Pulsatile Poiseuille flows in microfluidic channels with back-and-forth mode

Kwang Seok Kim; Myung-Suk Chun

Korea-Australia Rheology Journal, Vol.24, No.2, 89-95, June, 2012

DOI10.1007/s13367-012-0010-5 Export Citation

Pulsatile Poiseuille flows in microfluidic channels with back-and-forth mode

Kwang Seok Kim, and Myung-Suk Chun^†

Complex Fluids Laboratory, National Agenda Res. Div., Korea Institute of Science and Technology (KIST), Seongbuk-gu, Seoul 136-791, Republic of Korea

E-mail:

The numerical solver for the velocity field equation describing laminar pulsatile flows driven by a timedependent pressure drop in the straight microfluidic channel of square cross-section is developed. In the computational algorithm, an orthogonal collocation on finite element scheme for spatial discretizations is combined with an adaptive Runge-Kutta method for time integration. The algorithm with the 1,521 computational nodes and the accuracy up to O(10^(-5)) is applied to the flow in the back-and-forth standing mode with the channel hydraulic diameter (Dh) in the range 10 - 500 μm and the oscillating frequency (f) of 1 to 100 Hz. As a result, a periodic steady state is defined as the flow condition where there would be no net movement after long time elapses. Following by the retardation phenomena in a cycle, reversal of the axial velocity is observed at the channel center. Major attention is focused on the influences of the size of channel cross-section and the oscillating frequency. Increasing Dh and f results in the decrease in the amplitude of mean velocity but the increase in the start-up time. Larger time delay occurs by low-frequency pulsation.

Keywords:pulsatile flow;microfluidics;Navier-Stokes equation;orthogonal collocation;adaptive integration

[References]

Bialecki B, Fernandes RI, SIAM J. Numer. Anal., 47, 3429 (2009)
Bode K, Hooper RJ, Paterson WR, Wilson DI, Augustin W, Scholl S, Heat Transfer Eng., 28, 202 (2007)
Chun MS, Lee TS, Choi NW, J. Micromech.Microeng., 15, 710 (2005)
Chun MS, Phys.Rev. E., 036312/1-9, 83 (2011)
Edwards MF, Wilkinson MA, Trans. Inst. Chem.Eng., 49, 85 (1971)
Fan C, Chao BT, ZAMP., 16, 351 (1965)
Finlayson BA, Nonlinear Analysis in Chemical Engineering., McGraw-Hill, New York. (1980)
Fuerstman MJ, Lai A, Thurlow ME, Shevkoplyas SS, Stone HA, Whitesides GM, Lab Chip., 7, 1479 (2007)
Gong L, Wu J, Wang L, Cao K, Phys. Fluids., 063603/1-7., 20 (2008)
Hodis S, Zamir M, Phys. Rev. E., 051923/1-8., 83 (2011)
Hu Y, Gopal A, Lin K, Peng Y, Tasciotti E, Zhang X, Ferrari M, Biomicrofluidics., 013410/1-7, 5 (2011)
Kim KS, Simon L, Comput. Chem. Eng., 33(6), 1212 (2009)
Kim KS, Ryoo W, Chun MS, Chung GY, Lee SO, Korean J. Chem. Eng., 29(2), 162 (2012)
Leal LG, Laminar flow and convective transport, Butterworth-Heinemann, Boston (1992)
Lejeunes S, Boukamel A, Meo S, Comput. Struct., 89, 411 (2011)
Leslie DC, Easley CJ, Seker E, Karlinsey JM, Utz M, Begley MR, Landers JP, Nat. Phys., 5, 231 (2009)
Lide DR, CRC Handbook of Chemistry and Physics., 87th ed., CRC Press, Boca Raton. (2006)
Morris CJ, Forster FK, Exp. Fluids., 36, 928 (2004)
Stone HA, Stroock AD, Ajdari A, Annu. Rev. Fluid Mech., 36, 381 (2004)
Tikekar M, Singh SG, Agrawal A, Microfluid Nanofluid., 9, 1225 (2010)
Vedel S, Olesen LH, Bruus H, J. Micromech. Microeng., 035026/1-11, 20 (2010)
Womersley RJ, J. Physiol.-London., 126, 553 (1955)

[Referenced By]

[Related Articles]

[1] Bialecki B, Fernandes RI, SIAM J. Numer. Anal., 47, 3429 (2009)

[2] Bode K, Hooper RJ, Paterson WR, Wilson DI, Augustin W, Scholl S, Heat Transfer Eng., 28, 202 (2007)

[3] Chun MS, Lee TS, Choi NW, J. Micromech.Microeng., 15, 710 (2005)

[4] Chun MS, Phys.Rev. E., 036312/1-9, 83 (2011)

[5] Edwards MF, Wilkinson MA, Trans. Inst. Chem.Eng., 49, 85 (1971)

[6] Fan C, Chao BT, ZAMP., 16, 351 (1965)

[7] Finlayson BA, Nonlinear Analysis in Chemical Engineering., McGraw-Hill, New York. (1980)

[8] Fuerstman MJ, Lai A, Thurlow ME, Shevkoplyas SS, Stone HA, Whitesides GM, Lab Chip., 7, 1479 (2007)

[9] Gong L, Wu J, Wang L, Cao K, Phys. Fluids., 063603/1-7., 20 (2008)

[10] Hodis S, Zamir M, Phys. Rev. E., 051923/1-8., 83 (2011)

[11] Hu Y, Gopal A, Lin K, Peng Y, Tasciotti E, Zhang X, Ferrari M, Biomicrofluidics., 013410/1-7, 5 (2011)

[12] Kim KS, Simon L, Comput. Chem. Eng., 33(6), 1212 (2009)

[13] Kim KS, Ryoo W, Chun MS, Chung GY, Lee SO, Korean J. Chem. Eng., 29(2), 162 (2012)

[14] Leal LG, Laminar flow and convective transport, Butterworth-Heinemann, Boston (1992)

[15] Lejeunes S, Boukamel A, Meo S, Comput. Struct., 89, 411 (2011)

[16] Leslie DC, Easley CJ, Seker E, Karlinsey JM, Utz M, Begley MR, Landers JP, Nat. Phys., 5, 231 (2009)

[17] Lide DR, CRC Handbook of Chemistry and Physics., 87th ed., CRC Press, Boca Raton. (2006)

[18] Morris CJ, Forster FK, Exp. Fluids., 36, 928 (2004)

[19] Stone HA, Stroock AD, Ajdari A, Annu. Rev. Fluid Mech., 36, 381 (2004)

[20] Tikekar M, Singh SG, Agrawal A, Microfluid Nanofluid., 9, 1225 (2010)

[21] Vedel S, Olesen LH, Bruus H, J. Micromech. Microeng., 035026/1-11, 20 (2010)

[22] Womersley RJ, J. Physiol.-London., 126, 553 (1955)