Influence of a Pulsatile Electroosmotic Flow on the Dispersivity of a Non-Reactive Solute through a Microcapillary
The influence of a pulsatile electroosmotic flow (PEOF)
at the rate of spread, or dispersivity, for a non-reactive solute released
in a microcapillary with slippage at the boundary wall (modeled by
the Navier-slip condition) is theoretically analyzed. Based on the flow
velocity field developed under such conditions, the present study
implements an analytical scheme of scaling known as the Theory
of Homogenization, in order to obtain a mathematical expression for
the dispersivity, valid at a large time scale where the initial transients
have vanished and the solute spreads under the Taylor dispersion
influence. Our results show the dispersivity is a function of a slip
coefficient, the amplitude of the imposed electric field, the Debye
length and the angular Reynolds number, highlighting the importance
of the latter as an enhancement/detrimental factor on the dispersivity,
which allows to promote the PEOF as a strong candidate for chemical
species separation at lab-on-a-chip devices.
[1] Stone H. A, Stroock A. D., and Ajdari A. Engineering flows in small
devices: microfluidics toward a lab-on-a-chip. Annu. Rev. Fluid Mech.,
36:381–411, 2004.
[2] Mei C. C. and Vernescu B. Homogenization methods for multiscale
mechanics. World scientific, 2010.
[3] Tretheway D. C. and Meinhart C. D. Apparent fluid slip at hydrophobic
microchannel walls. Phys. Fluids, 14:9–12, 2002.
[4] J. Chakraborty, S. Ray, and S. Chakraborty. Role of streaming potential
on pulsating mass flow rate control in combined electroosmotic and
pressure-driven microfluidic devices. Electrophoresis, 33:419–425,
2012.
[5] Subhra Datta, , and Sandip Ghosal. Characterizing dispersion in
microfluidic channels. Lab Chip, 9:2537–2550, 2009.
[6] Lauga E., Brenner M., and Stone H. Microfluidics: The No-slip
Boundary Condition. Springer, Berlin Heidelberg, 2007.
[7] Huang H. F. and Lai C. L. Enhancement of mass transport and
separation of species by oscillatory electroosmotic flows. Proc. R. Soc.
A., 462:2017–2038, 2006.
[8] Probstein R. F. Physicochemical hydrodynamics: an introduction. John
Wiley and Sons, 1994.
[9] Green N. G., Ramos A., Gonzalez A., Morgan H., and Castellanos
A. Fluid flow induced by nonuniform ac electric fields in electrolytes
on microelectrodes. i. experimental measurements. Phys. Rev.,
61:4011–4018, 2000.
[10] Leal L. G. Advanced transport phenomena. Cambridge University Press,
2007.
[11] Rojas G., Arcos J., Peralta M., M´endez F., and Bautista O. Pulsatile
electroosmotic flow in a microcapillary with the slip boundary condition.
Colloid Surf. A-Physicochem. Eng. Asp, 513:57–65, 2017.
[12] Sandip Ghosal. Electrokinetic flow and dispersion in capillary
electrophoresis. Annu. Rev. Fluid Mech., 38:309–338, 2006.
[13] Oddy M. H., Santiago J. G., and Mikkelsen J. C. Electrokinetic
instability micromixing. Anal. Chem., 73:5822–5832, 2001.
[14] Taylor G. I. Dispersion of soluble matter in solvent flowing slowly
through a tube. Proc. R. Society A., 219:186–203, 1953.
[15] A. Mat´ıas, S. S´anchez, F. M´endez, and O. Bautista. Influence of slip
wall effect on a non-isothermal electro-osmotic flow of a viscoelastic
fluid. Int. J. Therm. Sci., 98:352–363, 2015.
[16] C. C. Mei, J. L. Auriault, and C. O. Ng. Some applications of the
homogenization theory. Advances in Applied Mechanics, 32:277–348,
1996.
[17] C. O. Ng. Dispersion in steady and oscillatory flows through a tube with
reversible and irreversible wall reactions. Proc. R. Soc. A, 462:481–515,
2006.
[18] Ng C. O. and Zhou Q. Dispersion due to electroosmotic flow in a circular
microchannel with slowly varying wall potential and hydrodynamic
slippage. Phys. Fluids., 24:112002, 2012.
[19] Suvadip Paul and Chiu-On Ng. Dispersion in electroosmotic flow
generated by oscillatory electric field interacting with oscillatory wall
potentials. Microfluid Nanofluid, 12:237–256, 2012.
[20] M. Peralta, J. Arcos, F. M´endez, and O Bautista. Oscillatory
electroosmotic flow in a parallel- plate microchannel under asymmetric
zeta potentials. Fluid Dyn. Res., 49:035514, 2017.
[21] Zhou Q. and Ng C. O. Electro-osmotic dispersion in a circular tube
with slip-stick striped wall qe11. Fluid Dyn. Res., 47:015502, 2015.
[22] Chakraborty S. and Ray S. Mass flow-rate control through time
periodic electro-osmotic flows in circular microchannels. Phys. Fluids.,
20(083602):1–11, 2008.
[1] Stone H. A, Stroock A. D., and Ajdari A. Engineering flows in small
devices: microfluidics toward a lab-on-a-chip. Annu. Rev. Fluid Mech.,
36:381–411, 2004.
[2] Mei C. C. and Vernescu B. Homogenization methods for multiscale
mechanics. World scientific, 2010.
[3] Tretheway D. C. and Meinhart C. D. Apparent fluid slip at hydrophobic
microchannel walls. Phys. Fluids, 14:9–12, 2002.
[4] J. Chakraborty, S. Ray, and S. Chakraborty. Role of streaming potential
on pulsating mass flow rate control in combined electroosmotic and
pressure-driven microfluidic devices. Electrophoresis, 33:419–425,
2012.
[5] Subhra Datta, , and Sandip Ghosal. Characterizing dispersion in
microfluidic channels. Lab Chip, 9:2537–2550, 2009.
[6] Lauga E., Brenner M., and Stone H. Microfluidics: The No-slip
Boundary Condition. Springer, Berlin Heidelberg, 2007.
[7] Huang H. F. and Lai C. L. Enhancement of mass transport and
separation of species by oscillatory electroosmotic flows. Proc. R. Soc.
A., 462:2017–2038, 2006.
[8] Probstein R. F. Physicochemical hydrodynamics: an introduction. John
Wiley and Sons, 1994.
[9] Green N. G., Ramos A., Gonzalez A., Morgan H., and Castellanos
A. Fluid flow induced by nonuniform ac electric fields in electrolytes
on microelectrodes. i. experimental measurements. Phys. Rev.,
61:4011–4018, 2000.
[10] Leal L. G. Advanced transport phenomena. Cambridge University Press,
2007.
[11] Rojas G., Arcos J., Peralta M., M´endez F., and Bautista O. Pulsatile
electroosmotic flow in a microcapillary with the slip boundary condition.
Colloid Surf. A-Physicochem. Eng. Asp, 513:57–65, 2017.
[12] Sandip Ghosal. Electrokinetic flow and dispersion in capillary
electrophoresis. Annu. Rev. Fluid Mech., 38:309–338, 2006.
[13] Oddy M. H., Santiago J. G., and Mikkelsen J. C. Electrokinetic
instability micromixing. Anal. Chem., 73:5822–5832, 2001.
[14] Taylor G. I. Dispersion of soluble matter in solvent flowing slowly
through a tube. Proc. R. Society A., 219:186–203, 1953.
[15] A. Mat´ıas, S. S´anchez, F. M´endez, and O. Bautista. Influence of slip
wall effect on a non-isothermal electro-osmotic flow of a viscoelastic
fluid. Int. J. Therm. Sci., 98:352–363, 2015.
[16] C. C. Mei, J. L. Auriault, and C. O. Ng. Some applications of the
homogenization theory. Advances in Applied Mechanics, 32:277–348,
1996.
[17] C. O. Ng. Dispersion in steady and oscillatory flows through a tube with
reversible and irreversible wall reactions. Proc. R. Soc. A, 462:481–515,
2006.
[18] Ng C. O. and Zhou Q. Dispersion due to electroosmotic flow in a circular
microchannel with slowly varying wall potential and hydrodynamic
slippage. Phys. Fluids., 24:112002, 2012.
[19] Suvadip Paul and Chiu-On Ng. Dispersion in electroosmotic flow
generated by oscillatory electric field interacting with oscillatory wall
potentials. Microfluid Nanofluid, 12:237–256, 2012.
[20] M. Peralta, J. Arcos, F. M´endez, and O Bautista. Oscillatory
electroosmotic flow in a parallel- plate microchannel under asymmetric
zeta potentials. Fluid Dyn. Res., 49:035514, 2017.
[21] Zhou Q. and Ng C. O. Electro-osmotic dispersion in a circular tube
with slip-stick striped wall qe11. Fluid Dyn. Res., 47:015502, 2015.
[22] Chakraborty S. and Ray S. Mass flow-rate control through time
periodic electro-osmotic flows in circular microchannels. Phys. Fluids.,
20(083602):1–11, 2008.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:77714", author = "Jaime Muñoz and José Arcos and Oscar Bautista Federico Méndez", title = "Influence of a Pulsatile Electroosmotic Flow on the Dispersivity of a Non-Reactive Solute through a Microcapillary", abstract = "The influence of a pulsatile electroosmotic flow (PEOF)
at the rate of spread, or dispersivity, for a non-reactive solute released
in a microcapillary with slippage at the boundary wall (modeled by
the Navier-slip condition) is theoretically analyzed. Based on the flow
velocity field developed under such conditions, the present study
implements an analytical scheme of scaling known as the Theory
of Homogenization, in order to obtain a mathematical expression for
the dispersivity, valid at a large time scale where the initial transients
have vanished and the solute spreads under the Taylor dispersion
influence. Our results show the dispersivity is a function of a slip
coefficient, the amplitude of the imposed electric field, the Debye
length and the angular Reynolds number, highlighting the importance
of the latter as an enhancement/detrimental factor on the dispersivity,
which allows to promote the PEOF as a strong candidate for chemical
species separation at lab-on-a-chip devices.", keywords = "Dispersivity, microcapillary, Navier-slip condition,
pulsatile electroosmotic flow, Taylor dispersion, Theory of
Homogenization.", volume = "12", number = "8", pages = "777-7", }
