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

doi:10.1007/s10483-018-2253-8

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (1): 125-152.doi: https://doi.org/10.1007/s10483-018-2253-8

• 论文 • 上一篇

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

Y. WANG¹, H. LEI², P. J. ATZBERGER¹

1. Department of Mathematics, University of California Santa Barbara, Santa Barbara, CA 93106, U. S. A;
2. Pacific Northwestern National Laboratories, Richland, WA 99354, U. S. A

收稿日期:2017-07-14 修回日期:2017-08-31 出版日期:2018-01-01 发布日期:2018-01-01
通讯作者: P. J. ATZBERGER E-mail:atzberg@gmail.com
基金资助:
Project supported by the Applied Mathematics Program within the Department of Energy (DOE) Office of Advanced Scientific Computing Research (ASCR) as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4) (No. DOE ASCR CM4 DE-SC0009254), the DOE National Laboratory Directed Research Development (No. LDRD69738), and the National Science Foudation of the United States (Nos. DMS-0956210, DMS-1616353, DMR-1121053, and NSF CNS-0960316)

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

Y. WANG¹, H. LEI², P. J. ATZBERGER¹

1. Department of Mathematics, University of California Santa Barbara, Santa Barbara, CA 93106, U. S. A;
2. Pacific Northwestern National Laboratories, Richland, WA 99354, U. S. A

Received:2017-07-14 Revised:2017-08-31 Online:2018-01-01 Published:2018-01-01
Contact: P. J. ATZBERGER E-mail:atzberg@gmail.com
Supported by:
Project supported by the Applied Mathematics Program within the Department of Energy (DOE) Office of Advanced Scientific Computing Research (ASCR) as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4) (No. DOE ASCR CM4 DE-SC0009254), the DOE National Laboratory Directed Research Development (No. LDRD69738), and the National Science Foudation of the United States (Nos. DMS-0956210, DMS-1616353, DMR-1121053, and NSF CNS-0960316)

摘要/Abstract

摘要： 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.

关键词: integro-differential equation, monotone iterative technique, extremal solution, stochastic Eulerian-Lagrangian method (SELM), ellipsoidal colloid, immersed boundary method, nanochannel, mobility, fluctuating hydrodynamics

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: integro-differential equation, monotone iterative technique, extremal solution, immersed boundary method, fluctuating hydrodynamics, nanochannel, stochastic Eulerian-Lagrangian method (SELM), mobility, ellipsoidal colloid

中图分类号:

Y. WANG, H. LEI, P. J. ATZBERGER. Fluctuating hydrodynamic methods for fluid-structure interactions in confined channel geometries[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(1): 125-152.

参考文献

[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)
[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)
[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)
[4] Kilic, M. S. and Bazant, M. Z. Induced-charge electrophoresis near a wall. Electrophoresis, 32, 614-628(2011)
[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)
[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)
[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)
[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)
[9] Squires, T. M. and Quake, S. R. Microfluidics:fluid physics at the nanoliter scale. Reviews of Modern Physics, 77, 977-1026(2005)
[10] Teh, S. Y., Lin, R., Hung, L. H., and Lee, A. P. Droplet microfluidics. Lab on a Chip, 8, 198-220(2008)
[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)
[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)
[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)
[14] Atzberger, P. J. Stochastic Eulerian Lagrangian methods for fluid structure interactions with thermal fluctuations. Journal of Computational Physics, 230, 2821-2837(2011)
[15] Landau, L. D. and Lifshitz, E. M. Course of theoretical physics. Statistical Physics (3rd ed.), Pergamon Press, Oxford (1980)
[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)
[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)
[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)
[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)
[20] Düenweg, B. and Ladd, A. J. C. Lattice Boltzmann simulations of soft matter systems. Advances in Polymer Science, 221, 89-166(2008)
[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)
[22] Peskin, C. S. The immersed boundary method. Acta Numerica, 11, 1-39(2002)
[23] Gardiner, C. W. Handbook of Stochastic Methods, Springer, Berlin (1985)
[24] Oksendal, B. Stochastic Differential Equations:An Introduction, Springer, Berlin (2000)
[25] Reichl, L. E. A Modern Course in Statistical Physics, John Wiley and Sons, New York (1998)
[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)
[27] Kloeden, P. E. and Platen, E. Numerical Solution of Stochastic Differential Equations, Springer, Berlin (1992)
[28] Chorin, A. J. Numerical solution of Navier-Stokes equations. Mathematics of Computation, 22, 745-762(1968)
[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)
[30] Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. Numerical Recipes in C, Cambridge University Press, Cambridge (1994)
[31] Atzberger, P. Spatially adaptive stochastic numerical methods for intrinsic fluctuations in reactiondiffusion systems. Journal of Computational Physics, 229, 3474-3501(2010)
[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)
[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)
[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)
[35] De la Torre, J. G. and Bloomfield, V. A. Hydrodynamic properties of macromolecular complexes I:translation. Biopolymers, 16, 1747-1763(1977)
[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)
[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)
[38] Benesch, T., Yiacoumi, S., and Tsouris, C. Brownian motion in confinement. Physical Review E Statistical Nonlinear and Soft Matter Physics, 68, 021401(2003)
[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)
[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)
[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)
[42] Frigo, M. and Johnson, S. G. The design and implementation of FFTW3. Proceedings of the IEEE, 93, 216-231(2005)

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

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

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