Abstract

A method is proposed for solving the problem of impurity transport in heterogeneous medium due to the classical diffusion and advection. The case when advection is absent was analyzed separately. It focuses on distances from the impurity source, which are much larger than the main body of its localization, and the asymptotic approach developed by one of the authors (P.S.K.) is used. The problem is reduced to solving a differential equation of the first order, which determines the linear trajectory of the concentration signal from the source that arises with this approach to the point of observation. The result for concentration is expressed in terms of one-dimensional integrals along the concentration signal line. The solution of the transport problem in the presence of advection is obtained by transition into the coordinate system accompanying advection. The key elements entering the resulting concentration expression are the effective time and impurity displacement, both are caused by advection.

中文翻译：

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非均质介质中的经典对流扩散

摘要

提出了一种解决经典扩散和对流引起的异质介质中杂质迁移问题的方法。没有平流的情况将分别进行分析。它着重于距杂质源的距离，该距离远大于其定位的主体，并且使用由一位作者（PSK）开发的渐近方法。该问题被简化为求解一阶微分方程，该微分方程确定了这种方法产生的来自观测点的来自源的浓度信号的线性轨迹。浓度结果用沿浓度信号线的一维积分表示。对流存在时的运输问题的解决方案是通过转换为伴随对流的坐标系而获得的。输入结果浓度表达式的关键因素是有效时间和杂质位移，两者都是由对流引起的。