Advertisement

Experimental and theoretical investigation of a low-Reynolds-number flow through deformable shallow microchannels with ultra-low height-to-width aspect ratios

  • Aryan Mehboudi
  • Junghoon YeomEmail author
Research Paper
  • 59 Downloads

Abstract

The emerging field of deformable microfluidics widely employed in the Lab-on-a-Chip and MEMS communities offers an opportunity to study a relatively under-examined physics. The main objective of this work is to provide a deeper insight into the underlying coupled fluid–solid interactions of a low-Reynolds-number, i.e. \(Re \sim O(10^{-2}\)\(10^{+1})\), fluid flow through a shallow deformable microchannel with ultra-low height-to-width-ratios, i.e. \(O(10^{-3})\). The fabricated deformable microchannels of several microns in height and few millimeters in width, whose aspect ratio is about two orders of magnitude smaller than that of the previous reports, allow us to investigate the fluid flow characteristics spanning a variety of distinct regimes from small wall deflections, where the deformable microchannel resembles its corresponding rigid one, to wall deflections much larger than the original height, where the height-independent characteristic behavior emerges. The effects of the microchannel geometry, membrane properties, and pressure difference across the channel are represented by a lumped variable called flexibility parameter. Under the same pressure drop across different channels, any difference in their geometries is reflected into the flexibility parameter of the channels, which can potentially cause the devices to operate under distinct regimes of the fluid–solid characteristics. For a fabricated microchannel with given membrane properties and channel geometry, on the other hand, a sufficiently large change in the applied pressure difference can alter the flow-structure behavior from one characteristic regime to another. By appropriately introducing the flexibility parameter and the dimensionless volumetric flow rate, a master curve is found for the fluid flow through any long and shallow deformable microchannel. A criterion is also suggested for determining whether the coupled or decoupled fluid–solid mechanics should be considered.

Keywords

Microfluidics Shallow microchannel Ultra-low aspect ratio microchannel Deformable microchannel Fluid–solid interaction Mathematical modeling 

Notes

Acknowledgements

Authors thank Dr. Baokang Bi and the staff of W. M. Keck Microfabrication Facility, and Karl Dersch and the staff of ECE Research Cleanroom in Michigan State University for their assistance with chemistry and cleanroom fabrication.

References

  1. Abate AR, Romanowsky MB, Agresti JJ, Weitz DA (2009) Valve-based flow focusing for drop formation. Appl Phys Lett 94(2):023503.  https://doi.org/10.1063/1.3067862. http://aip.scitation.org/doi/10.1063/1.3067862
  2. Beattie W, Qin X, Wang L, Ma H (2014) Clog-free cell filtration using resettable cell traps. Lab Chip 14(15):2657.  https://doi.org/10.1039/c4lc00306c. http://xlink.rsc.org/?DOI=c4lc00306c
  3. Chakraborty D, Prakash JR, Friend J, Yeo L (2012) Fluid-structure interaction in deformable microchannels. Phys Fluids 24(10):102002.  https://doi.org/10.1063/1.4759493 CrossRefGoogle Scholar
  4. Cheung P, Toda-Peters K, Shen AQ (2012) In situ pressure measurement within deformable rectangular polydimethylsiloxane microfluidic devices. Biomicrofluidics 6(2):026501.  https://doi.org/10.1063/1.4720394 CrossRefGoogle Scholar
  5. Christov IC, Cognet V, Shidhore TC, Stone HA (2018) Flow rate-pressure drop relation for deformable shallow microfluidic channels. J Fluid Mech 841:267.  https://doi.org/10.1017/jfm.2018.30. https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/flow-ratepressure-drop-relation-for-deformable-shallow-microfluidic-channels/798E21E2643E415BFA721DDD6298D4A6
  6. Gere JM (2004) Mechanics of materials, 6th edn. Brooks/Cole-Thomas Learning, BelmontGoogle Scholar
  7. Gerhardt T, Woo S, Ma H (2011) Chromatographic behaviour of single cells in a microchannel with dynamic geometry. Lab Chip 11(16):2731.  https://doi.org/10.1039/c1lc20092e. http://xlink.rsc.org/?DOI=c1lc20092e
  8. Gervais T, El-Ali J, Günther A, Jensen KF (2006) Flow-induced deformation of shallow microfluidic channels. Lab Chip 6(4):500.  https://doi.org/10.1039/b513524a. http://xlink.rsc.org/?DOI=b513524a
  9. Hardy BS, Uechi K, Zhen J, Pirouz Kavehpour H (2009) The deformation of flexible PDMS microchannels under a pressure driven flow. Lab Chip 9(7):935.  https://doi.org/10.1039/B813061B. http://xlink.rsc.org/?DOI=B813061B
  10. Huang SB, Wu MH, Lee GB (2009) A tunable micro filter modulated by pneumatic pressure for cell separation. Sens Actuators B Chem 142(1):389.  https://doi.org/10.1016/j.snb.2009.07.046. http://linkinghub.elsevier.com/retrieve/pii/S092540050900611X
  11. Huang SB, Zhao Y, Chen D, Lee HC, Luo Y, Chiu TK, Wang J, Chen J, Wu MH (2014) A clogging-free microfluidic platform with an incorporated pneumatically driven membrane-based active valve enabling specific membrane capacitance and cytoplasm conductivity characterization of single cells. Sens Actuators B Chem 190:928.  https://doi.org/10.1016/j.snb.2013.09.070. http://linkinghub.elsevier.com/retrieve/pii/S0925400513011118
  12. Jang K, Tanaka Y, Wakabayashi J, Ishii R, Sato K, Mawatari K, Nilsson M, Kitamori T (2012) Selective cell capture and analysis using shallow antibody-coated microchannels. Biomicrofluidics 6(4):044117.  https://doi.org/10.1063/1.4771968 CrossRefGoogle Scholar
  13. Javanmard M, Talasaz AH, Nemat-Gorgani M, Pease F, Ronaghi M, Davis RW (2007) Targeted cell detection based on microchannel gating. Biomicrofluidics 1(4):044103.  https://doi.org/10.1063/1.2815760 CrossRefGoogle Scholar
  14. Kang C, Roh C, Overfelt RA (2014) Pressure-driven deformation with soft polydimethylsiloxane (PDMS) by a regular syringe pump: challenge to the classical fluid dynamics by comparison of experimental and theoretical results. RSC Adv 4(7):3102CrossRefGoogle Scholar
  15. Lam EW, Cooksey GA, Finlayson BA, Folch A (2006) Microfluidic circuits with tunable flow resistances. Appl Phys Lett 89(16):164105.  https://doi.org/10.1063/1.2363931 CrossRefGoogle Scholar
  16. Leslie DC, Easley CJ, Seker E, Karlinsey JM, Utz M, Begley MR, Landers JP (2009) Frequency-specific flow control in microfluidic circuits with passive elastomeric features. Nat Phys 5(3):231.  https://doi.org/10.1038/nphys1196 CrossRefGoogle Scholar
  17. Luo C, Schneider TW, White RC, Currie J, Paranjape M (2003) A simple deflection-testing method to determine Poisson s ratio for MEMS applications. J. Micromech. Microeng. 13(1):129.  https://doi.org/10.1088/0960-1317/13/1/318. http://stacks.iop.org/0960-1317/13/i=1/a=318?key=crossref.81166d0e06484fabd83d63f992861edc
  18. Mehboudi A, Yeom J (2018) A two-step sealing-and-reinforcement SU8 bonding paradigm for the fabrication of shallow microchannels. J Micromech Microeng 28(3):035002. http://stacks.iop.org/0960-1317/28/i=3/a=035002
  19. Neelamegam R, Shankar V (2015) Experimental study of the instability of laminar flow in a tube with deformable walls. Phys Fluids 27(2):024102.  https://doi.org/10.1063/1.4907246 CrossRefGoogle Scholar
  20. Raj A, Sen AK (2016) Flow-induced deformation of compliant microchannels and its effect on pressure-flow characteristics. Microfluid Nanofluid 20(2):31.  https://doi.org/10.1007/s10404-016-1702-9 CrossRefGoogle Scholar
  21. Raj MK, DasGupta S, Chakraborty S (2017) Hydrodynamics in deformable microchannels. Microfluid Nanofluid 21(4):70.  https://doi.org/10.1007/s10404-017-1908-5 CrossRefGoogle Scholar
  22. Raj A, Halder R, Sajeesh P, Sen AK (2016) Droplet generation in a microchannel with a controllable deformable wall. Microfluid Nanofluid 20(7):102.  https://doi.org/10.1007/s10404-016-1768-4
  23. Raj A, Sen AK (2016) Flow-induced deformation of compliant microchannels and its effect on pressure–flow characteristics. Microfluid Nanofluid 20(2):31.  https://doi.org/10.1007/s10404-016-1702-9
  24. Seker E, Leslie DC, Haj-Hariri H, Landers JP, Utz M, Begley MR (2009) Nonlinear pressure-flow relationships for passive microfluidic valves. Lab Chip 9(18):2691.  https://doi.org/10.1039/b903960k. http://xlink.rsc.org/?DOI=b903960k
  25. Shidhore TC, Christov IC (2018) Static response of deformable microchannels: a comparative modelling study. J Phys Condensed Matter 30(5), 054002. http://stacks.iop.org/0953-8984/30/i=5/a=054002
  26. Smith JR, Arcibal IG, Polini A, Dokmeci MR, Khademhosseini A (2014) Research highlights. Lab Chip 14(1):157.  https://doi.org/10.1039/C3LC90120C. http://xlink.rsc.org/?DOI=C3LC90120C
  27. Song W, Vasdekis AE, Psaltis D (2012) Elastomer based tunable optofluidic devices. Lab Chip 12(19):3590.  https://doi.org/10.1039/c2lc40481h. http://xlink.rsc.org/?DOI=c2lc40481h
  28. Wang T, Zhang M, Dreher DD, Zeng Y (2013) Ultrasensitive microfluidic solid-phase ELISA using an actuatable microwell-patterned PDMS chip. Lab Chip 13(21):4190.  https://doi.org/10.1039/c3lc50783a. http://xlink.rsc.org/?DOI=c3lc50783a

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentMichigan State UniversityEast LansingUSA

Personalised recommendations