边界吸收效应对非定常剪切弥散的影响

EFFECT OF BOUNDARY ABSORPTION UPON UNSTEADY DISPERSION 1)

采用延迟扩散方程［７，９］描述了具有边界吸收条件下，非定常剪切流动中的剪切弥散特性．给出了记忆函数、中心位移函数的控制方程．特例分析结果表明：所采用的模型方程是合理的；边界吸收效应使得纵向浓度分布具有后倾的趋势．这主要是由于边界吸收使得低速强剪切区浓度减少，剪切弥散贡献减少，从而污染物对流速度高于断面的平均速度．

In the nature, mass transfer is dominated by shear dispersion when the shear effects in flow are very strong. It is G.I. Taylor (1953) who first investidated such problem and gotten a formula for laminar flow.Two exceptions to the Taylor's theory are early stage of dispersion process and shear dispersion with boundary absorption, which the Smith(1981, 1983) gave the description by a delay diffusion equation. Liu(1994) described the two dimensional contaminant dispersion with memory properties. In this paper, the author considered the early dispersion with boundary absorption for unsteady flow, in which the contaminant distribution is non Gauss. Using the delay diffusion equation derived by Smith (1981), Liu (1994), the author described the properties of unsteady dispersion with boundary absorption by following equation c 0 t +λ 0c 0 +u 00 c 0 x -k 00  2 c 0 x 2 +∫ ∞ 0  τ D · 2 x 2 c 0 (x-X 0, t-τ) d τ= q 0 -∑∫ ∞ ∫ τ Y m · x q m(x-X m, t-τ) d τThe governing equations of memory functions  τ D, displacement X t and advective velocity u ii had been obtained. The result from analysing a example shawn that the model is valid. Effect of boundary absorption on the distribution of concentration is that Gauss distribution has a tail: reducing concentration of contaminant in low velocity (the strong shear range) and contribution of dispersion, then increasing the advective velocity. When factor of boundary absorption reaction, β is approch to infinitive, the decay factor is constant, otherwise, β =0, the result is the same as those without boundary absorption.