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Predictive model for convective flows induced by surface reactivity contrast

Scott M. Davidson1, Rob G. H. Lammertink2, and Ali Mani1,*

  • 1Department of Mechanical Engineering, Stanford University, Stanford, California 94305, USA
  • 2Soft Matter, Fluidics and Interfaces, Mesa+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands

  • *Corresponding author: alimani@stanford.edu
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Phys. Rev. Fluids 3, 053701 – Published 17 May, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.053701

Abstract

Concentration gradients in a fluid adjacent to a reactive surface due to contrast in surface reactivity generate convective flows. These flows result from contributions by electro- and diffusio-osmotic phenomena. In this study, we have analyzed reactive patterns that release and consume protons, analogous to bimetallic catalytic conversion of peroxide. Similar systems have typically been studied using either scaling analysis to predict trends or costly numerical simulation. Here, we present a simple analytical model, bridging the gap in quantitative understanding between scaling relations and simulations, to predict the induced potentials and consequent velocities in such systems without the use of any fitting parameters. Our model is tested against direct numerical solutions to the coupled Poisson, Nernst-Planck, and Stokes equations. Predicted slip velocities from the model and simulations agree to within a factor of ≈2 over a multiple order-of-magnitude change in the input parameters. Our analysis can be used to predict enhancement of mass transport and the resulting impact on overall catalytic conversion, and is also applicable to predicting the speed of catalytic nanomotors.

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References (51)

  1. T. R. Kline, W. F. Paxton, Yang Wang, D. Velegol, T. E. Mallouk, and A. Sen, Catalytic micropumps: Microscopic convective fluid flow and pattern formation, J. Am. Chem. Soc. 127, 17150 (2005).
  2. W. F. Paxton, S. Sundararajan, T. E. Mallouk, and A. Sen, Chemical locomotion, Angew. Chem., Int. Ed. 45, 5420 (2006).
  3. C. Zhou, H. Zhang, Z. Li, and W. Wang, Chemistry pumps: A review of chemically powered micropumps, Lab Chip 16, 1797 (2016).
  4. T. M. Squires, R. J. Messinger, and S. R. Manalis, Making it stick: Convection, reaction, and diffusion in surface-based biosensors, Nat. Biotechnol. 26, 417 (2008).
  5. M. Z. Bazant and T. M. Squires, Induced-Charge Electrokinetic Phenomena: Theory and Microfluidic Applications, Phys. Rev. Lett. 92, 066101 (2004).
  6. T. M. Squires and M. Z. Bazant, Induced-charge electro-osmosis, J. Fluid Mech. 509, 217 (2004).
  7. A. Ramos, H. Morgan, N. G. Green, and A. Castellanos, Ac electrokinetics: A review of forces in microelectrode structures, J. Phys. D 31, 2338 (1998).
  8. A. Ramos, H. Morgan, N. G. Green, and A. Castellanos, AC electric-field-induced fluid flow in microelectrodes, J. Colloid Interface Sci. 217, 420 (1999).
  9. A. Ramos, A. González, A. Castellanos, N. G. Green, and H. Morgan, Pumping of liquids with ac voltages applied to asymmetric pairs of microelectrodes, Phys. Rev. E 67, 056302 (2003).
  10. J. L. Anderson, Colloid transport by interfacial forces, Annu. Rev. Fluid Mech. 21, 61 (1989).
  11. T. R. Kline, J. Iwata, P. E. Lammert, T. E. Mallouk, A. Sen, and D. Velegol, Catalytically driven colloidal patterning and transport, J. Phys. Chem. B 110, 24513 (2006).
  12. W. F. Paxton, P. T. Baker, T. R. Kline, Yang Wang, T. E. Mallouk, and A. Sen, Catalytically induced electrokinetics for motors and micropumps, J. Am. Chem. Soc. 128, 14881 (2006).
  13. M. E. Ibele, Yang Wang, T. R. Kline, T. E. Mallouk, and A. Sen, Hydrazine fuels for bimetallic catalytic microfluidic pumping, J. Am. Chem. Soc. 129, 7762 (2007).
  14. A. Afshar Farniya, M. J. Esplandiu, D. Reguera, and A. Bachtold, Imaging the proton concentration and mapping the spatial distribution of the electric field of catalytic micropumps, Phys. Rev. Lett. 111, 168301 (2013).
  15. I. K. Jun and H. Hess, A biomimetic, self-pumping membrane, Adv. Mater. 22, 4823 (2010).
  16. M. J. Esplandiu, A. A. Farniya, and A. Bachtold, Silicon-based chemical motors: An efficient pump for triggering and guiding fluid motion using visible light, ACS Nano 9, 11234 (2015).
  17. M. J. Esplandiu, A. A. Farniya, and D. Reguera, Key parameters controlling the performance of catalytic motors, J. Chem. Phys. 144, 124702 (2016).
  18. J. L. Anderson, M. E. Lowell, and D. C. Prieve, Motion of a particle generated by chemical gradients, part 1: Non-electrolytes, J. Fluid Mech. 117, 107 (1982).
  19. D. C. Prieve, J. L. Anderson, J. P. Ebel, and M. E. Lowell, Motion of a particle generated by chemical gradients, part 2: Electrolytes, J. Fluid Mech. 148, 247 (1984).
  20. Y. Hong, M. Diaz, U. M. Córdova-Figueroa, and A. Sen, Light-driven titanium-dioxide-based reversible microfireworks and micromotor/micropump systems, Adv. Funct. Mater. 20, 1568 (2010).
  21. R. Niu, P. Kreissl, A. T. Brown, G. Rempfer, D. Botin, C. Holm, T. Palberg, J. de Graaf, and A. Sen, Microfluidic pumping by micromolar salt concentrations, Soft Matter 13, 1505 (2017).
  22. P. Mitchell, Self-electrophoretic locomotion in microorganisms: Bacterial flagella as giant ionophores, FEBS Lett. 28, 1 (1972).
  23. P. E. Lammert, J. Prost, and R. Bruinsma, Ion drive for vesicles and cells, J. Theor. Biol. 178, 387 (1996).
  24. S. Fournier-Bidoz, A. C. Arsenault, I. Manners, and G. A. Ozin, Synthetic self-propelled nanorotors. Chem. Commun. 0, 441 (2005).
  25. W. F. Paxton, A. Sen, and T. E. Mallouk, Motility of catalytic nanoparticles through self-generated forces, Chem. Eur. J. 11, 6462 (2005).
  26. P. M. Wheat, N. A. Marine, J. L. Moran, and J. D. Posner, Rapid fabrication of bimetallic spherical motors, Langmuir 26, 13052 (2010).
  27. Yang Wang, R. M. Hernandez, D. J. Bartlett, J. M. Bingham, T. R. Kline, A. Sen, and T. E. Mallouk, Bipolar electrochemical mechanism for the propulsion of catalytic nanomotors in hydrogen peroxide solutions, Langmuir 22, 10451 (2006).
  28. J. Wang, Can man-made nanomachines compete with nature biomotors?, ACS Nano 3, 4 (2009).
  29. J. Wu, S. Balasubramanian, D. Kagan, K. M. Manesh, S. Campuzano, and J. Wang, Motion-based DNA detection using catalytic nanomotors, Nat. Commun. 1, 36 (2010).
  30. S. J. Ebbens, J. R. Howse, S. Balasubramanian, S. Sarrayasamitsathit, K. M. Manesh, G.-U. Flechsig, J. Wang, J. Wang, and V. H. Crespi, In pursuit of propulsion at the nanoscale, Soft Matter 6, 726 (2010).
  31. S. Sengupta, M. E. Ibele, and A. Sen, Fantastic voyage: Designing self-powered nanorobots, Angew. Chem., Int. Ed. 51, 8434 (2012).
  32. R. Golestanian, T. B. Liverpool, and A. Ajdari, Propulsion of a Molecular Machine by Asymmetric Distribution of Reaction Products, Phys. Rev. Lett. 94, 220801 (2005).
  33. J. L. Moran, P. M. Wheat, and J. D. Posner, Locomotion of electrocatalytic nanomotors due to reaction induced charge autoelectrophoresis, Phys. Rev. E 81, 065302 (2010).
  34. J. L. Moran and J. D. Posner, Electrokinetic locomotion due to reaction-induced charge auto-electrophoresis, J. Fluid Mech. 680, 31 (2011).
  35. J. L. Moran and J. D. Posner, Role of solution conductivity in reaction induced charge auto-electrophoresis, Phys. Fluids 26, 042001 (2014).
  36. E. Yariv, Electrokinetic self-propulsion by inhomogeneous surface kinetics, Proc. R. Soc. London, Ser. A 467, 1645 (2011).
  37. B. Sabass and U. Seifert, Nonlinear, electrocatalytic swimming in the presence of salt, J. Chem. Phys. 136, 214507 (2012).
  38. A. Nourhani, V. H. Crespi, and P. E. Lammert, Self-consistent nonlocal feedback theory for electrocatalytic swimmers with heterogeneous surface chemical kinetics, Phys. Rev. E 91, 062303 (2015).
  39. P. Kreissl, C. Holm, and J. De Graaf, The efficiency of self-phoretic propulsion mechanisms with surface reaction heterogeneity, J. Chem. Phys. 144, 204902 (2016).
  40. A. T. Brown, W. C. K. Poon, C. Holm, J. de Graaf, Q. He, D. Velegol, R. Golestanian, S. J. Ebbens, and T. Mallouk, Ionic screening and dissociation are crucial for understanding chemical self-propulsion in polar solvents, Soft Matter 13, 1200 (2017).
  41. S. B. Hall, E. A. Khudaish, and A. L. Hart, Electrochemical oxidation of hydrogen peroxide at platinum electrodes, part 1: An adsorption-controlled mechanism, Electrochim. Acta 43, 579 (1998).
  42. S. B. Hall, E. A. Khudaish, and A. L. Hart, Electrochemical oxidation of hydrogen peroxide at platinum electrodes, part II: Effect of potential, Electrochim. Acta 43, 2015 (1998).
  43. J. F. L. Duval, G. K. Huijs, W. F. Threels, J. Lyklema, and H. P. van Leeuwen, Faradaic depolarization in the electrokineitcs of the metal electrolyte solution interface, J. Colloid Interface Sci. 260, 95 (2003).
  44. E. Karatay, C. L. Druzgalski, and A. Mani, Simulation of chaotic electrokinetic transport: Performance of commercial software versus custom-built direct numerical simulation codes, J. Colloid Interface Sci. 446, 67 (2015).
  45. K. Salari and P. Knupp, Code verification by the method of manufactured solutions, Technical Report No. SAND2000-144, Sandia National Laboratory, Albuquerque, NM, and Sandia National Laboratory, Livermore, CA, June 2000.
  46. C. L. Druzgalski, M. B. Andersen, and A. Mani, Direct numerical simulation of electroconvective instability and hydrodynamic chaos near an ion-selective surface, Phys. Fluids 25, 110804 (2013).
  47. C. Druzgalski and A. Mani, Statistical analysis of electroconvection near an ion-selective membrane in the highly chaotic regime, Phys. Rev. Fluids 1, 073601 (2016).
  48. S. M. Davidson, M. B. Andersen, and A. Mani, Chaotic Induced-Charge Electro-Osmosis, Phys. Rev. Lett. 112, 128302 (2014).
  49. S. M. Davidson, M. Wessling, and A. Mani, On the dynamical regimes of pattern-accelerated electroconvection, Sci. Rep. 6, 22505 (2016).
  50. M. Z. Bazant, K. Thornton, and A. Ajdari, Diffuse-charge dynamics in electrochemical systems, Phys. Rev. E 70, 021506 (2004).
  51. I. Rubinstein and B. Zaltzman, Electro-osmotic slip of the second kind and instability in concentration polarization at electrodialysis membranes, Math. Models Methods Appl. Sci. 11, 263 (2001).

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Phys. Rev. Fluids 3, 053701– Published 17 May, 2018
  • Received 26 April 2017
Article part of CHORUS
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