Mesoscopic model for binary fluids

Abstract

We propose a model for studying binary fluids based on the mesoscopic molecular simulation technique known as multiparticle collision, where the space and state variables are continuous, and time is discrete. We include a repulsion rule to simulate segregation processes that does not require calculation of the interaction forces between particles, so binary fluids can be described on a mesoscopic scale. The model is conceptually simple and computationally efficient; it maintains Galilean invariance and conserves the mass and energy in the system at the micro- and macro-scale, whereas momentum is conserved globally. For a wide range of temperatures and densities, the model yields results in good agreement with the known properties of binary fluids, such as the density profile, interface width, phase separation, and phase growth. We also apply the model to the study of binary fluids in crowded environments with consistent results.

Keywords

multiparticle collision dynamics / mesoscopic models / phase separation / interface dynamics

References

[1] M.Müller, D.Charypar, and M.Gross, Particle-based fluid simulation for interactive applications, in: Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp 154–159(2003)

[2] S.Premžoe, T.Tasdizen, J.Bigler, A.Lefohn, and R. T.Whitaker, Particle-based simulation of fluids, Comput. Graph. Forum22(3), 401(2003)

[3] Z. G.Mills, W.Mao, and A.Alexeev, Mesoscale modeling: Solving complex flows in biology and biotechnology, Trends Biotechnol. 31(7), 426(2013)

[4] M. G.Saundersand G. A.Voth, Coarse-graining methods for computational biology, Annu. Rev. Biophys. 42(1), 73(2013)

[5] U.Frisch, B.Hasslacher, and Y.Pomeau, Lattice-gas automata for the Navier–Stokes equation, Phys. Rev. Lett. 56(14), 1505(1986)

[6] S.Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford: Oxford University Press, 2001

[7] G.Falcucci, S.Ubertini, and S.Succi, Lattice Boltzmann simulations of phase-separating flows at large density ratios: The case of doubly-attractive pseudopotentials, Soft Matter6(18), 4357(2010)

[8] G.Falcucci, G.Bella, G.Shiatti, S.Chibbaro, M.Sbragaglia, and S.Succi, Lattice Boltzmann models with mid-range interactions, Commun. Comput. Phys. 2, 1071(2007)

[9] G.Falcucci, S.Ubertini, C.Biscarini, S. D.Francesco,D.Chiappini, S.Palpacelli, A. D.Maio, and S.Succi, Lattice Boltzmann methods for multiphase flow simulations across scales, Commun. Comput. Phys. 9(02), 269(2011)

[10] P. J.Hoogerbruggeand J.Koelman, Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics, Europhys. Lett.19(3), 155(1992)

[11] R. D.Grootand P. B.Warren, Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation, J. Chem. Phys. 107(11), 4423(1997)

[12] P.Españoland M.Revenga, Smoothed dissipative particle dynamics, Phys. Rev. E67(2), 026705(2003)

[13] A.Malevanetsand R.Kapral, Mesoscopic model for solvent dynamics, J. Chem. Phys. 110(17), 8605(1999)

[14] A.Malevanetsand R.Kapral, Solute molecular dynamics in a mesoscale solvent, J. Chem. Phys. 112(16), 7260(2000)

[15] A.Malevanetsand R.Kapral, Mesoscopic multi-particle collision model for fluid ow and molecular dynamics, in: Novel Methods in Soft Matter Simulations, Eds. M Karttunen, I. Vattulainen, and A. Lukkarinen, Berlin: Springer, 2003

[16] G.Gompper, T.Ihle, K.Kroll, and R. G.Winkler, Multi-particle collision dynamics: A particle-based mesoscale simulation approach to the hydrodynamics of complex fluids, advanced computer simulation approaches for soft matter sciences III, Adv. Polym. Sci. 221, 1 (2009)

[17] J. T.Paddingand A. A.Louis, Hydrodynamic and Brownian fluctuations in sedimenting suspensions, Phys. Rev. Lett.93(22), 220601(2004)

[18] M.Hecht, J.Harting, M.Bier, J.Reinshagen, and H. J.Herrmann, Shear viscosity of claylike colloids in computer simulations and experiments, Phys. Rev. E74(2), 021403(2006)

[19] K.Mussawisade, M.Ripoll, R. G.Winkler, and G.Gompper, Dynamics of polymers in a particle-based mesoscopic solvent, J. Chem. Phys. 123(14), 144905(2005)

[20] M.Ripoll, R. G.Winkler, and G.Gompper, Hydrodynamic screening of star polymers in shear flow, Eur. Phys. J. E23(4), 349(2007)

[21] C.Echeverriaand R.Kapral, Macromolecular dynamics in crowded environments, J. Chem. Phys. 132(10), 104902(2010)

[22] C.Echeverria, Y.Togashi, A. S.Mikhailov, and R.Kapral, A mesoscopic model for protein enzymatic dynamics in solution, Phys. Chem. Chem. Phys. 13(22), 10527(2011)

[23] C.Echeverriaand R.Kapral, Molecular crowding and protein enzymatic dynamics, Phys. Chem. Chem. Phys. 14(19), 6755(2012)

[24] C.Echeverriaand R.Kapral, Diffusional correlations among multiple active sites in a single enzyme, Phys. Chem. Chem. Phys. 16(13), 6211(2014)

[25] H.Noguchiand G.Gompper, Dynamics of fluid vesicles in shear flow: Effect of membrane viscosity and thermal fluctuations, Phys. Rev. E72(1), 011901(2005)

[26] K.Rohlf, S.Fraser, and R.Kapral, Reactive multiparticle collision dynamics, Comput. Phys. Commun. 179(1–3), 132(2008)

[27] K.Tucciand R.Kapral, Mesoscopic model for diffusioninfluenced reaction dynamics, J. Chem. Phys. 120(17), 8262(2004)

[28] K.Tucciand R.Kapral, Mesoscopic multi-particle collision dynamics of reaction diffusion fronts, J. Phys. Chem. B109(45), 21300(2005)

[29] C.Echevería, K.Tucci, and R.Kapral, Diffusion and reaction in crowded environments, J. Phys.: Condens. Matter19(6), 065146(2007)

[30] C.Echeverriaand R.Kapral, Autocatalytic reaction dynamics in systems crowded by catalytic obstacles, Physica D239(11), 791(2010)

[31] Y.Hashimoto, Y.Chen, and H.Ohashi, Immiscible realcoded lattice gas, Comput. Phys. Commun. 129(1–3), 56(2000)

[32] Y.Inoue, Y.Chen, and H.Ohashi, A mesoscopic simulation model for immiscible multiphase fluids, J. Comput. Phys. 201(1), 191(2004)

[33] T.Sakai, Y.Chen, and H.Ohashi, Real-coded lattice gas model for ternary amphiphilic fluids, Phys. Rev. E65(3), 031503(2002)

[34] F.Drube, Selfdiffusiophoretic Janus Colloids, Doctoral dissertation, Ludwig-Maximilians-Universität, München, 2013

[35] E.Tüzel, G.Pan, T.Ihle, and D. M.Kroll, Mesoscopic model for the fluctuating hydrodynamics of binary and ternary mixtures,Europhys. Lett. 80(4), 40010(2007)

[36] T.Ihleand D. M.Kroll, Stochastic rotation dynamics: A Galilean-invariant mesoscopic model for fluid flow, Phys. Rev. E63(2), 020201(2001)

[37] M.Laradji, S.Toxvaerd, and O. G.Mouritsen, Molecular dynamics simulation of spinodal decomposition in three-dimensional binary fluids, Phys. Rev. Lett. 77(11), 2253(1996)

[38] S. A.Safran, Statistical Thermodynamics of Surfaces: Interfaces and Membranes, Addison-Wesley, 1994

[39] A. J.Bray, Theory of phase-ordering kinetics, Adv. Phys. 51, 481(2002)

[40] E.Díaz-Herrera, J.Alejandre, G.Ramirez-Santiago, and F.Forstmann, Interfacial tension behavior of binary and ternary mixtures of partially miscible Lennard- Jones fluids: A molecular dynamics simulation, J. Chem. Phys. 110(16), 8084(1999)

[41] S.Iatsevitchand F.Forstmann, Density profiles at liquid–vapor and liquid–liquid interfaces: An integral equation study, J. Chem. Phys. 107(17), 6925(1997)

[42] H. X.Zhou, G.Rivas, and A. P.Minton, Macromolecular crowding and confinement: Biochemical, biophysical, and potential physiological consequences, Annu. Rev. Biophys. 37(1), 375(2008)

[43] A. S.Verkman, Solute and macromolecule diffusion in cellular aqueous compartments, Trends Biochem. Sci.27(1), 27(2002)

[44] L.Stagg, S. Q.Zhang, M. S.Cheung, and P.Wittung- Stafshede, Molecular crowding enhances native structure and stability of a/bprotein flavodoxin, Proc. Natl. Acad. Sci. USA104(48), 18976(2007)

RIGHTS & PERMISSIONS

2017 Higher Education Press and Springer-Verlag Berlin Heidelberg