Department of Physics, New Jersey Institute of Technology, Newark, New Jersey 07102, USA.
J Chem Phys. 2017 Aug 14;147(6):061101. doi: 10.1063/1.4997934.
The classical description of nucleation of cavities in a stretched fluid relies on a one-dimensional Fokker-Planck equation (FPE) in the space of their sizes r, with the diffusion coefficient D(r) constructed for all r from macroscopic hydrodynamics and thermodynamics, as shown by Zeldovich. When additional variables (e.g., vapor pressure) are required to describe the state of a bubble, a similar approach to construct a diffusion tensor D^ generally works only in the direct vicinity of the thermodynamic saddle point corresponding to the critical nucleus. It is shown, nevertheless, that "proper" kinetic variables to describe a cavity can be selected, allowing to introduce D^ in the entire domain of parameters. In this way, for the first time, complete FPE's are constructed for viscous volatile and inertial fluids. In the former case, the FPE with symmetric D^ is solved numerically. Alternatively, in the case of an inertial fluid, an equivalent Langevin equation is considered; results are compared with analytics. The suggested approach is quite general and can be applied beyond the cavitation problem.
在拉伸流体中空穴成核的经典描述依赖于其大小 r 的一维福克-普朗克方程（FPE），其中扩散系数 D(r) 由泽尔多维奇（Zeldovich）从宏观流体力学和热力学构建，适用于所有 r。当需要附加变量（例如蒸汽压力）来描述气泡的状态时，通常仅在对应于临界核的热力学鞍点的直接邻近区域内，构造扩散张量 D^ 的类似方法才有效。然而，已经表明，可以选择“适当”的动力学变量来描述空穴，从而可以在整个参数域中引入 D^。通过这种方式，首次为粘性挥发和惯性流体构建了完整的 FPE。在前一种情况下，通过数值方法求解具有对称 D^ 的 FPE。或者，在惯性流体的情况下，考虑等效的朗之万方程；将结果与分析进行比较。所提出的方法非常通用，可以应用于除空化问题以外的其他问题。
