D.L. Ermak

A method for simulating the Brownian dynamics of N particles with the inclusion of hydrodynamic interactions is described. The particles may also be subject to the usual interparticle or external forces (e.g., electrostatic) which have been included in previous methods for simulating Brownian dynamics of particles in the absence of hydrodynamic interactions. The present method is derived from the Langevin equations for the N particle assembly, and the results are shown to be consistent with the corresponding Fokker–Planck results. Sample calculations on small systems illustrate the importance of including hydrodynamic interactions in Brownian dynamics simulations. The method should be useful for simulation studies of diffusion limited reactions, polymer dynamics, protein folding, particle coagulation, and other phenomena in solution.

A computer technique is presented for simulating the translational motion of ions in a liquid solution. In the model the diffusive motion of each ion is perturbed by the electrostatic force of the surrounding ions. Several polyelectrolyte systems of spherical polyions (10–50 Å in radius) and small ions (∼1 Å in radius) have been studied. For each system the polyion electrostatic shielding length and the average potential energy of each ion species was calculated. When the shielding length was sufficiently short, the computer results and the predictions of the zero polyion concentration Debye–Hückel theory were in good agreement.