Microfluidics and Nanofluidics

, Volume 8, Issue 3, pp 283–302 | Cite as

A review of the development of hybrid atomistic–continuum methods for dense fluids

Review

Abstract

In recent years, there has been an increasing interest in simulating dynamical phenomena of multiscale systems. This was brought about in large part by the ever growing field of nanotechnology, in which nanodevices are often part of larger systems. Molecular Dynamics (MD) provides a valuable tool for modeling systems at the nanoscale. However, the atomistic modeling of macroscopic problems is still beyond the reach of current MD simulations due to their prohibitive computational requirements. The development of hybrid techniques that combine continuum and atomistic descriptions can alleviate such limitations. This can be accomplished by limiting the use of MD to regions where the atomistic scales need to be resolved, while using a continuum-based solver for the remainder of the domain. The computational savings of such a formulation will strongly depend on the relative size of the MD region to that of the continuum, and the extent of the overlap where information is exchanged between the two subdomains. Such methods are crucial for the proficient advancement and better understanding of nanodevices interacting with microscale systems. In this article, an account of the development of hybrid atomistic–continuum (HAC) models for dense flows is presented. The focus is on domain-decomposition-based HAC models. Here, the domain is divided into a relatively small region where atomistic details are important, and a larger region where the continuum description of the fluid is applicable. Of primary concern is how to accurately couple the atomistic and continuum domains, a challenge that manifests itself in the imposition of boundary conditions in an internally consistent manner. Two main approaches: state variable (Dirichlet), and flux-exchange schemes are analyzed and compared. A review of some applications utilizing such HAC models is also provided.

Keywords

Hybrid atomistic–continuum Coupling Molecular dynamics Multiscale Dense fluids Microfluidics Nanofluidics 

References

  1. Allen M, Tildesley D (1987) Computer simulation of liquids. Clarendon Press, OxfordMATHGoogle Scholar
  2. Baldini G, Cannone F, Chirico G (2005) Pre-unfolding resonant oscillations of single green fluorescent protein molecules. Science 309(5737):1096–1100CrossRefGoogle Scholar
  3. Barrat J, Chiaruttini F (2003) Kapitza resistance at the liquid-solid interface. Mol Phys 101(11):1605–1610CrossRefGoogle Scholar
  4. Barsky S, Delgado-Buscalioni R, Coveney PV (2004) Comparison of molecular dynamics with hybrid continuum-molecular dynamics for a single tethered polymer in a solvent. J Chem Phys 121(5):2403–2411CrossRefGoogle Scholar
  5. Berendsen HJC, Postma JPM, Van Gunsteren WF, Dinola A, Haak JR (1984) Molecular dynamics with coupling to an external bath. J Chem Phys 81(8):3684–3690CrossRefGoogle Scholar
  6. Borgelt P, Hoheisel C, Stell G (1990) Exact molecular dynamics and kinetic theory results for thermal transport coefficients of the Lennard-Jones Argon fluid in a wide region of states. Phys Rev A 42(2):789–794CrossRefGoogle Scholar
  7. Brenner MP, Shi XD, Nagel SR (1994) Iterated instabilities during droplet fission. Phys Rev Lett 73(25):3391–3394CrossRefGoogle Scholar
  8. Broughton JQ, Meli CA, Vashishta P, Kalia RK (1997) Direct atomistic simulation of quartz crystal oscillators: bulk properties and nanoscale devices. Phys Rev B 56(2):611–618CrossRefGoogle Scholar
  9. Burt JM, Boyd ID (2009) A hybrid particle approach for continuum and rarefied flow simulation. J Comput Phys 228(2):460–475MATHCrossRefGoogle Scholar
  10. Chatterji A, Horbach J (2005) Combining molecular dynamics with Lattice Boltzmann: a hybrid method for the simulation of (charged) colloidal systems. J Chem Phys 122(18):1–12CrossRefGoogle Scholar
  11. Cui J, He G, Qi D (2006) A constrained particle dynamics for continuum-particle hybrid method in micro- and nano-fluidics. Acta Mech Sin 26(6):503–508CrossRefGoogle Scholar
  12. De Fabritiis G, Delgado-Buscalioni R, Coveney PV (2004) Energy controlled insertion of polar molecules in dense fluids. J Chem Phys 121(24):12139–12142CrossRefGoogle Scholar
  13. De Fabritiis G, Delgado-Buscalioni R, Coveney PV (2006) Multiscale modeling of liquids with molecular specificity. Phys Rev Lett 97(13):134501CrossRefGoogle Scholar
  14. Delgado-Buscalioni R, Coveney PV (2003) Continuum-particle hybrid coupling for mass, momentum, and energy transfers in unsteady fluid flow. Phys Rev E 67(4):046704CrossRefGoogle Scholar
  15. Delgado-Buscalioni R, Coveney PV (2003) USHER: an algorithm for particle insertion in dense fluids. J Chem Phys 119(2):978–987CrossRefGoogle Scholar
  16. Delgado-Buscalioni R, Coveney PV (2004) Hybrid molecular-continuum fluid dynamics. Philos Trans R Soc Lond A 362(1821):1639–1654CrossRefMathSciNetGoogle Scholar
  17. Delgado-Buscalioni R, De Fabritiis D (2007) Embedding molecular dynamics within fluctuating hydrodynamics in multiscale simulations of liquids. Phys Rev E 76(3):036709CrossRefGoogle Scholar
  18. Delgado-Buscalioni R, Flekkoy EG, Coveney PV (2005) Fluctuations and continuity in particle-continuum hybrid simulations of unsteady flows based on flux-exchange. Europhys Lett 69(6):959–965CrossRefGoogle Scholar
  19. Delgado-Buscalioni R, Coveney PV, De Fabritiis G (2008) Towards multi-scale modelling of complex liquids using hybrid particle-continuum schemes. Proc Inst Mech Eng C 222(5):769–776CrossRefGoogle Scholar
  20. Delgado-Buscalioni R, Kremer K, Praprotnik M (2008) Concurrent triple-scale simulation of molecular liquids. J Chem Phys 128(11):114110CrossRefGoogle Scholar
  21. Doyle PS, Ladoux B, Viovy JL (2000) Dynamics of a tethered polymer in shear flow. Phys Rev Lett 84(20):4769–4772CrossRefGoogle Scholar
  22. Dupuis A, Kotsalis EM, Koumoutsakos P (2007) Coupling Lattice Boltzmann and molecular dynamics models for dense fluids. Phys Rev E 75(4):046704CrossRefGoogle Scholar
  23. Espanol P, Revenga M (2003) Smoothed dissipative particle dynamics. Phys Rev E 67(2):026705CrossRefGoogle Scholar
  24. Evans DJ, Morriss GP (2007) Statistical mechanics of nonequilibrium liquids. ANU E Press, AustraliaGoogle Scholar
  25. Fedosov DA, Karniadakis GE (2009) Triple-Decker: interfacing atomistic-mesoscopic-continuum flow regimes. J Comput Phys 228(4):1157–1171MATHCrossRefMathSciNetGoogle Scholar
  26. Flekkoy EG, Wagner G, Feder J (2000) Hybrid model for combined particle and continuum dynamics. Europhys Lett 52(3):271–276CrossRefGoogle Scholar
  27. Flekkoy EG, Delgado-Buscalioni R, Coveney PV (2005) Flux boundary conditions in particle simulations. Phys Rev E 72(2):1–9CrossRefGoogle Scholar
  28. Frenkel D, Smith B (1996) Understanding molecular simulations. Academic Press, LondonGoogle Scholar
  29. Fyta M, Kaxiras E, Melchionna S, Succi S (2008) Multiscale simulation of nanobiological flows. Comput Sci Eng 10(4):10–19CrossRefGoogle Scholar
  30. Garcia AL, Bell JB, Crutchfield WY, Aldery BJ (1999) Adaptive mesh and algorithm refinement using direct simulation Monte Carlo. J Comput Phys 154:134–155MATHCrossRefGoogle Scholar
  31. Grest GS, Kremer K (1986) Molecular dynamics simulation for polymers in the presence of a heat bath. Phys Rev A 33(5):3628–3631CrossRefGoogle Scholar
  32. Guo Z, Zheng C, Shi B (2002) Discrete lattice effects on the forcing term in the Lattice Boltzmann method. Phys Rev E 65(4):046308CrossRefMathSciNetGoogle Scholar
  33. Hadjiconstantinou NG (1999) Hybrid atomistic-continuum formulations and the moving contact-line problem. J Comput Phys 154:245–265MATHCrossRefGoogle Scholar
  34. Hadjiconstantinou NG (2005) Discussion of recent developments in hybrid atomistic-continuum methods for multiscale hydrodynamics. Bull Pol Acad Sci Tech Sci 53(4):335–342Google Scholar
  35. Hadjiconstantinou NG, Patera AT (1997) Heterogeneous atomistic-continuum representations for dense fluid systems. Int J Mod Phys 8(4):967–976CrossRefGoogle Scholar
  36. Hadjiconstantinou NG, Garcia AL, Bazant MZ, He G (2003) Statistical error in particle simulations of hydrodynamic phenomena. J Comput Phys 187(1):274–297MATHCrossRefMathSciNetGoogle Scholar
  37. Hansen JP, McDonald IR (1986) Theory of simple liquids. Academic Press, LondonGoogle Scholar
  38. Hash DB, Hassan HA (1995) A hybrid DSMC/Navier-Stokes solver. AIAA Paper 95-0414Google Scholar
  39. Heyes DM (1988) Simple expressions for the self-diffusion coefficient, shear viscosity and thermal conductivity of Lennard-Jones fluids. Chem Phys Lett 153(4):319–321CrossRefGoogle Scholar
  40. Ho CM, Tai YC (1998) Micro-electro-mechanical-systems (MEMS) and fluid flows. Annu Rev Fluid Mech 30:579–612CrossRefGoogle Scholar
  41. Hoover WG, De Groot AJ, Hoover CG (1992) Massively parallel computer simulation of plane-strain elastic-plastic flow via nonequilibrium molecular dynamics and Lagrangian continuum mechanics. Comput Phys 6(2):155–167CrossRefGoogle Scholar
  42. Hu G, Li D (2007) Multiscale phenomena in microfluidics and nanofluidics. Chem Eng Sci 62(13):3443–3454CrossRefGoogle Scholar
  43. Johnson JK, Zollweg JA, Gubbins KE (1993) The Lennard-Jones equation of state revisited. Mol Phys 78(3):591–618CrossRefGoogle Scholar
  44. Kalweit M, Drikakis D (2008) Multiscale methods for micro/nano flows and materials. J Comput Theor Nanosci 5(9):1923–1938CrossRefGoogle Scholar
  45. Kalweit M, Drikakis D (2008) Coupling strategies for hybrid molecular-continuum simulation methods. Proc Inst Mech Eng C 222(5):797–806Google Scholar
  46. Karniadakis G, Beskok A, Aluru N (2005) Microflows and nanoflows, fundamentals and simulation. Springer, New YorkMATHGoogle Scholar
  47. Kevrekidis IG, Gear CW, Hyman JM, Panagiotis GK, Runborg O, Theodoropoulos C (2003) Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system-level analysis. Commun Math Sci 1(4):715–762MATHMathSciNetGoogle Scholar
  48. Kevrekidis IG, Gear CW, Hummer G (2004) Equation-free: the computer-aided analysis of complex multiscale systems. AIChE J 50(7):1346–1355CrossRefGoogle Scholar
  49. Kohlhoff S, Gumbsch P, Fischmeister HF (1991) Crack propagation in b.c.c. crystals studied with a combined finite-element and atomistic model. Philos Mag A 64(4):851–878CrossRefGoogle Scholar
  50. Koplik J, Banavar JR (1995) Continuum deductions from molecular hydrodynamics. Annu Rev Fluid Mech 27(1):257–292CrossRefGoogle Scholar
  51. Koplik J, Banavar JR (1995) Corner flow in the sliding plate problem. Phys Fluids 7(12):3118–3125MATHCrossRefGoogle Scholar
  52. Kotsalis EM, Walther JH, Koumoutsakos P (2007) Control of density fluctuations in atomistic-continuum simulations of dense liquids. Phys Rev E 76(1):016709CrossRefGoogle Scholar
  53. Kotsalis EM, Walther JH, Kaxiras E, Koumoutsakos P (2009) Control algorithm for multiscale flow simulations of water. Phys Rev E 79(4):045701CrossRefGoogle Scholar
  54. Koumoutsakos P (2005) Multiscale flow simulations using particles. Annu Rev Fluid Mech 37:457–487CrossRefMathSciNetGoogle Scholar
  55. Kunugi T, Muko K, Shibahara M (2004) Ultrahigh heat transfer enhancement using nano-porous layer. Superlattices Microstruct 35(3–6):531–542CrossRefGoogle Scholar
  56. Landau LD, Lifshitz EM (1959) Fluid mechanics. Pergamon Press, New YorkGoogle Scholar
  57. LeDuc P, Haber C, Bao G, Wirtz D (1999) Dynamics of individual flexible polymers in a shear flow. Nature 399(6736):564–566CrossRefGoogle Scholar
  58. Li J, Liao D, Yip S (1998) Coupling continuum to molecular-dynamics simulation: reflecting particle method and the field estimator. Phys Rev E 57(6):7259–7267CrossRefGoogle Scholar
  59. Li J, Liao D, Yip S (1999) Nearly exact solution for coupled continuum/MD fluid simulation. J Comput Aided Mater Des 6(2):95–102CrossRefGoogle Scholar
  60. Li J, Liao D, Yip S (1999) Imposing field boundary conditions in md simulation of fluids: optimal particle controller and buffer zone feedback. Mater Res Soc Symp Proc 538:473–478Google Scholar
  61. Lions PL (1988) On the Schwarz alternating method. In: Glowinski R (ed) First international symposium on domain decomposition methods for partial differential equations. SIAM, Philadelphia, USA, pp 1–42Google Scholar
  62. Liu J, Chen S, Nie X, Robbins MO (2007) A continuum-atomistic simulation of heat transfer in micro- and nano-flows. J Comput Phys 227(1):279–291MATHCrossRefGoogle Scholar
  63. Liu J, Chen S, Nie X, Robbins MO (2008) A continuum-atomistic multi-timescale algorithm for micro/nano flows. Commun Comput Phys 4(5):1279–1291Google Scholar
  64. Macpherson GB, Reese JM (2008) Molecular dynamics in arbitrary geometries: parallel evaluation of pair forces. Mol Simul 34(1):97–115CrossRefGoogle Scholar
  65. Maday Y, Patera AT (1989) Spectral element methods for the incompressible Navier-Stokes equations. In: Noor AK, Oden JT (ed) State-of-the-art surveys in computational mechanics. ASME, New York, USA, pp 71–143Google Scholar
  66. McCormick SF (1989) Multilevel adaptive methods for partial differential equations. SIAM, PhiladelphiaMATHGoogle Scholar
  67. Mukhopadhyay S, Abraham J (2009) A particle-based multiscale model for submicron fluid flows. Phys Fluids 21(2):027102CrossRefGoogle Scholar
  68. Nie XB, Chen SY, E WN, Robbins MO (2004) A continuum and molecular dynamics hybrid method for micro- and nano-fluid flow. J Fluid Mech 500:55–64MATHCrossRefGoogle Scholar
  69. Nie X, Chen S, Robbins MO (2004) Hybrid continuum-atomistic simulation of singular corner flow. Phys Fluids 16(10):3579–3591CrossRefGoogle Scholar
  70. Nie X, Robbins MO, Chen S (2006) Resolving singular forces in cavity flow: multiscale modeling from atomic to millimeter scales. Phys Rev Lett 96(13):134501CrossRefGoogle Scholar
  71. O’Connell ST, Thompson PA (1995) Molecular dynamics-continuum hybrid computations: a tool for studying complex fluid flows. Phys Rev E 52(6):R5792–R5795CrossRefGoogle Scholar
  72. Patera AT (1984) A spectral element method for fluid dynamics—laminar flow in a channel expansion. J Comput Phys 54(3):468–488MATHCrossRefMathSciNetGoogle Scholar
  73. Pivkin IV, Karniadakis GE (2006) Controlling density fluctuations in wall-bounded dissipative particle dynamics systems. Phys Rev Lett 96(20):206001CrossRefGoogle Scholar
  74. Praprotnik K, Delle Site L, Kremer K (2005) Adaptive resolution molecular-dynamics simulation: changing the degrees of freedom on the fly. J Chem Phys 123(22):1–14CrossRefGoogle Scholar
  75. Praprotnik K, Delle Site L, Kremer K (2006) Adaptive resolution scheme for efficient hybrid atomistic-mesoscale molecular dynamics simulations of dense liquids. Phys Rev E 73(6):066701CrossRefGoogle Scholar
  76. Praprotnik M, Site LD, Kremer K (2008) Multiscale simulation of soft matter: from scale bridging to adaptive resolution. Annu Rev Phys Chem 59:545–571CrossRefGoogle Scholar
  77. Ren W (2007) Analytical and numerical study of coupled atomistic-continuum methods for fluids. J Comput Phys 227(2):1353–1371MATHCrossRefMathSciNetGoogle Scholar
  78. Ren W, Weinan E (2005) Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics. J Comput Phys 204(1):1–26MATHCrossRefMathSciNetGoogle Scholar
  79. Saletan EJ, Cromer AH (1971) Theoretical mechanics. Wiley, New YorkGoogle Scholar
  80. Schmatko T, Hervet H, Leger L (2005) Friction and slip at simple fluid-solid interfaces: the roles of the molecular shape and the solid-liquid interaction. Phys Rev Lett 94(24):1–4CrossRefGoogle Scholar
  81. Schoch RB, Han J, Renaud P (2008) Transport phenomena in nanofluidics. Rev Mod Phys 80(3):839–883CrossRefGoogle Scholar
  82. Schubert K, Brandner J, Fichtner M, Linder G, Schygulla U, Wenka A (2001) Microstructure devices for applications in thermal and chemical process engineering. Microscale Thermophys Eng 5(1):17–39CrossRefGoogle Scholar
  83. Schwartzentruber TE, Scalabrin LC, Boyd ID (2007) A modular particle-continuum numerical method for hypersonic non-equilibrium gas flows. J Comput Phys 225(1):1159–1174MATHCrossRefMathSciNetGoogle Scholar
  84. Slater GW, Holm C, Chubynsky MV, de Haan HW, Dubé A, Grass K, Hickey OA, Kingsburry C, Sean D, Shendruk TN, Zhan L (2009) Modeling the separation of macromolecules: a review of current computer simulation methods. Electrophoresis 30(5):792–818CrossRefGoogle Scholar
  85. Stroock AD, Dertinger SKW, Ajdari A, Mezic I, Stone HA, Whitesides GM (2002) Chaotic mixer for microchannels. Science 295(5555):647–651CrossRefGoogle Scholar
  86. Succi S (2001) The Lattice Boltzmann equation, for fluid dynamics and beyond. Oxford University Press, OxfordMATHGoogle Scholar
  87. Succi S, Filippova O, Smith G, Kaxiras E (2001) Applying the Lattice Boltzmann equation to multiscale fluid problems. Comput Sci Eng 3(6):26–37CrossRefGoogle Scholar
  88. Sun Q, Boyd ID, Candler GV (2004) A hybrid continuum/particle approach for modeling subsonic, rarefied gas flows. J Comput Phys 194(1):256–277MATHCrossRefGoogle Scholar
  89. Sun J, He Y, Tao W (2009) Molecular dynamics-continuum hybrid simulation for condensation of gas flow in a microchannel. Microfluid Nanofluid 7(3):407–422Google Scholar
  90. Thompson PA, Robbins MO (1989) Simulations of contact-line motion: slip and the dynamic contact angle. Phys Rev Lett 63(7):766–769CrossRefGoogle Scholar
  91. Thompson PA, Robbins MO (1990) Origin of stick-slip motion in boundary lubrication. Science 250(4982):792–794CrossRefGoogle Scholar
  92. Thompson PA, Brickerhoff WB, Robbins MO (1993) Microscopic studies of static and dynamic contact angles. J Adhes Sci Technol 7(6):535–554CrossRefGoogle Scholar
  93. Wadsworth DC, Erwin DA (1990) One-dimensional hybrid continuum/particle simulation approach for rarefied hypersonic flows. AIAA Paper 90-1690Google Scholar
  94. Wagner G, Flekkoy EG (2004) Hybrid computations with flux exchange. Philos Trans R Soc Lond A 362(1821):1655–1665CrossRefMathSciNetGoogle Scholar
  95. Wagner G, Flekkoy E, Feder J, Jossang T (2002) Coupling molecular dynamics and continuum dynamics. Comput Phys Commun 147(1–2):670–673MATHCrossRefGoogle Scholar
  96. Wang Y, He G (2007) A dynamic coupling model for hybrid atomistic-continuum computations. Chem Eng Sci 62(13):3574–3579CrossRefMathSciNetGoogle Scholar
  97. Weinan E, Engquist B, Li X, Ren W, Vanden-Eijnden E (2007) Heterogeneous multiscale methods: a review. Commun Comput Phys 2(3):367–450MATHMathSciNetGoogle Scholar
  98. Werder T, Walther JH, Koumoutsakos P (2005) Hybrid atomistic-continuum method for the simulation of dense fluid flows. J Comput Phys 205(1):373–390MATHCrossRefMathSciNetGoogle Scholar
  99. Wijesinghe HS, Hadjiconstantinou NG (2004) Discussion of hybrid atomistic-continuum methods for multiscale hydrodynamics. Int J Multiscale Comput Eng 2(2):189–202CrossRefGoogle Scholar
  100. Wolf-Gladrow DA (2005) Lattice-gas cellular automata and Lattice Boltzmann models—an introduction. Springer, New YorkGoogle Scholar
  101. Yasuda S, Yamamoto R (2008) A model for hybrid simulations of molecular dynamics and computational fluid dynamics. Phys Fluids 20(11):113101CrossRefGoogle Scholar
  102. Yen TH, Soong CY, Tzeng PY (2007) Hybrid molecular dynamics-continuum simulation for nano/mesoscale channel flows. Microfluid Nanofluid 3(6):665–675CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Mechanical and Manufacturing EngineeringUniversity of CalgaryCalgaryCanada

Personalised recommendations