论文标题
玻尔兹曼的物理动力学用于深床过滤：求解希尔伯特空间中的操作员方程的均质化
Boltzmann Physical Kinetic for Deep Bed Filtration: Homogenization by solving operator equation in Hilbert space
论文作者
论文摘要
本文开发了用于微尺度颗粒流的玻尔兹曼方程的修改版，并用捕获和扩散描述了多孔介质中的胶体 - 悬浮纳诺传输。将等效的水槽项引入动力学方程而不是非零的初始数据，从而导致操作员方程在傅立叶空间中的解决方案和精确的均匀化。上尺度方程以封闭形式以及大规模模型系数的显式公式在微尺度参数方面获得。与载流子水速度相比，尺度揭示了颗粒传输的延迟，这是颗粒捕获和扩散的集体效应。派生的管程方程式概括了当前的多孔介质中悬浮式colloidal-nano运输的模型。
This paper develops a modified version of the Boltzmann equation for micro-scale particulate flow with capture and diffusion that describes the colloidal-suspension-nano transport in porous media. An equivalent sink term is introduced into the kinetic equation instead of non-zero initial data, resulting in the solution of an operator equation in the Fourier space and an exact homogenization. The upper scale equation is obtained in closed form together with explicit formulae for the large-scale model coefficients in terms of the micro-scale parameters. The upscaling reveals the delay in particle transport if compared with the carrier water velocity, which is a collective effect of the particle capture and diffusion. The derived governing equation generalizes the current models for suspension-colloidal-nano transport in porous media.
