Journal of Computational Applied Mechanics

Slip effect on the unsteady electroosmotic and pressure-driven flows of two-layer fluids in a rectangular microchannel

Document Type : Research Paper

Authors

1 department of computer science and engineering, Air university multan campus, Pakistan

2 PhD candidate at ABDUS SALAM SCHOOL OF MATHEMATICAL SCIENCES GC University, Lahore. 68-B, New MuslimTown, Lahore 54600, Pakistan

Abstract

Abstract of the paper:
Electroosmotic flows of two-layer immiscible Newtonian fluids under the influence of time-dependent pressure gradient in the flow direction and different zeta potentials on the walls have been investigated. The slippage on channel walls is, also, considered in the mathematical model. Solutions to fluid velocities in the transformed domain are determined by using the Laplace transform with respect to the time variable and the classical method of the ordinary differential equations. The inverse Laplace transforms are obtained numerically by using Talbot’s algorithm and the improved Talbot’s algorithm.
Numerical results corresponding to a time-exponential pressure gradient and translational motion with the oscillating velocity of the channel walls have been presented in graphical illustrations in order to study the fluid behaviour. It has been found that the ratio of the dielectric constant of fluid layers and the interface zeta potential difference have a significant influence on the fluid velocities.

Keywords

 

[1]  Stone, H.A., Stroock, A.D. and Ajdari, A., 2004. Engineering flows in small devices: microfluidics toward a lab-on-a-chip. Annu. Rev. Fluid Mech., 36, pp.381-411.

[2]  Hunter, R. J. (1981). Zeta potential in colloid science. Academic, San Diego.

[3]  Karniadakis, G., Beskok, A. and Aluru, N., 2006. Microflows and nanoflows: fundamentals and simulation (Vol. 29). Springer Science & Business Media.

[4]  Chang, H.T., Chen, H.S., Hsieh, M.M. and Tseng, W.L., 2000. Electrophoretic separation of DNA in the presence of electroosmotic flow. Reviews in Analytical Chemistry, 19(1), pp.45-74.

 

[5]  Anderson, G.P., King, K.D., Cuttino, D.S., Whelan, J.P., Ligler, F.S., MacKrell, J.F., Bovais, C.S., Indyke, D.K. and Foch, R.J., 1999. Biological agent detection with the use of an airborne biosensor. Field Analytical Chemistry & Technology, 3(4‐5), pp.307-314.

[6]  Chen, C.H., Zeng, S., Mikkelsen, J.C. and Santiago, J.G., 2000, November. Development of a planar electrokinetic micropump. In Proc of ASME Int Mech Eng Congress and Exposition (pp. 523-528).

[7]  Dutta, P. and Beskok, A., 2001. Analytical solution of time periodic electroosmotic flows: analogies to Stokes’ second problem. Analytical Chemistry, 73(21), pp.5097-5102.

[8]  Wang, X., Chen, B. and Wu, J., 2007. A semianalytical solution of periodical electro-osmosis in a rectangular microchannel. Physics of Fluids, 19(12), p.127101.

[9]  Jian, Y., Yang, L. and Liu, Q., 2010. Time periodic electro-osmotic flow through a microannulus. Physics of Fluids, 22(4), p.042001.

[10]  Liu, Q.S., Jian, Y.J. and Yang, L.G., 2011. Time periodic electroosmotic flow of the generalized Maxwell fluids between two micro-parallel plates. Journal of Non-Newtonian Fluid Mechanics, 166(9-10), pp.478-486.

[11]  Jian, Y.J., Liu, Q.S. and Yang, L.G., 2011. AC electroosmotic flow of generalized Maxwell fluids in a rectangular microchannel. Journal of Non-Newtonian Fluid Mechanics, 166(21-22), pp.1304-1314.

[12]  Su, J., Jian, Y. and Chang, L., 2012. Thermally fully developed electroosmotic flow through a rectangular microchannel. International Journal of Heat and Mass Transfer, 55(21-22), pp.6285-6290.

[13]  Keh, H.J. and Tseng, H.C., 2001. Transient electrokinetic flow in fine capillaries. Journal of colloid and Interface Science, 242(2), pp.450-459.

[14]  Deng, S.Y., Jian, Y.J., Bi, Y.H., Chang, L., Wang, H.J. and Liu, Q.S., 2012. Unsteady electroosmotic flow of power-law fluid in a rectangular microchannel. Mechanics Research Communications, 39(1), pp.9-14.

[15]  Brask, A., Goranovic, G. and Bruus, H., 2003. Electroosmotic pumping of nonconducting liquids by viscous drag from a secondary conducting liquid. Tech Proc Nanotech, 1, pp.190-193.

[16]  Shankar, V. and Sharma, A., 2004. Instability of the interface between thin fluid films subjected to electric fields. Journal of colloid and interface science, 274(1), pp.294-308.

[17]  Verma, R., Sharma, A., Kargupta, K. and Bhaumik, J., 2005. Electric field induced instability and pattern formation in thin liquid films. Langmuir, 21(8), pp.3710-3721.

[18]  Liu, M., Liu, Y., Guo, Q. and Yang, J., 2009. Modeling of electroosmotic pumping of nonconducting liquids and biofluids by a two-phase flow method. Journal of electroanalytical chemistry, 636(1-2), pp.86-92.

 

 

[19]  Gao, Y., Wong, T.N., Yang, C. and Ooi, K.T., 2005. Transient two-liquid electroosmotic flow with electric charges at the interface. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 266(1-3), pp.117-128.

[20]  Su, J., Jian, Y.J., Chang, L. and Li, Q.S., 2013. Transient electro-osmotic and pressure driven flows of two-layer fluids through a slit microchannel. Acta Mechanica Sinica, 29(4), pp.534-542.

[21]  Goswami, P. and Chakraborty, S., 2011. Semi-analytical solutions for electroosmotic flows with interfacial slip in microchannels of complex cross-sectional shapes. Microfluidics and nanofluidics, 11(3), pp.255-267.

[22]  Shit, G.C., Mondal, A., Sinha, A. and Kundu, P.K., 2016. Effects of slip velocity on rotating electro-osmotic flow in a slowly varying micro-channel. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 489, pp.249-255.

[23]  J. Abate, P. P. Valko, Multi-precision Laplace transform inversion, Int. J. Numer. Meth. Engng., 60 (2004) 979-993, doi:10.1002/nme.995.

[24]  B. Dingfelder, J. A. C. Weideman, An improved Talbot method for numerical Laplace transform inversion, Numer. Algor., 68 (2015) 167-183, doi: 10.1007/s11075-014-9895-z.

 

[1]  Stone, H.A., Stroock, A.D. and Ajdari, A., 2004. Engineering flows in small devices: microfluidics toward a lab-on-a-chip. Annu. Rev. Fluid Mech., 36, pp.381-411.
[2]  Hunter, R. J. (1981). Zeta potential in colloid science. Academic, San Diego.
[3]  Karniadakis, G., Beskok, A. and Aluru, N., 2006. Microflows and nanoflows: fundamentals and simulation (Vol. 29). Springer Science & Business Media.
[4]  Chang, H.T., Chen, H.S., Hsieh, M.M. and Tseng, W.L., 2000. Electrophoretic separation of DNA in the presence of electroosmotic flow. Reviews in Analytical Chemistry, 19(1), pp.45-74.
 
[5]  Anderson, G.P., King, K.D., Cuttino, D.S., Whelan, J.P., Ligler, F.S., MacKrell, J.F., Bovais, C.S., Indyke, D.K. and Foch, R.J., 1999. Biological agent detection with the use of an airborne biosensor. Field Analytical Chemistry & Technology, 3(4‐5), pp.307-314.
[6]  Chen, C.H., Zeng, S., Mikkelsen, J.C. and Santiago, J.G., 2000, November. Development of a planar electrokinetic micropump. In Proc of ASME Int Mech Eng Congress and Exposition (pp. 523-528).
[7]  Dutta, P. and Beskok, A., 2001. Analytical solution of time periodic electroosmotic flows: analogies to Stokes’ second problem. Analytical Chemistry, 73(21), pp.5097-5102.
[8]  Wang, X., Chen, B. and Wu, J., 2007. A semianalytical solution of periodical electro-osmosis in a rectangular microchannel. Physics of Fluids, 19(12), p.127101.
[9]  Jian, Y., Yang, L. and Liu, Q., 2010. Time periodic electro-osmotic flow through a microannulus. Physics of Fluids, 22(4), p.042001.
[10]  Liu, Q.S., Jian, Y.J. and Yang, L.G., 2011. Time periodic electroosmotic flow of the generalized Maxwell fluids between two micro-parallel plates. Journal of Non-Newtonian Fluid Mechanics, 166(9-10), pp.478-486.
[11]  Jian, Y.J., Liu, Q.S. and Yang, L.G., 2011. AC electroosmotic flow of generalized Maxwell fluids in a rectangular microchannel. Journal of Non-Newtonian Fluid Mechanics, 166(21-22), pp.1304-1314.
[12]  Su, J., Jian, Y. and Chang, L., 2012. Thermally fully developed electroosmotic flow through a rectangular microchannel. International Journal of Heat and Mass Transfer, 55(21-22), pp.6285-6290.
[13]  Keh, H.J. and Tseng, H.C., 2001. Transient electrokinetic flow in fine capillaries. Journal of colloid and Interface Science, 242(2), pp.450-459.
[14]  Deng, S.Y., Jian, Y.J., Bi, Y.H., Chang, L., Wang, H.J. and Liu, Q.S., 2012. Unsteady electroosmotic flow of power-law fluid in a rectangular microchannel. Mechanics Research Communications, 39(1), pp.9-14.
[15]  Brask, A., Goranovic, G. and Bruus, H., 2003. Electroosmotic pumping of nonconducting liquids by viscous drag from a secondary conducting liquid. Tech Proc Nanotech, 1, pp.190-193.
[16]  Shankar, V. and Sharma, A., 2004. Instability of the interface between thin fluid films subjected to electric fields. Journal of colloid and interface science, 274(1), pp.294-308.
[17]  Verma, R., Sharma, A., Kargupta, K. and Bhaumik, J., 2005. Electric field induced instability and pattern formation in thin liquid films. Langmuir, 21(8), pp.3710-3721.
[18]  Liu, M., Liu, Y., Guo, Q. and Yang, J., 2009. Modeling of electroosmotic pumping of nonconducting liquids and biofluids by a two-phase flow method. Journal of electroanalytical chemistry, 636(1-2), pp.86-92.
 
 
[19]  Gao, Y., Wong, T.N., Yang, C. and Ooi, K.T., 2005. Transient two-liquid electroosmotic flow with electric charges at the interface. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 266(1-3), pp.117-128.
[20]  Su, J., Jian, Y.J., Chang, L. and Li, Q.S., 2013. Transient electro-osmotic and pressure driven flows of two-layer fluids through a slit microchannel. Acta Mechanica Sinica, 29(4), pp.534-542.
[21]  Goswami, P. and Chakraborty, S., 2011. Semi-analytical solutions for electroosmotic flows with interfacial slip in microchannels of complex cross-sectional shapes. Microfluidics and nanofluidics, 11(3), pp.255-267.
[22]  Shit, G.C., Mondal, A., Sinha, A. and Kundu, P.K., 2016. Effects of slip velocity on rotating electro-osmotic flow in a slowly varying micro-channel. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 489, pp.249-255.
[23]  J. Abate, P. P. Valko, Multi-precision Laplace transform inversion, Int. J. Numer. Meth. Engng., 60 (2004) 979-993, doi:10.1002/nme.995.
[24]  B. Dingfelder, J. A. C. Weideman, An improved Talbot method for numerical Laplace transform inversion, Numer. Algor., 68 (2015) 167-183, doi: 10.1007/s11075-014-9895-z.
Journal of Computational Applied Mechanics
Volume 52, Issue 1
March 2021
Pages 12-26
  • Receive Date: 19 September 2019
  • Accept Date: 24 September 2019