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

October 5, 2011 to October 7, 2011
Location : ZCAM, Zaragoza, Spain


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



Ministerio de Ciencia e Innovación de España

Universidad Autónoma de Madrid


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.


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