Boltachev G Sh, Ivanov M G
Institute of Electrophysics, Ural Branch of Russian Academy of Sciences, Ekaterinburg, 620016, Amundsen str. 106, Russia.
G.G. Devyatykh Institute of Chemistry of High-Purity Substances, Russian Academy of Sciences, 49 Tropinin Str., Nizhny Novgorod, Russia.
Heliyon. 2020 Feb 6;6(2):e03295. doi: 10.1016/j.heliyon.2020.e03295. eCollection 2020 Feb.
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.
从理论上并借助数值模拟对纳米颗粒悬浮液的凝聚速率进行了分析。提出了分析表达式，这些表达式描述了悬浮在溶剂中的纳米颗粒的稳态凝聚速率（ ，其中 是颗粒浓度）以及特征凝聚时间 。与传统使用的方程不同，所提出的表达式不仅能够高精度地描述低浓度悬浮液（纳米颗粒的体积含量为 %）的稳态凝聚速率，还能描述浓度相当高的悬浮液（ %及更高，其中 是颗粒体积）的稳态凝聚速率，而这些高浓度悬浮液与大多数工业应用相关。针对与实际胶体相关的三维几何结构以及有助于比较解析解和数值模拟结果的二维几何结构都写出了分析表达式。在二维随机动力学方法的框架内进行了计算机实验。结果表明所获得的分析表达式与数值计算结果吻合良好。分析了凝聚时间对颗粒间能垒高度和悬浮液浓度的依赖性。结果表明，与所获得的理论表达式不同，传统使用的公式对高浓度悬浮液的特征凝聚时间的高估超过了一个数量级。
