Brownian particle dynamics

Dissipative particle dynamics (DPD) is a technique for simulating the motion of mesoscale beads. The technique is superficially similar to a Brownian dynamics simulation in that it incorporates equations of motion, a dissipative (random) force, and a viscous drag between moving beads. However, the simulation uses a modified velocity Verlet algorithm to ensure that total momentum and force symmetries are conserved. This results in a simulation that obeys the Navier-Stokes equations and can thus predict flow. In order to set up these equations, there must be parameters to describe the interaction between beads, dissipative force, and drag. 

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

Another largely unexplored area is the change of dynamics due to the influence of the surface. The dynamic behavior of a latex suspension as a model system for Brownian particles is determined by photon correlation spectroscopy in evanescent wave geometry [130] and reported to differ strongly from the bulk. Little information is available on surface motion and relaxation phenomena of polymers [10, 131]. The softening at the surface of polymer thin films is measured by a mechanical nano-indentation technique [132], where the applied force and the path during the penetration of a thin needle into the surface is carefully determined. Thus the structure, conformation and dynamics of polymer molecules at the free surface is still very much unexplored and only few specific examples have been reported in the literature. 

F. Ould-Kaddour and D. Levesque, Determination of the friction coefficient of a Brownian particle by molecular-dynamics simulation, J. Chem. Phys. 118, 7888 (2003). 

Adhesive force, non-Brownian particles, 549 Admicelle formation, 277 Adsorption flow rate, 514 mechanism, 646-647 on reservoir rocks, 224 patterns, on kaolinite, 231 process, kinetics, 487 reactions, nonporous surfaces, 646 surface area of sand, 251 surfactant on porous media, 510 Adsorption-desorption equilibria, dynamic, 279-239 Adsorption plateau, calcium concentration, 229... 

Kramers idea was to give a more realistic description of the dynamics in the reaction coordinate by including dynamical effects of the solvent. Instead of giving a deterministic description, which is only possible in a large-scale molecular dynamics simulation, he proposed to give a stochastic description of the motion similar to that of the Brownian motion of a heavy particle in a solvent. From the normal coordinate analysis of the activated complex, a reduced mass pi has been associated with the motion in the reaction coordinate, so the proposal is to describe the motion in that coordinate as that of a Brownian particle of mass g in the solvent. 

When one is interested in slow modes of motion of the system, each macromolecule of the system can be schematically described in a coarse-grained way as consisting of N + 1 linearly-coupled Brownian particles, and we shall be able to look at the system as a suspension of n(N + 1) interacting Brownian particles. An anticipated result for dynamic equation of the chains in equilibrium situation can be presented as a system of stochastic non-Markovian equations... 

The fourth term on the right hand side of (3.4) represents the elastic forces on each Brownian particle due to its neighbours along the chain the forces ensure the integrity of the macromolecule. Note that this term in equation (3.4) can be taken to be identical to the similar term in equation for dynamic of a single macromolecule due to a remarkable phenomenon - screening of intramolecular interactions, which was already discussed in Section 1.6.2. The last term on the right hand side of (3.4) represents a stochastic thermal force. The correlation function of the stochastic forces is connected... 

The system of dynamic equations (3.37) for a chain of Brownian particles with local anisotropy of mobility appears to be rather complicated for direct analysis, and one ought to use numerical methods, described in the next Section,... 

As was demonstrated by Pyshnograi (1994), the last term in (6.7) can be written in symmetric form, if the continuum of Brownian particles is considered incompressible. In equation (6.7), the sum is evaluated over the particles in a given macromolecule. The monomolecular approximation ensures that the stress tensor of the system is the sum of the contributions of all the macromolecules. In this form, the expression for the stresses is valid for any dynamics of the chain. One can consider the system to be a dilute polymer solution or a concentrated solution and melt of polymers. In any case the system is considered as a suspension of interacting Brownian particles. 

One of the first attempts to find a molecular interpretation of viscoelastic behaviour of entangled polymers was connected with investigation of the dynamics of a macromolecule in a form of generalised Rouse dynamics (Pokrovskii and Volkov 1978a Ronca 1983 Hess 1986). It formally means that, instead of assumption that the environment of the macromolecule is a viscous medium, Brownian particles of the chain are considered moving in a viscoelastic liquid with the stress tensor... 

In the simplest case, at N = 1, the considered subchain model of a macromolecule reduces to the dumbbell model consisting of two Brownian particles connected with an elastic force. It can be called relaxator as well. The re-laxator is the simplest model of a macromolecule. Moreover, the dynamics of a macromolecule in normal co-ordinates is equivalent to the dynamics of a set of independent relaxators with various coefficients of elasticity and internal viscosity. In this way, one can consider a dilute solution of polymer as a suspension of independent relaxators which can be considered here to be identical for simplicity. The latter model is especially convenient for the qualitative analysis of the effects in polymer solutions under motion. 

Dynamics of deposition of Brownian particles or cells on surfaces... 

---