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In the study a simple model of coagulation for nanoparticles is developed to  study the effect of diffusion on the particle coagulation in the  one-dimensional domain using the Taylor-series expansion method of moments.  The distributions of number concentration, mass concentration, and particle  average volume induced by coagulation and diffusion are obtained

A simple moment model to study the effect of diffusion on the coagulation of nanoparticles due to Brownian motion in the free molecule regime