Penetration of nanometer-sized, diffusive aerosol particles through a circular tube has been determined by two numerical methods. One method consisted in the simulation of the trajectories of Brownian particles suspended in a flowing fluid medium. The other was the numerical solution of the advection–diffusion equation. For any given value of the particle diffusion coefficient, penetration, i.e. the fraction of particles that avoid diffusion loss to the wall and exit the tube, calculated by the two methods agreed fairly well with each other for the three types of fluid flow tested (uniform, developing, and fully developed parabolic flows). For the case of parabolic flow there exists an analytical series solution which has been successfully compared with experimental results in a relatively large number of past investigations. The results obtained by the two numerical methods have also shown an excellent agreement with this analytical solution. The Brownian dynamics simulation method requires a larger computer time, but its simplicity allows examination of other aerosol flow processes too difficult to study either experimentally or by means of conventional differential equations. Aerosol penetration in transient, developing flow has never been addressed before, neither experimentally nor theoretically. The results reported in this paper are the first ones.

中文翻译：

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气溶胶通过管的扩散渗透：布朗粒子轨迹的蒙特卡洛模拟与平流-扩散方程的数值解之间的比较


纳米级扩散气溶胶颗粒通过圆管的渗透率已通过两种数值方法确定。一种方法包括模拟悬浮在流动流体介质中的布朗粒子的轨迹。另一个是平流-扩散方程的数值解。对于粒子扩散系数的任何给定值，穿透力，即避免扩散损失到壁面并离开管的粒子的分数，通过两种方法计算得出，对于测试的三种类型的流体流动（均匀、发展和完全发展的抛物线流），彼此相当一致。对于抛物线流的情况，存在一个分析级数解，该解已与过去相对大量的研究中的实验结果成功进行了比较。通过两种数值方法获得的结果也表明与该解析解非常吻合。布朗动力学模拟方法需要更多的计算机时间，但其简单性允许检查其他气溶胶流动过程，这些过程太难通过实验或常规微分方程进行研究。气溶胶在瞬时、发展中的流动中的渗透以前从未被解决过，无论是在实验上还是在理论上。本文报道的结果是第一个。