Journal of Mathematical Chemistry

, Volume 55, Issue 9, pp 1833–1848 | Cite as

A hybrid fluctuating hydrodynamics and kinetic Monte Carlo method for modeling chemically-powered nanoscale motion

  • Saranah Selmi
  • Dan J. Mitchell
  • Valipuram S. Manoranjan
  • Nikolaos K. Voulgarakis
Original Paper

Abstract

We present a stochastic multiscale method for modeling heterogeneous catalysis at the nanoscale. The system is decomposed into the fluid domain and the catalyst-fluid interface. We implemented the fluctuating hydrodynamics framework to model the diffusion of the chemical species in the fluid domain, and the chemical master equation to describe the catalytic activity at the interface. The coupling between the domains occurs simultaneously. Using a simple one-dimensional (1D) linear model, we showed that the predictions of our scheme are in excellent agreement with deterministic simulations. The method was specifically developed to model the spatially asymmetric catalysis on the surface of self-propelled nanoswimmers. Numerical simulations showed that our approach can estimate the uncertainty in the swimming velocity resulting from inherent stochastic nature of the chemical reactions at the catalytic interface. Although the method has been applied to simple 1D and 2D models, it can be generalized to handle different geometries and more sophisticated chemical reactions. Therefore, it can serve as a practical mathematical tool to study how the efficiency of chemically powered nanomachines is affected by the interplay between structural complexity, nonlinear reactivity, and nonequilibrium fluctuations.

Keywords

Fluctuating hydrodynamics Kinetic Monte Carlo Hybrid methodologies Nanocatalysis Self-phoretic motion Self-propelled nano devices 

References

  1. 1.
    R. Kapral, J. Chem. Phys. 138, 020901 (2013)CrossRefGoogle Scholar
  2. 2.
    J. Wang, K.M. Manesh, Small 6, 338 (2010)CrossRefGoogle Scholar
  3. 3.
    E. Lauga, T.R. Powers, Rep. Prog. Phys. 72, 096601 (2009)CrossRefGoogle Scholar
  4. 4.
    L. Soler, S. Sánchez, Nanoscale 6, 7175 (2014)CrossRefGoogle Scholar
  5. 5.
    S. Campuzano, D. Kagan, J. Orozco, J. Wang, Analyst 136, 4621 (2011)CrossRefGoogle Scholar
  6. 6.
    W. Gao, J. Wang, Nanoscale 6, 10486 (2014)CrossRefGoogle Scholar
  7. 7.
    J. Wang, Nanomachines: Fundamentals and Applications (Wiley, London, 2013)CrossRefGoogle Scholar
  8. 8.
    P.J. Atzberger, P.R. Kramer, C.S. Peskin, J. Comput. Phys. 224, 1255 (2007)CrossRefGoogle Scholar
  9. 9.
    P.J. Atzberger, J. Comput. Phys. 230, 2821 (2011)CrossRefGoogle Scholar
  10. 10.
    F. Balboa Usabiaga, R. Delgado-Buscalioni, B.E. Griffith, A. Donev, Comput. Methods Appl. Mech. Eng. 269, 139 (2014)CrossRefGoogle Scholar
  11. 11.
    F.B. Usabiaga, I. Pagonabarraga, R. Delgado-Buscalioni, J. Comput. Phys. 235, 701 (2013)CrossRefGoogle Scholar
  12. 12.
    N.K. Voulgarakis, B.Z. Shang, J.-W. Chu, Phys. Rev. E 88, 023305 (2013)CrossRefGoogle Scholar
  13. 13.
    B. Uma, T.N. Swaminathan, R. Radhakrishnan, D.M. Eckmann, P.S. Ayyaswamy, Phys. Fluids 23, 073602 (2011)CrossRefGoogle Scholar
  14. 14.
    C.S. Peskin, Acta Numer. 11, 479 (2002)CrossRefGoogle Scholar
  15. 15.
    H.H. Hu, Int. J. Multiph. Flow 22, 335 (1996)CrossRefGoogle Scholar
  16. 16.
    D. Mei, G. Lin, Catal. Today 165, 56 (2011)CrossRefGoogle Scholar
  17. 17.
    S. Matera, K. Reuter, Catal. Lett. 133, 156 (2009)CrossRefGoogle Scholar
  18. 18.
    S. Matera, K. Reuter, J. Catal. 295, 261 (2012)CrossRefGoogle Scholar
  19. 19.
    S. Matera, K. Reuter, Phys. Rev. B 82, 085446 (2010)CrossRefGoogle Scholar
  20. 20.
    A. Balter, G. Lin, A.M. Tartakovsky, Phys. Rev. E 85, 016707 (2012)CrossRefGoogle Scholar
  21. 21.
    A. Saedi, J. Electroanal. Chem. 588, 267 (2006)CrossRefGoogle Scholar
  22. 22.
    H.A. Stone, A.D.T. Samuel, Phys. Rev. Lett. 77, 4102 (1996)CrossRefGoogle Scholar
  23. 23.
    R. Golestanian, T.B. Liverpool, A. Ajdari, New J. Phys. 9, 126 (2007)CrossRefGoogle Scholar
  24. 24.
    U.M. Córdova-Figueroa, J.F. Brady, Phys. Rev. Lett. 100, 158303 (2008)CrossRefGoogle Scholar
  25. 25.
    U.M. Córdova-Figueroa, J.F. Brady, S. Shklyaev, Soft Matter 9, 6382 (2013)CrossRefGoogle Scholar
  26. 26.
    S. Michelin, E. Lauga, J. Fluid Mech. 747, 572 (2014)CrossRefGoogle Scholar
  27. 27.
    M.N. Popescu, S. Dietrich, M. Tasinkevych, J. Ralston, Eur. Phys. J. E 31, 351 (2010)CrossRefGoogle Scholar
  28. 28.
    B. Sabass, U. Seifert, J. Chem. Phys. 136, 064508 (2012)CrossRefGoogle Scholar
  29. 29.
    N. Sharifi-Mood, J. Koplik, C. Maldarelli, Phys. Fluids 25, 012001 (2013)CrossRefGoogle Scholar
  30. 30.
    E.J. Banigan, J.F. Marko, Phys. Rev. E 93, 012611 (2016)CrossRefGoogle Scholar
  31. 31.
    M. Sandoval, N.K. Marath, G. Subramanian, E. Lauga, J. Fluid Mech. 742, 50 (2014)CrossRefGoogle Scholar
  32. 32.
    R. Golestanian, T.B. Liverpool, A. Ajdari, Phys. Rev. Lett. 94, 220801 (2005)CrossRefGoogle Scholar
  33. 33.
    R. Golestanian, Phys. Rev. Lett. 102, 188305 (2009)CrossRefGoogle Scholar
  34. 34.
    J.L. Moran, J.D. Posner, Annu. Rev. Fluid Mech. 49, 511 (2017). doi:10.1146/Annurev-Fluid-122414-034456 CrossRefGoogle Scholar
  35. 35.
    G. De Fabritiis, M. Serrano, R. Delgado-Buscalioni, P. Coveney, Phys. Rev. E 75, 026307 (2007)CrossRefGoogle Scholar
  36. 36.
    J.B. Bell, A.L. Garcia, S.A. Williams, Phys. Rev. E 76, 016708 (2007)CrossRefGoogle Scholar
  37. 37.
    N.K. Voulgarakis, J.-W. Chu, J. Chem. Phys. 130, 134111 (2009)CrossRefGoogle Scholar
  38. 38.
    F.B. Usabiaga, J.B. Bell, R. Delgado-Buscalioni, A. Donev, T.G. Fai, B.E. Griffith, C.S. Peskin, SIAM J. Multiscale Model. Simul. 10, 1369 (2012). doi:10.1137/120864520
  39. 39.
    B.Z. Shang, N.K. Voulgarakis, J.-W. Chu, J. Chem. Phys. 137, 044117 (2012)CrossRefGoogle Scholar
  40. 40.
    S. Delong, B.E. Griffith, E. Vanden-Eijnden, A. Donev, Phys. Rev. E 87, 033302 (2013)CrossRefGoogle Scholar
  41. 41.
    N.K. Voulgarakis, S. Satish, J.-W. Chu, J. Chem. Phys. 131, 234115 (2009)CrossRefGoogle Scholar
  42. 42.
    N.K. Voulgarakis, S. Satish, J.-W. Chu, Mol. Simul. 36, 552 (2010)CrossRefGoogle Scholar
  43. 43.
    B.Z. Shang, N.K. Voulgarakis, J.-W. Chu, J. Chem. Phys. 135, 044111 (2011)CrossRefGoogle Scholar
  44. 44.
    A. Chaudhri, J.B. Bell, A.L. Garcia, A. Donev, Phys. Rev. E 90, 033014 (2014)CrossRefGoogle Scholar
  45. 45.
    K. Lazaridis, L. Wickham, N.K. Voulgarakis, Phys. Lett. A 381, 1431 (2017)CrossRefGoogle Scholar
  46. 46.
    A.K. Bhattacharjee, K. Balakrishnan, A.L. Garcia, J.B. Bell, A. Donev, J. Chem. Phys. 142, 224107 (2015)CrossRefGoogle Scholar
  47. 47.
    K. Balakrishnan, A.L. Garcia, A. Donev, J.B. Bell, Phys. Rev. E 89, 013017 (2014)CrossRefGoogle Scholar
  48. 48.
    S.A. Isaacson, SIAM J. Appl. Math. 70, 77 (2009)CrossRefGoogle Scholar
  49. 49.
    S. Smith, R. Grima, Phys. Rev. E 93, 052135 (2016)CrossRefGoogle Scholar
  50. 50.
    A. Balter, G. Lin, A.M. Tartakovsky, Phys. Rev. E 85, 016707 (2012)CrossRefGoogle Scholar
  51. 51.
    B. Uma, T.N. Swaminathan, P.S. Ayyaswamy, D.M. Eckmann, R. Radhakrishnan, J. Chem. Phys. 135, 114104 (2011)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsWashington State UniversityPullmanUSA
  2. 2.Department of ChemistryWashington State UniversityRichlandUSA

Personalised recommendations