Comparative evaluation of microfluidic circuit model performance for electroviscous flow

Microfluidic circuit models are useful tools for conceptualising and designing lab-on-chip devices. We evaluate the ability of two different microfluidic circuit models to accurately predict electroviscous (pressure driven) flow behaviour in a particular contraction-expansion geometry over an experimentally relevant range of inlet concentrations and surface charge densities. We show that a linear `total current model' based on a relatively simple ion species constraint at circuit nodes performs well compared to a non-linear `ion current model' that conserves species exactly. Specifically, the total current model over-predicts the total pressure and potential differences by less than 2% and 7% respectively for silica channels. References P. Abgrall and A. -M. Gue. Lab-on-chip technologies: making a microfluidic network and coupling it into a complete microsystem---a review. J. Micromech. Microeng. , 17:R15--R49, 2007. doi:10.1088/0960-1317/17/5/R01 . A. Ajdari. Steady flows in networks of microfluidic channels: building on the analogy with electrical circuits. C. R. Phys. , 5:539--546, 2004. doi:10.1016/j.crhy. 2004.02. 012 . S. H. Behrens and D. G. Grier. The charge of glass and silica surfaces. J. Chem. Phys. , 115(14):6716--6721, 2001. doi:10.1063/1.1404988 . C. L. A. Berli. Theoretical modelling of electrokinetic flow in microchannel networks. Colloids Surf. , A , 301:271--280, 2007. doi:10.1016/j.colsurfa. 2006.12. 066 . C. J. C. Biscombe, M. R. Davidson, and D. J. E. Harvie. Microfluidic circuit analysis. II: Implications of ion conservation for microchannels connected in series, submitted to J. Colloid Interface Sci. L. Bousse, C. Cohen, T. Nikiforov, A. Chow, A. R. Kopf-Sill, R. Dubrow, and J. W. Parce. Electrokinetically controlled microfluidic analysis systems. Annu. Rev. Biophys. Biomol. Struct. , 29:155--181, 2000. doi:10.1146/annurev.biophys. 29.1. 155 . H. -C. Chang and G. Yossifon. Understanding electrokinetics at the nanoscale: a perspective. Biomicrofluidics , 3(1):012001, 2009. doi:10.1063/1.3056045 . D. Erickson. Towards numerical prototyping of labs-on-chip: modeling for integrated microfluidic devices. Microfluid. Nanofluid. , 1:301--318, 2005. doi:10.1007/s10404-005-0041-z . D. J. E. Harvie, C. J. C. Biscombe, and M. R. Davidson. Microfluidic circuit analysis. I: Ion current relationships for thin slits and pipes, submitted to J. Colloid Interface Sci. W. M. Haynes, editor. CRC Handbook of Chemistry and Physics (Internet version). CRC Press/Taylor and Francis, Boca Raton, Florida, USA, 91st edition, 2011. R. J. Hunter. Zeta Potential in Colloid Science: Principles and Applications . Academic Press, London, 1981. S. Levine, J. R. Marriott, and K. Robinson. Theory of electrokinetic flow in a narrow parallel-plate channel. J. Chem. Soc. , Faraday Trans. 2 , 71:1--11, 1975. doi:10.1039/F29757100001 . K. Ohno, K. Tachikawa, and A. Manz. Microfluidics: applications for analytical purposes in chemistry and biochemistry. Electrophoresis , 29:4443--4453, 2008. doi:10.1002/elps.200800121 . R. B. Schoch and P. Renaud. Ion transport through nanoslits dominated by the effective surface charge. Appl. Phys. Lett. , 86(25):253111, 2005. doi:10.1063/1.1954899 . D. Stein, M. Kruithof, and C. Dekker. Surface-charge-governed ion transport in nanofluidic channels. Phys. Rev. Lett. , 93(3):035901, 2004. doi:10.1103/PhysRevLett.93. 035901 . F. H. J. van der Heyden, D. Stein, and C. Dekker. Streaming currents in a single nanofluidic channel. Phys. Rev. Lett. , 95(11):116104, 2005. doi:10.1103/PhysRevLett.95. 116104 . X. Xuan and D. Li. Analysis of electrokinetic flow in microfluidic networks. J. Micromech. Microeng. , 14:290--298, 2004. doi:10.1088/0960-1317/14/2/018 .