Flow inside Micro-Channel Bounded by Superhydrophobic Surface with Eccentric Micro-Grooves
The superhydrophobic surface is widely used to reduce
friction for the flow inside micro-channel and can be used to
control/manipulate fluid, cells and even proteins in lab-on-chip.
Fabricating micro grooves on hydrophobic surfaces is a common
method to obtain such superhydrophobic surface. This study
utilized the numerical method to investigate the effect of eccentric
micro-grooves on the friction of flow inside micro-channel. A detailed
parametric study was conducted to reveal how the eccentricity of
micro-grooves affects the micro-channel flow under different grooves
sizes, channel heights, Reynolds number. The results showed that
the superhydrophobic surface with eccentric micro-grooves induces
less friction than the counter part with aligning micro-grooves, which
means requiring less power for pumps.
[1] H. A. Stone, A. D. Stroock, A. Ajdari, Engineering flows in small
devices: microfluidics toward a lab-on-a-chip, Annu. Rev. Fluid Mech.
36 (2004) 381–411.
[2] G. Hagen, Uber den Einfluss der Temperatur auf die Bewegung des
Wasser in R¨ohren, Math. Abh. Akad. Wiss. 17.
[3] H. Darcy, Recherches exp´erimentales relatives au mouvement de l’eau
dans les tuyaux, Mallet-Bachelier, 1857.
[4] J. Nikuradse, Str¨omungsgesetze in Rauhen Rohren,
VDI-Forschungscheft 361; also NACA TM 1292 (1950) .
[5] L. F. Moody, N. J. Princeton, Friction factors for pipe flow, Trans. ASME
66 (8) (1944) 671–684.
[6] R. Garc´ıa-Mayoral, J. Jim´enez, Drag reduction by riblets, Philosophical
Transactions of the Royal Society of London A: Mathematical, Physical
and Engineering Sciences 369 (1940) (2011) 1412–1427.
[7] J. P. Rothstein, Slip on superhydrophobic surfaces, Annual Review of
Fluid Mechanics 42 (2010) 89–109.
[8] W. Barthlott, C. Neinhuis, Purity of the sacred lotus, or escape from
contamination in biological surfaces, Planta 202 (1) (1997) 1–8.
[9] C. Navier, M´emoire sur les lois du mouvement des fluides, M´emoires
de L’Acad´emie Royale de Sciences de L’Institut de France 6 (1823)
389–440.
[10] J. C. Maxwell, On stresses in rarified gases arising from inequalities of
temperature, Philosophical Transactions of the royal society of London
170 (1879) 231–256.
[11] J. Ou, B. Perot, J. P. Rothstein, Laminar drag reduction in microchannels
using ultrahydrophobic surfaces, Physics of Fluids 16 (12) (2004)
4635–4643.
[12] B. Woolford, K. Jeffs, D. Maynes, B. Webb, Laminar fully-developed
flow in a microchannel with patterned ultrahydrophobic walls, in: ASME
2005 Summer Heat Transfer Conference collocated with the ASME 2005
Pacific Rim Technical Conference and Exhibition on Integration and
Packaging of MEMS, NEMS, and Electronic Systems, American Society
of Mechanical Engineers, 481–488, 2005.
[13] O. I. Vinogradova, Slippage of water over hydrophobic surfaces,
International journal of mineral processing 56 (1) (1999) 31–60.
[14] G. E. Karniadakis, A. Beskok, N. Aluru, Microflows and nanoflows:
fundamentals and simulation, vol. 29, Springer Science & Business
Media, 2006.
[15] E. Lauga, M. Brenner, H. Stone, Microfluidics: the no-slip boundary
condition, in: Springer handbook of experimental fluid mechanics, Springer, 1219–1240, 2007.
[16] X. Zhang, F. Shi, J. Niu, Y. G. Jiang, Z. Q. Wang, Superhydrophobic
surfaces: from structural control to functional application, Journal of
Materials Chemistry 18 (6) (2008) 621–633.
[17] M. Zhou, J. Li, C. X. Wu, X. K. Zhou, L. Cai, Fluid drag reduction on
superhydrophobic surfaces coated with carbon nanotube forests (CNTs),
Soft Matter 7 (9) (2011) 4391–4396.
[18] L. C. Gao, T. J. McCarthy, A perfectly hydrophobic surface (θA/θR=
180/180), Journal of the American Chemical Society 128 (28) (2006)
9052–9053.
[19] D. Qu´er´e, Wetting and roughness, Annu. Rev. Mater. Res. 38 (2008)
71–99.
[20] M. Reyssat, J. M. Yeomans, D. Qu´er´e, Impalement of fakir drops,
Europhys. Lett. 81 (2008) 26006.
[21] M. A. Samaha, H. V. Tafreshi, M. Gad-el Hak, Modeling drag reduction
and meniscus stability of superhydrophobic surfaces comprised of
random roughness, Physics of Fluids 23 (1) (2011) 012001.
[22] E. Lauga, H. A. Stone, Effective slip in pressure-driven Stokes flow,
Journal of Fluid Mechanics 489 (2003) 55–77.
[23] C.-H. Choi, C.-J. Kim, Large slip of aqueous liquid flow over a
nanoengineered superhydrophobic surface, Physical Review Letters
96 (6) (2006) 066001.
[24] C. Lee, C.-H. Choi, et al., Structured surfaces for a giant liquid slip,
Physical review letters 101 (6) (2008) 064501.
[25] C. Ybert, C. Barentin, C. Cottin-Bizonne, P. Joseph, L. Bocquet,
Achieving large slip with superhydrophobic surfaces: Scaling laws for
generic geometries, Physics of Fluids (1994-present) 19 (12) (2007)
123601.
[26] J. Davies, D. Maynes, B. W. Webb, B. Woolford, Laminar flow in a
microchannel with superhydrophobic walls exhibiting transverse ribs,
Physics of Fluids 18 (8) (2006) 87110.
[27] S. Gogte, P. Vorobieff, R. Truesdell, A. Mammoli, F. van Swol, P. Shah,
C. J. Brinker, Effective slip on textured superhydrophobic surfaces,
Physics of fluids 17 (5) (2005) 51701–51701.
[28] Y. P. Cheng, C. J. Teo, B. C. Khoo, Microchannel flows with
superhydrophobic surfaces: Effects of Reynolds number and pattern
width to channel height ratio, Physics of Fluids 21 (2009) (2009) 1–12.
[29] A. Steinberger, C. Cottin-Bizonne, P. Kleimann, E. Charlaix, High
friction on a bubble mattress, Nature materials 6 (9) (2007) 665–668.
[30] A. M. Davis, E. Lauga, Geometric transition in friction for flow over a
bubble mattress, Physics of Fluids (1994-present) 21 (1) (2009) 011701.
[31] C.-O. Ng, C. Wang, Stokes shear flow over a grating: implications for
superhydrophobic slip, Physics of Fluids (1994-present) 21 (1) (2009)
013602.
[32] J. Hyv¨aluoma, J. Harting, Slip flow over structured surfaces with
entrapped microbubbles, Physical review letters 100 (24) (2008) 246001.
[33] C. J. Teo, B. C. Khoo, Flow past superhydrophobic surfaces containing
longitudinal grooves: Effects of interface curvature, Microfluidics and
Nanofluidics 9 (2-3) (2010) 499–511.
[34] C. J. Teo, B. C. Khoo, Effects of interface curvature on Poiseuille flow
through microchannels and microtubes containing superhydrophobic
surfaces with transverse grooves and ribs, Microfluidics and Nanofluidics
17 (5) (2014) 891–905.
[35] N. Kashaninejad, N.-T. Nguyen, W. K. Chan, Eccentricity effects of
microhole arrays on drag reduction efficiency of microchannels with a
hydrophobic wall, Physics of Fluids 24 (11) (2012) 112004.
[36] C. J. Teo, B. C. Khoo, Analysis of Stokes flow in microchannels with
superhydrophobic surfaces containing a periodic array of micro-grooves,
Microfluidics and Nanofluidics 7 (3) (2009) 353–382.
[37] W. Ren, C. Shu, J.Wu,W. Yang, Boundary condition-enforced immersed
boundary method for thermal flow problems with Dirichlet temperature
condition and its applications, Computers & Fluids 57 (2012) 40–51.
[38] W. Ren, J. Wu, C. Shu, W. Yang, A stream function–vorticity
formulation-based immersed boundary method and its applications,
International Journal for Numerical Methods in Fluids 70 (5) (2012)
627–645.
[39] C. Shu, W. Ren, W. Yang, Novel immersed boundary methods for
thermal flow problems, International Journal of Numerical Methods for
Heat & Fluid Flow 23 (1) (2013) 124–142.
[40] Y. Cheng, J. Xu, Y. Sui, Numerical study on drag reduction and heat
transfer enhancement in microchannels with superhydrophobic surfaces
for electronic cooling, Applied Thermal Engineering (2014) 1–11.
[1] H. A. Stone, A. D. Stroock, A. Ajdari, Engineering flows in small
devices: microfluidics toward a lab-on-a-chip, Annu. Rev. Fluid Mech.
36 (2004) 381–411.
[2] G. Hagen, Uber den Einfluss der Temperatur auf die Bewegung des
Wasser in R¨ohren, Math. Abh. Akad. Wiss. 17.
[3] H. Darcy, Recherches exp´erimentales relatives au mouvement de l’eau
dans les tuyaux, Mallet-Bachelier, 1857.
[4] J. Nikuradse, Str¨omungsgesetze in Rauhen Rohren,
VDI-Forschungscheft 361; also NACA TM 1292 (1950) .
[5] L. F. Moody, N. J. Princeton, Friction factors for pipe flow, Trans. ASME
66 (8) (1944) 671–684.
[6] R. Garc´ıa-Mayoral, J. Jim´enez, Drag reduction by riblets, Philosophical
Transactions of the Royal Society of London A: Mathematical, Physical
and Engineering Sciences 369 (1940) (2011) 1412–1427.
[7] J. P. Rothstein, Slip on superhydrophobic surfaces, Annual Review of
Fluid Mechanics 42 (2010) 89–109.
[8] W. Barthlott, C. Neinhuis, Purity of the sacred lotus, or escape from
contamination in biological surfaces, Planta 202 (1) (1997) 1–8.
[9] C. Navier, M´emoire sur les lois du mouvement des fluides, M´emoires
de L’Acad´emie Royale de Sciences de L’Institut de France 6 (1823)
389–440.
[10] J. C. Maxwell, On stresses in rarified gases arising from inequalities of
temperature, Philosophical Transactions of the royal society of London
170 (1879) 231–256.
[11] J. Ou, B. Perot, J. P. Rothstein, Laminar drag reduction in microchannels
using ultrahydrophobic surfaces, Physics of Fluids 16 (12) (2004)
4635–4643.
[12] B. Woolford, K. Jeffs, D. Maynes, B. Webb, Laminar fully-developed
flow in a microchannel with patterned ultrahydrophobic walls, in: ASME
2005 Summer Heat Transfer Conference collocated with the ASME 2005
Pacific Rim Technical Conference and Exhibition on Integration and
Packaging of MEMS, NEMS, and Electronic Systems, American Society
of Mechanical Engineers, 481–488, 2005.
[13] O. I. Vinogradova, Slippage of water over hydrophobic surfaces,
International journal of mineral processing 56 (1) (1999) 31–60.
[14] G. E. Karniadakis, A. Beskok, N. Aluru, Microflows and nanoflows:
fundamentals and simulation, vol. 29, Springer Science & Business
Media, 2006.
[15] E. Lauga, M. Brenner, H. Stone, Microfluidics: the no-slip boundary
condition, in: Springer handbook of experimental fluid mechanics, Springer, 1219–1240, 2007.
[16] X. Zhang, F. Shi, J. Niu, Y. G. Jiang, Z. Q. Wang, Superhydrophobic
surfaces: from structural control to functional application, Journal of
Materials Chemistry 18 (6) (2008) 621–633.
[17] M. Zhou, J. Li, C. X. Wu, X. K. Zhou, L. Cai, Fluid drag reduction on
superhydrophobic surfaces coated with carbon nanotube forests (CNTs),
Soft Matter 7 (9) (2011) 4391–4396.
[18] L. C. Gao, T. J. McCarthy, A perfectly hydrophobic surface (θA/θR=
180/180), Journal of the American Chemical Society 128 (28) (2006)
9052–9053.
[19] D. Qu´er´e, Wetting and roughness, Annu. Rev. Mater. Res. 38 (2008)
71–99.
[20] M. Reyssat, J. M. Yeomans, D. Qu´er´e, Impalement of fakir drops,
Europhys. Lett. 81 (2008) 26006.
[21] M. A. Samaha, H. V. Tafreshi, M. Gad-el Hak, Modeling drag reduction
and meniscus stability of superhydrophobic surfaces comprised of
random roughness, Physics of Fluids 23 (1) (2011) 012001.
[22] E. Lauga, H. A. Stone, Effective slip in pressure-driven Stokes flow,
Journal of Fluid Mechanics 489 (2003) 55–77.
[23] C.-H. Choi, C.-J. Kim, Large slip of aqueous liquid flow over a
nanoengineered superhydrophobic surface, Physical Review Letters
96 (6) (2006) 066001.
[24] C. Lee, C.-H. Choi, et al., Structured surfaces for a giant liquid slip,
Physical review letters 101 (6) (2008) 064501.
[25] C. Ybert, C. Barentin, C. Cottin-Bizonne, P. Joseph, L. Bocquet,
Achieving large slip with superhydrophobic surfaces: Scaling laws for
generic geometries, Physics of Fluids (1994-present) 19 (12) (2007)
123601.
[26] J. Davies, D. Maynes, B. W. Webb, B. Woolford, Laminar flow in a
microchannel with superhydrophobic walls exhibiting transverse ribs,
Physics of Fluids 18 (8) (2006) 87110.
[27] S. Gogte, P. Vorobieff, R. Truesdell, A. Mammoli, F. van Swol, P. Shah,
C. J. Brinker, Effective slip on textured superhydrophobic surfaces,
Physics of fluids 17 (5) (2005) 51701–51701.
[28] Y. P. Cheng, C. J. Teo, B. C. Khoo, Microchannel flows with
superhydrophobic surfaces: Effects of Reynolds number and pattern
width to channel height ratio, Physics of Fluids 21 (2009) (2009) 1–12.
[29] A. Steinberger, C. Cottin-Bizonne, P. Kleimann, E. Charlaix, High
friction on a bubble mattress, Nature materials 6 (9) (2007) 665–668.
[30] A. M. Davis, E. Lauga, Geometric transition in friction for flow over a
bubble mattress, Physics of Fluids (1994-present) 21 (1) (2009) 011701.
[31] C.-O. Ng, C. Wang, Stokes shear flow over a grating: implications for
superhydrophobic slip, Physics of Fluids (1994-present) 21 (1) (2009)
013602.
[32] J. Hyv¨aluoma, J. Harting, Slip flow over structured surfaces with
entrapped microbubbles, Physical review letters 100 (24) (2008) 246001.
[33] C. J. Teo, B. C. Khoo, Flow past superhydrophobic surfaces containing
longitudinal grooves: Effects of interface curvature, Microfluidics and
Nanofluidics 9 (2-3) (2010) 499–511.
[34] C. J. Teo, B. C. Khoo, Effects of interface curvature on Poiseuille flow
through microchannels and microtubes containing superhydrophobic
surfaces with transverse grooves and ribs, Microfluidics and Nanofluidics
17 (5) (2014) 891–905.
[35] N. Kashaninejad, N.-T. Nguyen, W. K. Chan, Eccentricity effects of
microhole arrays on drag reduction efficiency of microchannels with a
hydrophobic wall, Physics of Fluids 24 (11) (2012) 112004.
[36] C. J. Teo, B. C. Khoo, Analysis of Stokes flow in microchannels with
superhydrophobic surfaces containing a periodic array of micro-grooves,
Microfluidics and Nanofluidics 7 (3) (2009) 353–382.
[37] W. Ren, C. Shu, J.Wu,W. Yang, Boundary condition-enforced immersed
boundary method for thermal flow problems with Dirichlet temperature
condition and its applications, Computers & Fluids 57 (2012) 40–51.
[38] W. Ren, J. Wu, C. Shu, W. Yang, A stream function–vorticity
formulation-based immersed boundary method and its applications,
International Journal for Numerical Methods in Fluids 70 (5) (2012)
627–645.
[39] C. Shu, W. Ren, W. Yang, Novel immersed boundary methods for
thermal flow problems, International Journal of Numerical Methods for
Heat & Fluid Flow 23 (1) (2013) 124–142.
[40] Y. Cheng, J. Xu, Y. Sui, Numerical study on drag reduction and heat
transfer enhancement in microchannels with superhydrophobic surfaces
for electronic cooling, Applied Thermal Engineering (2014) 1–11.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:76335", author = "Yu Chen and Weiwei Ren and Xiaojing Mu and Feng Zhang and Yi Xu", title = "Flow inside Micro-Channel Bounded by Superhydrophobic Surface with Eccentric Micro-Grooves", abstract = "The superhydrophobic surface is widely used to reduce
friction for the flow inside micro-channel and can be used to
control/manipulate fluid, cells and even proteins in lab-on-chip.
Fabricating micro grooves on hydrophobic surfaces is a common
method to obtain such superhydrophobic surface. This study
utilized the numerical method to investigate the effect of eccentric
micro-grooves on the friction of flow inside micro-channel. A detailed
parametric study was conducted to reveal how the eccentricity of
micro-grooves affects the micro-channel flow under different grooves
sizes, channel heights, Reynolds number. The results showed that
the superhydrophobic surface with eccentric micro-grooves induces
less friction than the counter part with aligning micro-grooves, which
means requiring less power for pumps.", keywords = "Superhydrophobic, transverse grooves, heat transfer,
slip length, microfluidics.", volume = "11", number = "9", pages = "1579-6", }
