# Workshops

## Multiscale Modeling of Simple and Complex Liquid Flow Using Particle-Continuum Hybrids

### Organisers

- Rafael Delgado-Buscalioni
*(Autonomous University of Madrid , Spain)* - Ignacio Pagonabarraga
*(CECAM EPFL, Switzerland)*

### Supports

CECAM

Ministerio de Ciencia e Innovación de España

Universidad Autónoma de Madrid

### Description

Particle and continuum hydrodynamics are intimately connected for several reasons. First, rheological properties of liquids are ultimately determined by the structure of their constituent molecules, and second, many liquids contain dispersed particles (e.g. pollutants) or large molecules (polymers, colloids) in suspension, which can substantially alter their dynamical behaviour. Another important aspect of this general question is how interactions at molecular scale may affect the fluid boundary conditions, at walls, soft interfaces etc... The range of fundamental and applied problems requiring some description of the interaction between particle and continuum fluid dynamics is huge and covers many time and length scales: from molecular dynamics (MD) research (e.g. the effect of flow on polymeric chains at low Reynolds number), to computational fluid dynamics (CFD) macroscopic problems (e.g. dispersion of pollutants in turbulent flows), including Non-Newtonian hydrodynamics (polymeric liquids), fluid-structure interaction (relevant for many biological applications), and so forth. Due to the large scope in the applied field, recent advances in computational methods for particle-continuum coupling are being developed by quite different communities whose work and ideas remain, quite often, isolated from each other. Albeit, an eagle-eye inspection on the literature reveals that most of these techniques share fundamental aspects and face similar challenges. On the other hand, due to the fast and independent growth of these different communities, there is a growing need to connect researchers working in theoretical modeling, applied science and software/hardware development.

Averaged particle effects or molecular information of the liquid bulk and of its physical boundaries have been traditionally included into the (not-closed) set of hydrodynamic equations via constitutive relations and phenomenological boundary conditions. In a sequential multiscale research program these relations are obtained from independent molecular simulations. However, the sequential approach fails whenever the particles and fluid structure are dynamically coupled due to their mutual interactions. This workshop focuses on multiscale computational methods which concurrently combine different techniques to solve particle and fluid dynamics. In this sense these type of methods are usually called hybrids.

Particle-continuum hybrids can be divided in three classes.

A: Domain decomposition. Some problems require to resolve a certain domain of interest at molecular detail and connect its dynamics with a hydrodynamic description of the surrounding flow field. These techniques are particularly suited at non-trivial or complex boundary conditions, which might contain singularities, interfaces or even macromolecules. Among the different techniques, one can mention , state coupling, flux coupling, Schwartz method or density control [1,2,3,4].

B: Constitutive modeling based on molecular simulations. A way to overcome the need of constitutive relations is to obtain the time evolution of the pressure tensor at each Eulerian node from a set of independent microscopic (molecular or stochastic) non-equilibrium simulations with the local velocity gradient thereby imposed. Since the pioneer work of Laso and Ottinger [5], there have been several important contributions, setting the general mathematical framework [6,7] and applications in scale-bridging molecular and macroscopic scales of polymeric liquid flow [8].

C: Particles in flow. There are several computational methods to solve the hydrodynamic interactions between solute (particles) and solvent (fluid) flow. Typical problems are the dynamics of colloidal or polymeric suspensions or larger particles dispersed in a liquid. Eulerian-Lagrangian hybrids solve the fluid component in an Eulerian mesh, while the particle dynamics are described in a Lagrangian fashion (continuum space) [9]. The same idea is applied in hybrids based on lattice Boltzmann (LB) and molecular dynamics [10]; the flexibility of the LB method makes feasible generalizations to allow for simulations of charged fluid flow [11], or colloids in binary fluids [11b]. Interpolation techniques are required to distribute the force between the particle and the fluid. Details of this force are highly dependent on the flow parameters (Reynolds number, Stokes number, particle size). In small devices it is usually approximated by the Stokes friction force [9-11] but it may demand more involved schemes inspired on the Immersed Boundary Method [12] for fluid-structure interaction. For instance, the direct forcing approach derives the force imposing the no-slip boundary condition at the particle surface [13,14]. Finally, fully Lagrangian (partlcle-particle) methods like Smooth Particle Hydrodynamics [16] or Multiparticle Collision Dynamics treat similar problems, with the benefit of simplifying the treatment of complex boundary conditions [15]. Albeit, comparisons among different schemes (benchmarks) and ranges of applicability are lacking in the literature.

### References

[1] G. De Fabritiis, R. Delgado-Buscalioni and P. Coveney, Modelling the mesoscale with molecular specificity. Phys. Rev. Lett 97, 134,501 (2006)

[2] X. Nie, M. O. Robbins, and S. Chen, Resolving Singular Forces in Cavity Flow: Multiscale Modeling from Atomic to Millimeter Scales. Phys. Rev. Lett. 96, 134501 (2006)

[3] P. Koutmousakos: Multiscale flow simulations using particles. Ann. Rev. Fluid Mech. 37, 457 (2005)

[4] M. Praprotnik, L. Delle Site and K. Kremer: Multiscale simulation of soft matter: From scale bridging to adaptive resolution. Annu. Rev. Phys. Chem. 59, 545 (2008)

[5] Laso M. and Ottinger H. C., Calculation of viscoelastic flow using molecular models: the connffessit approach J. Non-Newtonian Fluid Mech. 47, 1 (1993)

[6] Engquist, W.E.B., Li, X., Ren, W., Vanden-Eijden, E.: Heterogeneous multiscale methods: A review. Commun. Comput. Phys. 2, 367 (2007)

[7] Kevrekidis, I.G., Gear, C.W., Hummer, G.: Equation free: The computer-aided analysis of complex multiscale systems. AIChE J.50, 1346 (2004)

[8] Yasuda S. and Yamamoto R., Multiscale modeling and simulation of polymer melt flows between parallel plates, Phys. Rev. E 81, 036308 (2010)

[9] G. De Fabritiis, G. Giuponni and P.V. Coveney, J. Chem. Phys.

[10] Tri T. Pham, Ulf D. Schiller, J. Ravi Prakash, and B. Dunweg, Implicit and explicit solvent models for the simulation of a single polymer chain in solution: Lattice Boltzmann vs Brownian dynamics, Journal of Chemical Physics 131,

164114 (2009).

[11] B. Rotenberg, I. Pagonabarraga and D. Frenkel, "Coarse-grained simulations of charge, current and flow in heterogeneous media", Faraday Discussions 144, 223 (2010)

[11b] K. Stratford, R. Adhikari, I. Pagonabarraga, J.-C. Desplat and M.E. Cates, Colloidal jamming at interfaces: a route to fluid-bicontinuous gels, Science 309, 2198 (2005)

[12] Atzberger P.J, Kramer P.R. And Peskin C.S, A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales, J. Comptut. Phys. 224, 1255 (2007)

[13] Uhlmann, M. Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime. Phys Fluids 20, 053305 (2008)

[14] A. Pinelli, I. Naqavi, U. Piomilli and J. Favier, Immersed Boundary methods for general finite-difference and finite volume Navier-Sotkes solvers (submitted).

[15] Ripoll, M.; Holmqvist, P.; Winkler, R. G.; Gompper, G.; Dhont, J. K. G.; Lettinga, M. P. Attractive Colloidal rods in shear flow, Phys. Rev. Lett. 101, 168302 (2008)

[16] A. Vazquez, M. Ellero, P. Espanol: Smoothed particle hydrodynamic model for viscoelastic fluids with thermal fluctuations, Phys. Rev. E 79 056707 (2009)

[17] Borg, M.K and Reese J. M. A Hybrid Particle-Continuum Framework. ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels, paper no. ICNMM2008-62288 pp. 995-1004 (2008)

[18] Flekkoy, E.G., Delgado-Buscalioni, R., Coveney, P.V.: Flux boundary condition on particle systems.Phys. Rev. E 72, 026703 (2005)

[19] Liu, J., Chen, S., Nie, X., Robbins, M.O.: A continuum-atomistic simulation of heat transfer in micro- and nano-flows. J. Comput. Phys. 227, 279 (2007)

[20] Delgado-Buscalioni, R., Kremer, K., Praprotnik, M.: Coupling atomistic and continuum hydrodynamics through a mesoscopic model: Application to liquid water. J. Chem. Phys. 131, 244107 (2009)

[21] Poblete, S., Praprotnik, M., Kremer, K., Site, L.D.: Coupling different levels of resolution in molecular simulations. J. Chem. Phys. 132, 114101 (2010)

[22] C. Junghans and S. Poblete A reference implementation of the adaptive resolution scheme in ESPResSo, Computer Physics Communications 181 1449 (2010)

[23] Weinan, E., Ren, W. and Vanden-Eijden, E.: A general strategy for designing seamless multiscale methods J. Comp. Phys 228, 5437 (2009)

[24] Dirk O. Riese and Gerard H. Wegdam Sound Propagation in Suspensions of Colloidal Spheres with Viscous Coupling Phys. Rev. Lett. 82, 16761679 (1999). S. Oberti, Adrian Neild,Raymond Quach and Jürg Dual, The use of acoustic radiation forces to position particles within fluid droplets, Ultrasonics, 49, 47 (2009).

[25] Donev A., Bell, J.B., Garcia, A.L. and Alder, B.J.: A hybrid particle-continuum method for hydrodynamics of complex fluids. Multiscale Model. Simul. 8, 871 (2010)

[26] N. K. Voulgarakis, S, Satish and J. W. Chu Modeling the nanoscale viscoelasticity of fluids by bridging non-Markovian fluctuating hydrodynamics and molecular dynamics simulations, J. Chem. Phys. 131, 234115 (2009)

[27] K. Stratford and I. Pagonabarraga. Parallel simulation of particle suspensions with the lattice Boltzmann method, Computers and Mathematics with Applications 55, 1585 (2008)