Transport of Analytes under Mixed Electroosmotic and Pressure Driven Flow of Power Law Fluid

Authors: Naren Bag, S. Bhattacharyya, Partha P. Gopmandal

Abstract:

In this study, we have analyzed the transport of analytes under a two dimensional steady incompressible flow of power-law fluids through rectangular nanochannel. A mathematical model based on the Cauchy momentum-Nernst-Planck-Poisson equations is considered to study the combined effect of mixed electroosmotic (EO) and pressure driven (PD) flow. The coupled governing equations are solved numerically by finite volume method. We have studied extensively the effect of key parameters, e.g., flow behavior index, concentration of the electrolyte, surface potential, imposed pressure gradient and imposed electric field strength on the net average flow across the channel. In addition to study the effect of mixed EOF and PD on the analyte distribution across the channel, we consider a nonlinear model based on general convective-diffusion-electromigration equation. We have also presented the retention factor for various values of electrolyte concentration and flow behavior index.

Keywords: Electric double layer, finite volume method, flow behavior index, mixed electroosmotic/pressure driven flow, Non-Newtonian power-law fluids, numerical simulation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1340098

References:

[1] R. J. Hunter, Foundations of colloid science, Oxford University Press, 2001.
[2] R. F. Probstein, Physicochemical hydrodynamics, Wiley, 1994.
[3] J. H. Masliyah, S. Bhattacharjee, Electrokinetic and colloid transport phenomena, John Wiley & Sons, 2006.
[4] H. A. Stone, A. D. Stroock, A. Ajdari, Engineering flows in small devices: microfluidics toward a lab-on-a-chip, Annu. Rev. Fluid Mech. 36 (2004) 381–411.
[5] X. Wang, C. Cheng, S. Wang, S. Liu, Electroosmotic pumps and their applications in microfluidic systems, Microfluidics and Nanofluidics 6 (2) (2009) 145–162.
[6] F. Kamis¸li, Flow analysis of a power-law fluid confined in an extrusion die, International journal of engineering science 41 (10) (2003) 1059–1083.
[7] W. Zimmerman, J. Rees, T. Craven, Rheometry of non-newtonian electrokinetic flow in a microchannel t-junction, Microfluidics and Nanofluidics 2 (6) (2006) 481–492.
[8] M. Das, V. Jain, P. Ghoshdastidar, Fluid flow analysis of magnetorheological abrasive flow finishing (mraff) process, International Journal of Machine Tools and Manufacture 48 (3) (2008) 415–426.
[9] Y. Koh, N. Ong, X. Chen, Y. Lam, J. Chai, Effect of temperature and inlet velocity on the flow of a nonnewtonian fluid, International communications in heat and mass transfer 31 (7) (2004) 1005–1013.
[10] A. Y. Malkin, Rheology Fundamentals, ChemTec, 1994.
[11] S. Das, S. Chakraborty, Analytical solutions for velocity, temperature and concentration distribution in electroosmotic microchannel flows of a non-Newtonian bio-fluid, Analytica Chimica Acta 559 (1) (2006) 15–24.
[12] C. Zhao, E. Zholkovskij, J. H. Masliyah, C. Yang, Analysis of electroosmotic flow of power-law fluids in a slit microchannel, Journal of colloid and interface science 326 (2) (2008) 503–510.
[13] C. Rice, R. Whitehead, Electrokinetic flow in a narrow cylindrical capillary, The Journal of Physical Chemistry 69 (11) (1965) 4017–4024.
[14] G. Tang, X. Li, Y. He, W. Tao, Electroosmotic flow of non-Newtonian fluid in microchannels, Journal of Non-Newtonian Fluid Mechanics 157 (1) (2009) 133–137.
[15] N. Vasu, S. De, Electroosmotic flow of power-law fluids at high zeta potentials, Colloids and Surfaces A: Physicochemical and Engineering Aspects 368 (1) (2010) 44–52.
[16] A. Babaie, A. Sadeghi, M. H. Saidi, Combined electroosmotically and pressure driven flow of power-law fluids in a slit microchannel, Journal of Non-Newtonian Fluid Mechanics 166 (14) (2011) 792–798.
[17] S. Pennathur, J. G. Santiago, Electrokinetic transport in nanochannels. 1. theory, Analytical chemistry 77 (21) (2005) 6772–6781.
[18] S. K. Griffiths, R. H. Nilson, Electroosmotic fluid motion and late-time solute transport for large zeta potentials, Analytical chemistry 72 (20) (2000) 4767–4777.
[19] X. Xuan, D. Li, Solute separation in nanofluidic channels: Pressure-driven or electric field-driven?, Electrophoresis 28 (4) (2007) 627–634.
[20] C. A. Fletcher, Computational techniques for fluid dynamics vol 2, 2nd edn, Springer, Berlin, 1991.
[21] S. Patankar, Numerical heat transfer and fluid flow, CRC Press, 1980.
[22] D. Gillespie, S. Pennathur, Separation of ions in nanofluidic channels with combined pressure-driven and electro-osmotic flow, Analytical chemistry 85 (5) (2013) 2991–2998.