Effect of nanoparticle concentration on coagulation rate of colloidal suspensions

Theoretically and with the help of numerical simulation the coagulation rate of nanoparticle suspensions is analyzed. Analytical expressions are proposed that describes the rate of stationary coagulation of the nanoparticles suspended in a solvent ( $$ , where $$ is the particle concentration) and the characteristic coagulation time $$ . In the contrast to traditionally used equations, the proposed expressions allow one to describe with high accuracy the rate of stationary coagulation of not only low concentrated suspensions, where the volume content of nanoparticles is $$ %, but also rather highly concentrated ones, at $$ % and more ( $$ where $$ is a particle volume), which are relevant for most of the industrial applications. Analytical expressions are written for both three-dimensional geometry, which is relevant for real colloids, and two-dimensional geometry, which is useful to compare results of the analytical solution and numerical simulation. Computer experiments are performed in the framework of the two-dimensional method of stochastic dynamics. Satisfactory agreement of the obtained analytical expressions with the results of numerical calculations is demonstrated. The dependences of the coagulation time on the height of the interparticle energy barrier and on the suspension concentration are analyzed. It is shown that, in contrast to the obtained theoretical expressions, the traditionally used formulas overestimate the characteristic coagulation time for highly concentrated suspensions by more than an order of magnitude.