Electroviscous Effects in Low Reynolds Number Flow through a Microfluidic Contraction with Rectangular Cross-Section
The electrokinetic flow resistance (electroviscous
effect) is predicted for steady state, pressure-driven liquid flow at
low Reynolds number in a microfluidic contraction of rectangular
cross-section. Calculations of the three dimensional flow are
performed in parallel using a finite volume numerical method. The
channel walls are assumed to carry a uniform charge density and the
liquid is taken to be a symmetric 1:1 electrolyte. Predictions are
presented for a single set of flow and electrokinetic parameters. It is
shown that the magnitude of the streaming potential gradient and the
charge density of counter-ions in the liquid is greater than that in
corresponding two-dimensional slit-like contraction geometry. The
apparent viscosity is found to be very close to the value for a
rectangular channel of uniform cross-section at the chosen Reynolds
number (Re = 0.1). It is speculated that the apparent viscosity for the
contraction geometry will increase as the Reynolds number is
reduced.
[1] G. Whitesides and A. Stroock, "Flexible methods for microfluidics,"
Phys. Fluids, vol. 54, no. 6, pp. 42-48, 2001.
[2] M. Gad-El-Hak (ed.), The MEMS Handbook, second edition, CRC Press,
Boca Raton, 2006.
[3] H. A. Stone and S. Kim, "Microfluidics: basic issues, applications, and
challenges," AIChE J., vol. 47. No. 6, pp. 1250-1254, 2001
[4] H. A. Stone, A.D. Stroock and A. Ajdari, "Engineering flows in small
devices: microfluidics towards a lab-on-a-chip," Annu. Rev. Fluid
Mech., vol. 36, pp. 381-411, 2004.
[5] D. Li, Electrokinetics in Microfluidics. Interface Science and
Technology, Vol. 2 (ed. A. Hibbard), Academic Press, 2004.
[6] R.J. Hunter, Zeta Potential in Colloid Science: Principles and
Application. Academic Press, New York, 1981.
[7] G.M. Mala, D. Li and J.D. Dale, "Heat transfer and fluid flow in
microchannels," Int. J. Heat Mass Transfer, vol. 40, pp. 3079-3088,
1997.
[8] G.M. Mala, D. Li, C. Werner and H. Jacobasch, "Flow characteristics of
water through a microchannel between two parallel plates with
electrokinetic effects," Int. J. Heat and Fluid Flow, vol. 18, no. 5, pp.
489-496, 1997
[9] M. Chun and H.W. Kwak, "Electrokinetic flow and electroviscous effect
in a charged slit-like microfluidic channel with nonlinear Poisson-
Boltzmann field," Korea-Australia Rheology J., vol. 15, no. 2, pp. 83-
90, 2003.
[10] W.R. Bowen and F. Jenner, "Electroviscous effects in charged
capillaries," J. Coll. Interface Sci., vol. 173, pp. 388-395, 1995.
[11] D. Brutin and L. Tadrist, "Modeling of surface-fluid electrokinetic
coupling on the laminar flow friction factor in microtubes," Microscale
Thermophysical Engineering, vol.9, pp. 33-48, 2005.
[12] J. Hsu, C. Kao, S. Tseng, and C. Chen, "Electrokinetic flow through an
elliptical microchannel: Effects of aspect ratio and electrical boundary
conditions," J. Coll. Interface Sci., vol. 248, pp. 176-184, 2002.
[13] L. Ren, D. Li and W. Qu, "Electro-viscous effects on liquid flow in
microchannels," J. Coll. Interface Sci., vol. 233, pp. 12-22, 2001.
[14] D. Li, "Electro-viscous effects on pressure-driven liquid flow in
microchannels," Colloids and Surfaces A, vol. 195, pp. 35-57, 2001.
[15] M.R. Davidson and D.J.E. Harvie, "Electroviscous effects in low
Reynolds number liquid flow through a slit-like microfluidic
contraction," Chem. Eng. Sci., vol. 62, pp. 4229-4240, 2007.
[16] M.R. Davidson, D.J.E. Harvie and P. Liovic, "Electrokinetic flow
resistance in pressure-driven liquid flow through a slit-like microfluidic
contraction," in Proc. 16th Australasian Fluid Mechanics Conf., Gold
Coast, Australia, 2-7 Dec. 2007, pp. 798-802.
[17] R.P. Bharti, D.J.E. Harvie and M.R. Davidson, "Steady flow of ionic
liquid through a cylindrical microfluidic contraction-expansion pipe:
Electroviscous effects and pressure drop," Chem. Eng. Sci, accepted for
publication.
[18] M. Rudman, "A volume-tracking method for incompressible multifluid
flows with large density variations," Int. J. for Numerical Methods in
Fluids, vol. 28, pp. 357-378, 1998.
[19] D.J.E Harvie, M.R. Davidson, J.J. Cooper-White and M. Rudman, "A
parametric study of droplet deformation through a microfluidic
contraction: Shear thinning liquids," Int. J. Multiphase Flow, vol. 33, pp.
545-556, 2007.
[20] P.Liovic, D.Lakehal, "Multi-physics treatment in the vicinity of
arbitrarily deformable gas-liquid interfaces, " J. Comput. Phys., vol. 222,
pp. 504-535, 2007.
[1] G. Whitesides and A. Stroock, "Flexible methods for microfluidics,"
Phys. Fluids, vol. 54, no. 6, pp. 42-48, 2001.
[2] M. Gad-El-Hak (ed.), The MEMS Handbook, second edition, CRC Press,
Boca Raton, 2006.
[3] H. A. Stone and S. Kim, "Microfluidics: basic issues, applications, and
challenges," AIChE J., vol. 47. No. 6, pp. 1250-1254, 2001
[4] H. A. Stone, A.D. Stroock and A. Ajdari, "Engineering flows in small
devices: microfluidics towards a lab-on-a-chip," Annu. Rev. Fluid
Mech., vol. 36, pp. 381-411, 2004.
[5] D. Li, Electrokinetics in Microfluidics. Interface Science and
Technology, Vol. 2 (ed. A. Hibbard), Academic Press, 2004.
[6] R.J. Hunter, Zeta Potential in Colloid Science: Principles and
Application. Academic Press, New York, 1981.
[7] G.M. Mala, D. Li and J.D. Dale, "Heat transfer and fluid flow in
microchannels," Int. J. Heat Mass Transfer, vol. 40, pp. 3079-3088,
1997.
[8] G.M. Mala, D. Li, C. Werner and H. Jacobasch, "Flow characteristics of
water through a microchannel between two parallel plates with
electrokinetic effects," Int. J. Heat and Fluid Flow, vol. 18, no. 5, pp.
489-496, 1997
[9] M. Chun and H.W. Kwak, "Electrokinetic flow and electroviscous effect
in a charged slit-like microfluidic channel with nonlinear Poisson-
Boltzmann field," Korea-Australia Rheology J., vol. 15, no. 2, pp. 83-
90, 2003.
[10] W.R. Bowen and F. Jenner, "Electroviscous effects in charged
capillaries," J. Coll. Interface Sci., vol. 173, pp. 388-395, 1995.
[11] D. Brutin and L. Tadrist, "Modeling of surface-fluid electrokinetic
coupling on the laminar flow friction factor in microtubes," Microscale
Thermophysical Engineering, vol.9, pp. 33-48, 2005.
[12] J. Hsu, C. Kao, S. Tseng, and C. Chen, "Electrokinetic flow through an
elliptical microchannel: Effects of aspect ratio and electrical boundary
conditions," J. Coll. Interface Sci., vol. 248, pp. 176-184, 2002.
[13] L. Ren, D. Li and W. Qu, "Electro-viscous effects on liquid flow in
microchannels," J. Coll. Interface Sci., vol. 233, pp. 12-22, 2001.
[14] D. Li, "Electro-viscous effects on pressure-driven liquid flow in
microchannels," Colloids and Surfaces A, vol. 195, pp. 35-57, 2001.
[15] M.R. Davidson and D.J.E. Harvie, "Electroviscous effects in low
Reynolds number liquid flow through a slit-like microfluidic
contraction," Chem. Eng. Sci., vol. 62, pp. 4229-4240, 2007.
[16] M.R. Davidson, D.J.E. Harvie and P. Liovic, "Electrokinetic flow
resistance in pressure-driven liquid flow through a slit-like microfluidic
contraction," in Proc. 16th Australasian Fluid Mechanics Conf., Gold
Coast, Australia, 2-7 Dec. 2007, pp. 798-802.
[17] R.P. Bharti, D.J.E. Harvie and M.R. Davidson, "Steady flow of ionic
liquid through a cylindrical microfluidic contraction-expansion pipe:
Electroviscous effects and pressure drop," Chem. Eng. Sci, accepted for
publication.
[18] M. Rudman, "A volume-tracking method for incompressible multifluid
flows with large density variations," Int. J. for Numerical Methods in
Fluids, vol. 28, pp. 357-378, 1998.
[19] D.J.E Harvie, M.R. Davidson, J.J. Cooper-White and M. Rudman, "A
parametric study of droplet deformation through a microfluidic
contraction: Shear thinning liquids," Int. J. Multiphase Flow, vol. 33, pp.
545-556, 2007.
[20] P.Liovic, D.Lakehal, "Multi-physics treatment in the vicinity of
arbitrarily deformable gas-liquid interfaces, " J. Comput. Phys., vol. 222,
pp. 504-535, 2007.
@article{"International Journal of Chemical, Materials and Biomolecular Sciences:58012", author = "Malcolm R Davidson and Ram P. Bharti and Petar Liovic and Dalton J.E. Harvie", title = "Electroviscous Effects in Low Reynolds Number Flow through a Microfluidic Contraction with Rectangular Cross-Section", abstract = "The electrokinetic flow resistance (electroviscous
effect) is predicted for steady state, pressure-driven liquid flow at
low Reynolds number in a microfluidic contraction of rectangular
cross-section. Calculations of the three dimensional flow are
performed in parallel using a finite volume numerical method. The
channel walls are assumed to carry a uniform charge density and the
liquid is taken to be a symmetric 1:1 electrolyte. Predictions are
presented for a single set of flow and electrokinetic parameters. It is
shown that the magnitude of the streaming potential gradient and the
charge density of counter-ions in the liquid is greater than that in
corresponding two-dimensional slit-like contraction geometry. The
apparent viscosity is found to be very close to the value for a
rectangular channel of uniform cross-section at the chosen Reynolds
number (Re = 0.1). It is speculated that the apparent viscosity for the
contraction geometry will increase as the Reynolds number is
reduced.", keywords = "Contraction, Electroviscous, Microfluidic,Numerical.", volume = "2", number = "4", pages = "40-5", }
