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Applied Mathematics and Mechanics

, Volume 39, Issue 1, pp 125–152 | Cite as

Fluctuating hydrodynamic methods for fluid-structure interactions in confined channel geometries

  • Y. Wang
  • H. Lei
  • P. J. AtzbergerEmail author
Article
  • 166 Downloads

Abstract

We develop computational methods for the study of fluid-structure interactions subject to thermal fluctuations when confined within channels with slit-like geometry. The methods take into account the hydrodynamic coupling and diffusivity of microstructures when influenced by their proximity to no-slip walls. We develop stochastic numerical methods subject to no-slip boundary conditions using a staggered finite volume discretization. We introduce techniques for discretizing stochastic systems in a manner that ensures results consistent with statistical mechanics. We show how an exact fluctuation-dissipation condition can be used for this purpose to discretize the stochastic driving fields and combined with an exact projection method to enforce incompressibility. We demonstrate our computational methods by investigating how the proximity of ellipsoidal colloids to the channel wall affects their active hydrodynamic responses and passive diffusivity. We also study for a large number of interacting particles collective drift-diffusion dynamics and associated correlation functions. We expect the introduced stochastic computational methods to be broadly applicable to applications in which confinement effects play an important role in the dynamics of microstructures subject to hydrodynamic coupling and thermal fluctuations.

Key words

fluctuating hydrodynamics immersed boundary method stochastic Eulerian-Lagrangian method (SELM) ellipsoidal colloid mobility nanochannel 

Chinese Library Classification

O2 O4 

2010 Mathematics Subject Classification

74S10 74S60 70F99 37A99 

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References

  1. [1]
    Han, Y., Alsayed, A., Nobili, M., and Yodh, A. G. Quasi-two-dimensional diffusion of single ellipsoids: aspect ratio and confinement effects. Physical Review E Statistical Nonlinear and Soft Matter Physics, 80, 011403 (2009)CrossRefGoogle Scholar
  2. [2]
    Han, Y., Alsayed, A. M., Nobili, M., Zhang, J., Lubensky, T. C., and Yodh, A. G. Brownian motion of an ellipsoid. Science, 314, 626–630 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Kihm, K. D., Banerjee, A., Choi, C. K., and Takagi, T. Near-wall hindered brownian diffusion of nanoparticles examined by three-dimensional ratiometric total internal reflection fluorescence microscopy (3-D RTIRFM). Experiments in Fluids, 37, 811–824 (2004)CrossRefGoogle Scholar
  4. [4]
    Kilic, M. S. and Bazant, M. Z. Induced-charge electrophoresis near a wall. Electrophoresis, 32, 614–628 (2011)CrossRefGoogle Scholar
  5. [5]
    Napoli, M., Atzberger, P., and Pennathur, S. Experimental study of the separation behavior of nanoparticles in micro- and nano-channels. Microfluidics and Nanofluidics, 10, 69–80 (2011)CrossRefGoogle Scholar
  6. [6]
    Wynne, T. M., Dixon, A. H., and Pennathur, S. Electrokinetic characterization of individual nanoparticles in nanofluidic channels. Microfluidics and Nanofluidics, 12, 411–421 (2012)CrossRefGoogle Scholar
  7. [7]
    Chen, Y. L., Graham, M. D., de Pablo, J. J., Randall, G. C., Gupta, M., and Doyle, P. S. Conformation and dynamics of single DNA molecules in parallel-plate slit microchannels. Physical Review E Statistical Nonlinear and Soft Matter Physics, 70, 060901 (2004)CrossRefGoogle Scholar
  8. [8]
    Lin, P. K., Fu, C. C., Chen, Y. L., Chen, Y. R., Wei, P. K., Kuan, C. H., and Fann, W. S. Static conformation and dynamics of single DNA molecules confined in nanoslits. Physical Review E Statistical Nonlinear and Soft Matter Physics, 76, 011806 (2007)CrossRefGoogle Scholar
  9. [9]
    Squires, T. M. and Quake, S. R. Microfluidics: fluid physics at the nanoliter scale. Reviews of Modern Physics, 77, 977–1026 (2005)CrossRefGoogle Scholar
  10. [10]
    Teh, S. Y., Lin, R., Hung, L. H., and Lee, A. P. Droplet microfluidics. Lab on a Chip, 8, 198–220 (2008)CrossRefGoogle Scholar
  11. [11]
    Volkmuth, W. D., Duke, T., Wu, M. C., Austin, R. H., and Szabo, A. DNA electrodiffusion in a 2d array of posts. Physical Review Letters, 72, 2117–2120 (1994)CrossRefGoogle Scholar
  12. [12]
    Drescher, K., Dunkel, J., Cisneros, L. H., Ganguly, S., and Goldstein, R. E. Fluid dynamics and noise in bacterial cell-cell and cell-surface scattering. Proceedings of the National Academy of Sciences of the United States of America, 108, 10940–10945 (2011)CrossRefGoogle Scholar
  13. [13]
    Wioland, H., Woodhouse, F. G., Dunkel, J., Kessler, J. O., and Goldstein, R. E. Confinement stabilizes a bacterial suspension into a spiral vortex. Physical Review Letters, 110, 268102 (2013)CrossRefGoogle Scholar
  14. [14]
    Atzberger, P. J. Stochastic Eulerian Lagrangian methods for fluid structure interactions with thermal fluctuations. Journal of Computational Physics, 230, 2821–2837 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    Landau, L. D. and Lifshitz, E. M. Course of theoretical physics. Statistical Physics (3rd ed.), Pergamon Press, Oxford (1980)Google Scholar
  16. [16]
    Atzberger, P. J., Kramer, P. R., and Peskin, C. S. A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales. Journal of Computational Physics, 224, 1255–1292 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    Balboa, F. B., Bell, J. B., Delgado-Buscalioni, R., Donev, A., Fai, T. G., Griffith, B. E., and Peskin, C. S. Staggered schemes for fluctuating hydrodynamics. Multiscale Modeling and Simulation, 10, 1369–1408 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    Bell, J. B., Garcia, A. L., and Williams, S. A. Computational fluctuating fluid dynamics. ESAIM: Mathematical Modelling and Numerical Analysis, 44, 1085–1105 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    De Fabritiis, G., Serrano, M., Delgado-Buscalioni, R., and Coveney, P. V. Fluctuating hydrodynamic modeling of fluids at the nanoscale. Physical Review E Statistical Nonlinear and Soft Matter Physics, 75, 026307 (2007)CrossRefGoogle Scholar
  20. [20]
    Düenweg, B. and Ladd, A. J. C. Lattice Boltzmann simulations of soft matter systems. Advances in Polymer Science, 221, 89–166 (2008)Google Scholar
  21. [21]
    Tabak, G. and Atzberger, P. Stochastic reductions for inertial fluid-structure interactions subject to thermal fluctuations. SIAM Journal on Applied Mathematics, 75, 1884–1914 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    Peskin, C. S. The immersed boundary method. Acta Numerica, 11, 1–39 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    Gardiner, C. W. Handbook of Stochastic Methods, Springer, Berlin (1985)Google Scholar
  24. [24]
    Oksendal, B. Stochastic Differential Equations: An Introduction, Springer, Berlin (2000)zbMATHGoogle Scholar
  25. [25]
    Reichl, L. E. A Modern Course in Statistical Physics, John Wiley and Sons, New York (1998)zbMATHGoogle Scholar
  26. [26]
    Sigurdsson, J. K., Brown, F. L., and Atzberger, P. J. Hybrid continuum-particle method for fluctuating lipid bilayer membranes with diffusing protein inclusions. Journal of Computational Physics, 252, 65–85 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    Kloeden, P. E. and Platen, E. Numerical Solution of Stochastic Differential Equations, Springer, Berlin (1992)CrossRefzbMATHGoogle Scholar
  28. [28]
    Chorin, A. J. Numerical solution of Navier-Stokes equations. Mathematics of Computation, 22, 745–762 (1968)MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    Cooley, J. W. and Tukey, J. W. An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation, 19, 297–301 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. Numerical Recipes in C, Cambridge University Press, Cambridge (1994)zbMATHGoogle Scholar
  31. [31]
    Atzberger, P. Spatially adaptive stochastic numerical methods for intrinsic fluctuations in reactiondiffusion systems. Journal of Computational Physics, 229, 3474–3501 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    Atzberger, P. J. Incorporating shear into stochastic Eulerian Lagrangian methods for rheological studies of complex fluids and soft materials. Physica D: Nonlinear Phenomena, 265, 57–70 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    Kim, Y. and Lai, M. C. Simulating the dynamics of inextensible vesicles by the penalty immersed boundary method. Journal of Computational Physics, 229, 4840–4853 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    Liu, D., Keaveny, E., Maxey, M., and Karniadakis, G. Force coupling method for flow with ellipsoidal particles. Journal of Computational Physics, 228, 3559–3581 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    De la Torre, J. G. and Bloomfield, V. A. Hydrodynamic properties of macromolecular complexes I: translation. Biopolymers, 16, 1747–1763 (1977)CrossRefGoogle Scholar
  36. [36]
    Perrin, F. Mouvement brownien d’un ellipsoide II: rotation libre et dépolarisation des fluorescences— translation et diffusion de molécules ellipsoidales. Journal de Physique et le Radium, 7, 1–11 (1936)CrossRefzbMATHGoogle Scholar
  37. [37]
    Chwang, A. T. and Wu, T. Y. T. Hydromechanics of low-Reynolds-number flow I: rotation of axisymmetric prolate bodies. Journal of Fluid Mechanics, 63, 607–622 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  38. [38]
    Benesch, T., Yiacoumi, S., and Tsouris, C. Brownian motion in confinement. Physical Review E Statistical Nonlinear and Soft Matter Physics, 68, 021401 (2003)CrossRefGoogle Scholar
  39. [39]
    Faucheux, L. P. and Libchaber, A. J. Confined Brownian motion. Physical Review E Statistical Physics Plasmas Fluids and Related Interdisciplinary Topics, 49, 5158–5163 (1994)Google Scholar
  40. [40]
    Weeks, J. D., Chandler, D., and Andersen, H. C. Role of repulsive forces in determining the equilibrium structure of simple liquids. Journal of Chemical Physics, 54, 5237–5247 (1971)CrossRefGoogle Scholar
  41. [41]
    Wang, Y., Sigurdsson, J. K., Brandt, E., and Atzberger, P. J. Dynamic implicit-solvent coarsegrained models of lipid bilayer membranes: fluctuating hydrodynamics thermostat. Physical Review E Statistical Nonlinear and Soft Matter Physics, 88, 023301 (2013)CrossRefGoogle Scholar
  42. [42]
    Frigo, M. and Johnson, S. G. The design and implementation of FFTW3. Proceedings of the IEEE, 93, 216–231 (2005)CrossRefGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California Santa BarbaraSanta BarbaraUSA
  2. 2.Pacific Northwestern National LaboratoriesRichlandUSA

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