The Brownian Dynamic Simulation Of Two Colloidal Particles In An External Potential

The colloidal suspension system which is formed by diffusing small particles in solvent, is a sort of soft matter. The force on each Brownian particle in colloidal suspensions system is therefore composed of three terms: a friction force which tends to decrease the particle energy, a random force which tendsto increase the particle energy, and a systematic force due to the interaction potential energy betweenBrownian particles plus any external force. At present, particular emphasis is placed on statistical properties of well-characterized colloidal dispersions in different confining situations, in laser-optical, magnetic and electric fields as well as under shear. There are very active research areas where different complementary methods such as experiments, computer simulations and theory have been applied in parallel. Recently discovered novel phase transitions, generated and triggered by an external field, are described. The research of colloidal dynamics is useful for us to understand some problems of microorganism dynamics.Generally, there are three numerical simulation methods used to study colloidal suspension system: Monte Carlo method, Molecular dynamics simulation and Brownian dynamics simulation. Presently the simulation technique is applicable to spherically symmetric Brownian particles and particles composed of spherically symmetric subunits. This article investigates a simple colloidal suspension system by Brownian dynamics simulation method: in low Reynolds number fluid systems, two micron-sized colloidal particles are held at varying distance in novel optical tweezers. In 1998, Jen-Christian Meinersand and Stephen R. Quake have researched this model experimentally and found an interesting phenomenon in which the autocorrelation functions of these two particles are exponential decay, and surprisingly, the cross-correlation function between them shows a pronounced, time-delayed anticorrelation. This can be explained well on the basis of considering the effect of hydrodynamic interaction which is reflected by diffusion tensor. The conclusion is well in agreement with the result obtained from Brownian dynamics simulation. Furthermore, it can be found that if diffusion tensors with different approximation order are used, results will change: when the distance between two particles is far enough, difference between numerical simulation result and analytic result will disappear; the closer the distance is, the greater the difference will be. Accordingly, the applicable range for these diffusion tensors is acquired. In the same way, the method may be applied to the model which two colloidal spheres are held by a spring in a solution. The similar conclusion can be obtained.Sample calculations on small systems illustrate the importance of including hydrodynamic interactions in Brownian dynamics simulation. The method should be useful for simulation studies of polymer dynamics, protein folding, particle coagulation, and other phenomena in solution.