157–167
Cruz DOA, Pinho FT, Oliveira PJ (2005) Analytical solutions for fully developed laminar flow of some viscoelastic liquids with a Newtonian solvent contribution. J Non-Newtonian Fluid Mech 132: 28–35
Alves MA, Pinho FT, Oliveira PJ (2001) Study of steady pipe and channel flows of a single-mode Phan Thien–Tanner fluid. J Non-Newtonian Fluid Mech 101: 55–76
Dutta P, A Beskok (2001) Analytical solution of combined electroosmotic /pressure driven flows in two-dimensional straight channels: finite debye layer effects. Anal Chem 73: 1979–1986
Burgreen D, Nakache FR (1964) Electrokinetic flow in ultrafine capillary slits. J Phys Chem 68: 1084–1091
Press WH, Flannery PP, Teukolsky SA, Vetterling WT (1992) Numerical recipes in Fortran: the art of scientific computing. 2nd Edn, Cambridge University Press
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Afonso, A.M., Alves, M.A. & Pinho, F.T. Electro-osmotic flow of viscoelastic fluids in microchannels under asymmetric zeta potentials. J Eng Math 71, 15–30 (2011). https://doi.org/10.1007/s10665-010-9421-9
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DOI: https://doi.org/10.1007/s10665-010-9421-9