Taking into account the dust grain size distribution, the Bohm criterion is revisited by means of a one-dimensional, stationary, and non-magnetized theoretical model. An argon plasma is considered where the electrons are characterized by the Boltzmann distribution; however, the other species are described by the fluid equations. The dust grain charge number is described by the orbit motion limited model and their size is modeled by a Gaussian law. The generalized Bohm criterion has been calculated by using the Sagdeev's pseudo-potential approach. The numerical results show that the Bohm velocity values are greater than those of the classical model where the dust grains are absent, and they exhibit a peak. Moreover, by taking into account the dust size distribution, the obtained Bohm velocity values are practically comparable to those found in the mono-size model for a mean radius of the dust grains. Furthermore, it is found that the presence of mono-energetic electrons increases the Bohm velocity values. The dust grain surface potential at equilibrium is also calculated and discussed.

中文翻译：

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尘埃颗粒尺寸分布对等离子体中玻姆鞘准则的影响

考虑到粉尘粒度分布，通过一维、静止和非磁化理论模型重新审视 Bohm 准则。考虑使用氩等离子体，其中电子以 Boltzmann 分布为特征；然而，其他种类由流体方程描述。尘埃粒子电荷数由轨道运动限制模型描述，其大小由高斯定律建模。广义玻姆准则已通过使用 Sagdeev 的赝势方法计算得到。数值结果表明，Bohm 速度值大于没有尘埃颗粒的经典模型的 Bohm 速度值，并且它们表现出峰值。此外，通过考虑粉尘粒径分布，对于灰尘颗粒的平均半径，获得的玻姆速度值实际上与在单一尺寸模型中发现的那些值相当。此外，发现单能电子的存在增加了玻姆速度值。还计算和讨论了平衡状态下的尘埃颗粒表面电位。