Applied Mathematics and Mechanics

, Volume 24, Issue 12, pp 1475–1485

# Fluid-solid coupling mathematical model of contaminant transport in unsaturated zone and its asymptotical solution

• Xue Qiang
• Liang Bing
• Liu Xiao-li
• Li Hong-yan
Article

## Abstract

The process of contaminant transport is a problem of multicomponent and multiphase flow in unsaturated zone. Under the presupposition that gas existence affects water transport, a coupled mathematical model of contaminant transport in unsaturated zone has been established based on fluid-solid interaction mechanics theory. The asymptotical solutions to the nonlinear coupling mathematical model were accomplished by the perturbation and integral transformation method. The distribution law of pore pressure, pore water velocity and contaminant concentration in unsaturated zone has been presented under the conditions of with coupling and without coupling gas phase. An example problem was used to provide a quantitative verification and validation of the model. The asymptotical solution was compared with Faust model solution. The comparison results show reasonable agreement between asymptotical solution and Faust solution, and the gas effect and media deformation has a large impact on the contaminant transport. The theoretical basis is provided for forecasting contaminant transport and the determination of the relationship among pressure-saturation-permeability in laboratory.

## Key words

contaminant transport unsaturated zone numerical model fluid-solid coupling interaction asymptotical solution

TU411

## 2000 Mathematics Subject Classification

65L15 74R99 34B08

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© Editorial Committee of Applied Mathematics and Mechanics 2003

## Authors and Affiliations

• Xue Qiang
• 1
• Liang Bing
• 1
• Liu Xiao-li
• 1
• Li Hong-yan
• 2
1. 1.Department of Mechanics Engineering and ScienceLiaoning Technical UniversityFuxin, LiaoningP.R. China
2. 2.Institute of Environmental SciencesBeijing Normal UniversityBeijingP.R. China