Abstract
Processes involving diffusion of small entities onto the surface of much larger inclusions and incorporation of these small entities into the much larger inclusions, are commonly found in nature and industry. There were many researches by computer simulation for diffusion-limited processes, but the researches for the non-diffusion-limited were a few. In this research, we suppose that there are many randomly distributed particles in space. By using boundary collocation method and Monte-Carlo simulation I compute the normalized overall rate constants of reaction when the surface reaction rate is finite. We can control the surface reaction rate to be finite or not by a dimensionless parameter P. As P=0, the process is diffusion limited. And as P→∞, the process is reaction-limited. When particles are randomly distributed in space, we see that normalized overall rate constants increase as increasing the volume fraction of particles, and normalized overall rate constants decrease as increasing the P value. If we compare normalized overall rate constants obtained from particles in random or in regular arrays, we see when the volume fraction of particles is smaller than 0.6, normalized overall rate constants of particles of random arrays are smaller.But when particles in are a very dilute situation, normalized overall rate constants increase with increasing the P value. And when particles are arranged in a rod (1D), square (2D) or cube (3D), normalized overall rate constant and the number of particle (N) will have the following relation ( D: fractal number ) : as D>1 as D=1 If we use the slopes from the equations and P value to make a plot, the plot can be separated into three regions：P=0~0.1, P=0.1-10, P=10-infinite. And the slopes decrease dramatically when P value change 0.1 from 10.