Multiparticle hydrodynamic interactions

A semirigorous multiple-scattering theory of Shaqfeh and Fredrickson (1990) that accounts for multiparticle hydrodynamic interactions for slender bodies has verified Batchelor s theory and has given a slightly improved formula for str ... 

As a result of multiparticle hydrodynamic interactions, the fiij all depend on the positions of all particles in the system, in a way that is usefully split into pair interactions, three-body interactions, and higher terms. Note that and therefore Dij are divided between their self and distinct parts, including for i = j... 

Multiparticle collision dynamics can be combined with full molecular dynamics in order to describe the behavior of solute molecules in solution. Such hybrid MPC-MD schemes are especially useful for treating polymer and colloid dynamics since they incorporate hydrodynamic interactions. They are also useful for describing reactive systems where diffusive coupling among solute species is important. 

Most descriptions of the dynamics of molecular or particle motion in solution require a knowledge of the frictional properties of the system. This is especially true for polymer solutions, colloidal suspensions, molecular transport processes, and biomolecular conformational changes. Particle friction also plays an important role in the calculation of diffusion-influenced reaction rates, which will be discussed later. Solvent multiparticle collision dynamics, in conjunction with molecular dynamics of solute particles, provides a means to study such systems. In this section we show how the frictional properties and hydrodynamic interactions among solute or colloidal particles can be studied using hybrid MPC-MD schemes. 

The nature of the solvent influences both the structure of the polymer in solution and its dynamics. In good solvents the polymer adopts an expanded configuration and in poor solvents it takes on a compact form. If the polymer solution is suddenly changed from good to poor solvent conditions, polymer collapse from the expanded to compact forms will occur [78], A number of models have been suggested for the mechanism of the collapse [79-82], Hydrodynamic interactions are expected to play an important part in the dynamics of the collapse and we show how MPC simulations have been used to investigate this problem. Hybrid MD-MPC simulations of the collapse dynamics have been carried out for systems where bead-solvent interactions are either explicitly included [83] or accounted for implicitly in the multiparticle collision events [84, 85]. 

The effect of hydrodynamic interactions on polymer collapse has also been studied using MPC dynamics, where the polymer beads are included in the multiparticle collision step [28, 84]. Hydrodynamic interactions can be turned off by replacing multiparticle collisions in the cells by sampling of the particle velocities from a Boltzmann distribution. Collapse occurs more rapidly in the... 

Multiparticle collision dynamics describes the interactions in a many-body system in terms of effective collisions that occur at discrete time intervals. Although the dynamics is a simplified representation of real dynamics, it conserves mass, momentum, and energy and preserves phase space volumes. Consequently, it retains many of the basic characteristics of classical Newtonian dynamics. The statistical mechanical basis of multiparticle collision dynamics is well established. Starting with the specification of the dynamics and the collision model, one may verify its dynamical properties, derive macroscopic laws, and, perhaps most importantly, obtain expressions for the transport coefficients. These features distinguish MPC dynamics from a number of other mesoscopic schemes. In order to describe solute motion in solution, MPC dynamics may be combined with molecular dynamics to construct hybrid schemes that can be used to explore a variety of phenomena. The fact that hydrodynamic interactions are properly accounted for in hybrid MPC-MD dynamics makes it a useful tool for the investigation of polymer and colloid dynamics. Since it is a particle-based scheme it incorporates fluctuations so that the reactive and nonreactive dynamics in small systems where such effects are important can be studied. 

Brownian motion, multiparticle collision dynamics, hydrodynamic interactions, 118—121... 

Monte Carlo heat flow simulation, nonequilibrium molecular dynamics, 79—81 multiparticle collision dynamics hydrodynamic interactions, 118-121 single-particle friction and diffusion, 114-118... 

The Kirkwood-Riseman calculation is sufficiently detailed that we shall not discuss it further here. The interested reader is referred to Bird et al. (1987). However, the issue raised in considering complex shapes is the same one that arises when one questions whether the particle is not an isolated particle in suspension, which is the only situation for which we have outlined results. It is evident in a multiparticle suspension that the hydrodynamic interactions between the particles become important. For example, from what we have shown... 

The first technique is known as the stochastic rotational dynamics (SRD) method or multiparticle collision dynamics, which is a particle-based algorithm suited to account for hydrodynamic interactions on the mesoscale. The coarse-grained solvent is described as ideal-gas particles that propagate via streaming and collision steps, which are constructed such that the dynamics conserves mass, momentum, and energy. 

When two particles are in near contact, the fluid flow in the gap cannot be resolved. For particle sizes that are typically used in multiparticle simulations (a < 5/ ), the lubrication breakdown in the calculation of the hydrodynamic interaction occurs at gaps of the order of 0. la. However, in some flows, notably the shearing of a dense suspension, quaUtatively important physics occurs at smaller separations, typically down to 0.01a. Here we outline a method to implement lubrication corrections into a LB simulation. 

Multiparticle collision dynamics provides an ideal way to simulate the motion of small self-propelled objects since the interaction between the solvent and the motor can be specified and hydrodynamic effects are taken into account automatically. It has been used to investigate the self-propelled motion of swimmers composed of linked beads that undergo non-time-reversible cyclic motion [116] and chemically powered nanodimers [117]. The chemically powered nanodimers can serve as models for the motions of the bimetallic nanodimers discussed earlier. The nanodimers are made from two spheres separated by a fixed distance R dissolved in a solvent of A and B molecules. One dimer sphere (C) catalyzes the irreversible reaction A + C B I C, while nonreactive interactions occur with the noncatalytic sphere (N). The nanodimer and reactive events are shown in Fig. 22. The A and B species interact with the nanodimer spheres through repulsive Lennard-Jones (LJ) potentials in Eq. (76). The MPC simulations assume that the potentials satisfy Vca = Vcb = Vna, with c.,t and Vnb with 3- The A molecules react to form B molecules when they approach the catalytic sphere within the interaction distance r < rc. The B molecules produced in the reaction interact differently with the catalytic and noncatalytic spheres. 

Multiparticle collision dynamics (continued) hydrodynamic equations, 104—107 flow simulation, 107 friction interactions, 118-121 immiscible fluids, 138-139 macroscopic laws and transport coefficients, 99-104... 

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