论文标题

压力波动,粘度和布朗运动

Pressure fluctuations, viscosity, and Brownian motion

论文作者

Munley, Frank

论文摘要

布朗运动发生在各种流体中,从稀有气体到液体。兰格文方程描述了统计平衡中摩擦和搅动力,是治疗现象的最成功方法之一。在罕见的气体中,可以根据粒子独立的分子影响来对摩擦和搅动进行建模。但是,在相对密度的流体(例如在标准温度和压力下的水和空气)中,流体分子碰撞之间的平均自由路径远小于布朗颗粒的尺寸,摩擦通常被视为由Stokes'定律描述的介质粘膜效应,该定律将流体连续处理为连续。使用Stokes定律的适当性将根据在非常短的时间范围内发生的弹道或“沿海”运动阶段的实验研究来讨论。鉴于摩擦力相对密集的液体的介质性质,我们应该期望搅动力也是介观。但是,它通常是不切实际的建模为不相关的个​​人影响。偶尔建议介观压波动适用于较密集的流体。本文的目的是模拟由于介绍压力波动而导致的摩擦。首先,简单的随机步行将用于近似弹道运动开始的时间和空间尺度,并进行扩散运动末端。随后,将引入压力波动和相关的时间尺度,以解释布朗运动。尽管压力波动模型对于许多流体来说都是成功的,但对于甘油等流体而言,它的粘液量将失败,而甘油的粘度是一千倍或更多的水。

Brownian motion occurs in a variety of fluids, from rare gases to liquids. The Langevin equation, describing friction and agitation forces in statistical balance, is one of the most successful ways to treat the phenomenon. In rare gases, it is appropriate to model both friction and agitation in terms of independent molecular impacts with the particle. But in relatively dense fluids, such as water and air at standard temperature and pressure, the mean free path between collisions of fluid molecules is much smaller than the size of the Brownian particle, and the friction is normally treated as a mesoscopic viscous effect described by Stokes' Law which treats the fluid as continuous. The appropriateness of using Stokes' Law will be discussed in terms of recent experimental research in the ballistic or "coasting" phase of motion occurring at a very short time scale. Given the mesoscopic nature of the friction force for relatively dense fluids, we should expect the agitation force to also be mesoscopic. But it is often unrealistically modeled as uncorrelated individual impacts. It has been suggested occasionally that mesoscopic pressure fluctuations are appropriate for denser fluids. The purpose of this paper is to model friction as a result of mesoscopic pressure fluctuations. First, the simple random walk will be used to approximate the time and space scales below which ballistic motion begins and diffusive motion ends. Following that, pressure fluctuations and the associated time scale will be introduced to explain Brownian motion. As successful as the pressure fluctuation model is for many fluids, it will be shown to fail for fluids like glycerin that have viscosities a thousand times and more that of water.

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