- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Interfacial instability of thin films in soft microfluidic configurations actuated by electro-osmotic flow

Evgeniy Boyko, Dotan Ilssar, Moran Bercovici*, and Amir D. Gat†

  • Faculty of Mechanical Engineering, Technion–Israel Institute of Technology, Haifa, Israel

  • *mberco@technion.ac.il
  • †amirgat@technion.ac.il
PDF

Phys. Rev. Fluids 5, 104201 – Published 1 October, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.104201

Abstract

We analyze the interfacial instability of a thin film confined between a rigid surface and a prestretched elastic sheet, triggered by nonuniform electro-osmotic flow. We derive a nonlinear viscous−elastic equation governing the deformation of the elastic sheet, describing the balance between viscous resistance, the dielectric and electro-osmotic effects, and the restoring effect of elasticity. Our theoretical analysis, validated by numerical simulations, shows several distinct modes of instability depending on the electro-osmotic pattern, controlled by a nondimensional parameter representing the ratio of electro-osmotic to elastic forces. We consider several limiting cases and present approximate asymptotic expressions predicting the electric field required for triggering of the instability. Through dynamic numerical simulations of the governing equation, we study the hysteresis of the system and show that the instability can result in an asymmetric deformation pattern, even for symmetric actuation. Finally, we validate our theoretical model with finite-element simulations of the two-way coupled Navier equations for the elastic solid, the unsteady Stokes equations for the fluid, and the Laplace equation for the electric potential, showing very good agreement. The mechanism illustrated in this work, together with the provided analysis, may be useful in toward the implementation of instability-based soft actuators for lab-on-a-chip and soft-robotic applications.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (38)

  1. A. Oron, S. H. Davis, and S. G. Bankoff, Long-scale evolution of thin liquid films, Rev. Mod. Phys. 69, 931 (1997).
  2. R. V. Craster and O. K. Matar, Dynamics and stability of thin liquid films, Rev. Mod. Phys. 81, 1131 (2009).
  3. A. Juel, D. Pihler-Puzović, and M. Heil, Instabilities in blistering, Annu. Rev. Fluid Mech. 50, 691 (2018).
  4. M. Gomez, D. E. Moulton, and D. Vella, Passive Control of Viscous Flow Via Elastic Snap-Through, Phys. Rev. Lett. 119, 144502 (2017).
  5. R. Huang and Z. Suo, Wrinkling of a compressed elastic film on a viscous layer, J. Appl. Phys. 91, 1135 (2002).
  6. L. Pocivavsek, R. Dellsy, A. Kern, S. Johnson, B. Lin, K. Y. C. Lee, and E. Cerda, Stress and fold localization in thin elastic membranes, Science 320, 912 (2008).
  7. O. Kodio, I. M. Griffiths, and D. Vella, Lubricated wrinkles: Imposed constraints affect the dynamics of wrinkle coarsening, Phys. Rev. Fluids 2, 014202 (2017).
  8. A. E. Hosoi and L. Mahadevan, Peeling, Healing, and Bursting in a Lubricated Elastic Sheet, Phys. Rev. Lett. 93, 137802 (2004).
  9. J. R. Lister, G. G. Peng, and J. A. Neufeld, Viscous Control of Peeling an Elastic Sheet by Bending and Rulling, Phys. Rev. Lett. 111, 154501 (2013).
  10. D. Pihler-Puzović, P. Illien, M. Heil, and A. Juel, Suppression of Complex Fingerlike Patterns at the Interface between Air and a Viscous Fluid by Elastic Membranes, Phys. Rev. Lett. 108, 074502 (2012).
  11. T. T. Al-Housseiny, I. C. Christov, and H. A. Stone, Two-Phase Fluid Displacement and Interfacial Instabilities Under Elastic Membranes, Phys. Rev. Lett. 111, 034502 (2013).
  12. Z. Zheng, H. Kim, and H. A. Stone, Controlling Viscous Fingering using Time-Dependent Strategies, Phys. Rev. Lett. 115, 174501 (2015).
  13. A. Tulchinsky and A. D. Gat, Transient dynamics of an elastic Hele-Shaw cell due to external forces with application to impact mitigation, J. Fluid Mech. 800, 517 (2016).
  14. T. Gervais, J. El-Ali, A. Günther, and K. F. Jensen, Flow-induced deformation of shallow microfluidic channels, Lab Chip 6, 500 (2006).
  15. D. Dendukuri, S. S. Gu, D. C. Pregibon, T. A. Hatton, and P. S. Doyle, Stop-flow lithography in a microfluidic device, Lab Chip 7, 818 (2007).
  16. B. S. Hardy, K. Uechi, J. Zhen, and H. P. Kavehpour, The deformation of flexible PDMS microchannels under a pressure driven flow, Lab Chip 9, 935 (2009).
  17. P. Panda, K. P. Yuet, D. Dendukuri, T. A. Hatton, and P. S. Doyle, Temporal response of an initially defected PDMS channel, New J. Phys. 11, 115001 (2009).
  18. U. Mukherjee, J. Chakraborty, and S. Chakraborty, Relaxation characteristics of a compliant microfluidic channel under electroosmotic flow, Soft Matter 9, 1562 (2013).
  19. I. C. Christov, V. Cognet, T. C. Shidhore, and H. A. Stone, Flow rate-pressure drop relation for deformable shallow microfluidic channels, J. Fluid Mech. 841, 267 (2018).
  20. C. Majidi, Soft robotics: a perspective - current trends and prospects for the future, Soft Robotics 1, 5 (2014).
  21. D. Rus and M. T. Tolley, Design, fabrication and control of soft robots, Nature 521, 467 (2015).
  22. P. Polygerinos, N. Correll, S. A. Morin, B. Mosadegh, C. D. Onal, K. Petersen, M. Cianchetti, M. T. Tolley, and R. F. Shepherd, Soft robotics: Review of fluid-driven intrinsically soft devices; manufacturing, sensing, control, and applications in human-robot interaction, Adv. Eng. Mater. 19, 1700016 (2017).
  23. Y. Matia, T. Elimelech, and A. D. Gat, Leveraging internal viscous flow to extend the capabilities of beam-shaped soft robotic actuators, Soft Robotics 4, 126 (2017).
  24. T. C. Inamdar, X. Wang, and I. C. Christov, Unsteady fluid-structure interactions in a soft-walled microchannel: A one-dimensional lubrication model for finite Reynolds number, Phys. Rev. Fluids 5, 064101 (2020).
  25. A. Martínez-Calvo, A. Sevilla, G. G. Peng, and H. A. Stone, Start-up ow in shallow deformable microchannels, J. Fluid Mech. 885, A25 (2020).
  26. S. Rubin, A. Tulchinky, A. D. Gat, and M. Bercovici, Elastic deformations driven by nonuniform lubrication flows, J. Fluid Mech. 812, 841 (2017).
  27. E. Boyko, R. Eshel, K. Gommed, A. D. Gat, and M. Bercovici, Elastohydrodynamics of a prestretched finite elastic sheet lubricated by a thin viscous film with application to microfluidic soft actuators, J. Fluid Mech. 862, 732 (2019).
  28. E. Boyko, R. Eshel, A. D. Gat, and M. Bercovici, Nonuniform Electro-Osmotic Flow Drives Fluid-Structure Instability, Phys. Rev. Lett. 124, 024501 (2020).
  29. L. G. Leal, Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes (Cambridge University Press, Cambridge, UK, 2007).
  30. R. J. Hunter, Foundations of colloid science (Oxford University Press, Oxford, UK, 2000).
  31. S. Ghosal, Lubrication theory for electro-osmotic flow in a microfluidic channel of slowly varying cross-section and wall charge, J. Fluid Mech. 459, 103 (2002).
  32. P. Howell, G. Kozyreff, and J. Ockendon, Applied Solid Mechanics (Cambridge University Press, Cambridge, UK, 2009).
  33. S. Timoshenko and S. Woinkowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, New York, 1987).
  34. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon Press, Bristol, 1960).
  35. E. Boyko, S. Rubin, A. D. Gat, and M. Bercovici, Flow patterning in Hele-Shaw configurations using nonuniform electro-osmotic slip, Phys. Fluids 27, 102001 (2015).
  36. S. B. Elbaz and A. D. Gat, Dynamics of viscous liquid within a closed elastic cylinder subject to external forces with application to soft robotics, J. Fluid Mech. 758, 221 (2014).
  37. M. J. Tan, S. G. Bankoff, and S. H. Davis, Steady thermocapillary flows of thin liquid layers. I. Theory, Phys. Fluids A 2, 313 (1990).
  38. S. S. Bahga, M. Bercovici, and J. G. Santiago, Robust and high-resolution simulations of nonlinear electrokinetic processes in variable cross-section channels, Electrophoresis 33, 3036 (2012).

Outline

Information

Phys. Rev. Fluids 5, 104201– Published 1 October, 2020
  • Received 29 March 2020
  • Accepted 10 September 2020
Crossmark - Check for updates button

©2020 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation