Brownian dynamics hydrodynamic effects

The pairwise Brownian dynamics method has several advantages over numerical methods based on Smoluchowski s [9] approach (e.g., finite element method), and we discuss these here. The primary advantage of the method is the ease of mathematical formulation even for cases involving complex reaction site geometries, hydrodynamic interactions, charge effects, anisotropic diffusion and flow fields. Furthermore the method obviates the need to solve complex diffusion equations to obtain the concentration field from which the rate constant is calculated in the Smoluchowski method. In contrast, the rate constant is obtained directly in the pairwise Brownian dynamics method. The effective rate constants for different reaction conditions may be obtained from a single simulation this is not possible using the finite element method. 

In a later article [59] the importance of hydrodynamic interactions in the formation of certain microphases was demonstrated by close comparison of simulations using DPD and Brownian dynamics (BD). Whilst both simulation methods describe the same conservative force field, and hence should return the same equilibrium structure, they differ in the evolution algorithms. As mentioned above, DPD correctly models hydrodynamic interactions, whereas these are effectively screened in BD. Distinctly different equilibrium structures were obtained using the two techniques in long simulations of a quenched 2400 A3B7 polymer system, as shown in Fig. 1. Whilst DPD ordered efficiently into the expected state of hexagonal tubes, BD remained trapped in a structure of interconnected tubes. By way of contrast, both DPD and BD reproduced the expected lamellar equilibrium structure of A5B5 on similar time scales, see Fig. 2. 

It should be mentioned that the above results are vahd if the hydrodynamic interactions do not affect particle transport through the adsorption layer of thickness 2a. This seems justified for smaller colloid particles and proteins. However, for micrometer-sized particles placed in shearing flows, the hydrodynamic forces play a significant role due to the coupling with the repulsive electrostatic interactions. This leads to enhanced blocking effects called hydrodynamic scattering effects and discussed extensively in recent review works [7,14]. These results have been interpreted theoretically in terms of the Brownian dynamics simulations [14], which are, however, considerably more time-consuming than the RSA simulations. 

At very low shear rates (i.e., flow velocities), particles in a chemically stable suspension approximately follow the layers of constant velocities, as indicated in Fig. 2. But at higher shear rates hydro-dynamic forces drive particles out of layers of constant velocity. The competition between hydrodynamic forces that distort the microstructure of the suspension and drive particles together, and the Brownian motion and repulsive interparticle forces keeping particles apart, leads to a shear dependency of the viscosity of suspensions. These effects depend on the effective volume fraction of... 

Kikuchi et al. demonstrated, however, that MMC is not restricted to the calculation of equilibrium properties, but can also be used to study dynamic properties. Specifically, they applied the MMC method to the study of Brownian motion of a harmonically bound particle [19]. The same authors further extended the method to study interacting Brownian particles including the effects of hydrodynamic interactions [20]. 

The dynamics of an isolated Kuhn segment chain in its bead-and-spring form is considered in a viscous medium without hydrodynamic backflow or excluded-volume effects. The treatment is based on the Langevin equation generalized for Brownian particles with internal degrees of freedom. A first, crude formalism of this sort was reported by Kargin and Slonimskii [45]. In-... 

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