Under harsh conditions (such as high temperature, high pressure, and millisecond lifetime chemical reaction), a long-standing challenge remains to accurately predict the growth characteristics of nanosize spherical particles and to determine the rapid chemical reaction flow field characteristics. The growth characteristics of similar spherical oxide nanoparticles are further studied by successfully introducing the space-time conservation element–solution element (CE/SE) algorithm with the monodisperse Kruis model. This approach overcomes the nanosize particle rapid growth limit set and successfully captures the characteristics of the rapid gaseous chemical reaction process. The results show that this approach quantitatively captures the characteristics of the rapid chemical reaction, nanosize particle growth and size distribution. To reveal the growth mechanism for numerous types of oxide nanoparticles, it is very important to choose a rational numerical method and particle physics model.

在苛刻的条件下（例如高温，高压和毫秒级化学反应），准确预测纳米球形颗粒的生长特性并确定快速化学反应流场特性仍然是一项长期的挑战。通过成功地引入具有单分散Kruis模型的时空守恒元素-溶液元素（CE / SE）算法，可以进一步研究相似球形氧化物纳米颗粒的生长特性。这种方法克服了纳米级颗粒快速增长的限制，并成功地捕获了快速气态化学反应过程的特征。结果表明，该方法定量地捕获了快速化学反应，纳米级颗粒生长和尺寸分布的特征。