Abstract
In the paper a Direct Numerical Simulation (DNS) scheme, named Fluctuating Immersed MATerial (FIMAT) dynamics, for the Brownian motion of particles is presented. In this approach the thermal fluctuations are included in the fluid equations via random stress terms. Solving the fluctuating hydrodynamic equations coupled with the particle equations of motion results in the Brownian motion of the particles. There is no need to add a random force term in the particle equations. The particles acquire random motion through the hydrodynamic force acting on its surface from the surrounding fluctuating fluid. The random stresses in the fluid equations are easy to calculate unlike the random terms in the conventional Brownian Dynamics (BD) type approaches.
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References
Brady, J.F. and Bossis, G., 1988, Stokesian dynamics, Annual Rev. Fluid Mech. 20, 111–157.
Chen, Y., Sharma, N. and Patankar, N.A., 2005, Fluctuating Immersed Material (FIMAT) dynamics for the direct simulation of the Brownian motion of particles, J. Fluid Mech., submitted.
Ermak, D.L. and McCammon, J.A., 1978, Brownian dynamics with hydrodynamic interactions, J. Chem. Phys. 69(4), 1352–1360.
Glowinski, R., Pan, T.W., Hesla, T.I. and Joseph, D.D., 1999, A distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiphase Flow 25, 755–794.
Grmela, M. and Öttinger, H.C., 1997, Dynamics and thermodynamics of complex fluids. I. Development of a general formalism, Phys. Rev. E 56(6), 6620–6632.
Hauge, E.H. and Martin-Löf, A., 1973, Fluctuating hydrodynamics and Brownian motion, J. Stat. Phys. 7(3), 259–281.
Hasimoto, H., 1959, On the periodic fundamental solution of the Stokes equations and their application to viscous flow past a cubic array of spheres, J. Fluid Mech. 5, 317–328.
Hu, H.H., Joseph, D.D. and Crochet, M.J., 1992, Direct numerical simulation of fluid particle motions, Theoret. Comput. Fluid Dynam. 3, 285–306.
Hu, H.H., Patankar, N.A. and Zhu, M.Y., 2001, Direct numerical simulations of fluid solid systems using Arbitrary Lagrangian—Eulerian technique, J. Comput. Phys. 169, 427–462.
Ladd, A.J.C., 1993, Short time motion of colloidal particles: Numerical simulation via a fluctuating Lattice-Boltzmann equation, Phys. Rev. Lett. 70(9), 1339–1342.
Landau, L.D. and Lifshitz, E.M., 1959, Fluid Mechanics, Pergamon Press, London.
Öttinger, H.C. and Grmela, M., 1997, Dynamics and thermodynamics of complex fluids. II. Development of a general formalism, Phys. Rev. E 56(6), 6633–6655.
Patankar, N.A., 2001, A formulation for fast computations of rigid particulate flows, Center for Turbulence Research, Annual Research Briefs, 185–196.
Patankar, N.A., 2002, Direct Numerical Simulation of moving charged, flexible bodies with thermal fluctuations, in Technical Proceedings of the 2002 International Conference on Modeling and Simulation of Microsystems, pp. 32–35.
Patankar, N.A., Singh, P., Joseph, D.D., Glowinski, R. and Pan, T.W., 2000, A new formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiphase Flow 26, 1509–1524.
Serrano, M. and Espaôol, P., 2001, Thermodynamically consistent mesoscopic fluid particle model, Phys. Rev. E 64(4), 046115.
Serrano, M., Gianni, D.F., Espaôol, P., Flekkøy, E.G. and Coveney, P.V., 2002, Mesoscopic dynamics of Voronoi fluid particles, J. Phys. A: Math. Gen. 35(7), 1605–1625.
Sharma, N. and Patankar, N.A., 2004, Direct numerical simulation of the Brownian motion of particles by using fluctuating hydrodynamic equations, J. Comput. Phys. 201, 466–486.
Sharma, N. and Patankar, N.A., 2005, A fast computation technique for the Direct Numerical Simulation of rigid particulate flows, J. Comput. Phys. 205, 439–457.
Sharma, N., Chen, Y. and Patankar, N.A., 2005, A Distributed Lagrange Multiplier method based computational method for the simulation of particulate Stokes flow, Comput. Meth. Appl. Mech. Engng. 194, 4716–4730.
Zick, A.A. and Homsy, G.M., 1982, Stokes flow through periodic arrays of spheres, J. Fluid Mech. 115, 13–26.
Zwanzig, R., 1964, Hydrodynamic fluctuations and Stokes’ law friction, J. Res. Natl. Bur. Std. (U.S.) 68B, 143–145.
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Chen, Y., Sharma, N., Patankar, N.A. (2006). Fluctuating Immersed Material (FIMAT) Dynamics for the Direct Simulation of the Brownian Motion of Particles. In: Balachandar, S., Prosperetti, A. (eds) IUTAM Symposium on Computational Approaches to Multiphase Flow. Fluid Mechanics and Its Applications, vol 81. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4977-3_13
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DOI: https://doi.org/10.1007/1-4020-4977-3_13
Publisher Name: Springer, Dordrecht
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