考虑吸附-解吸效应的多孔介质中颗粒加速迁移问题解析解

建立考虑吸附-解吸效应的颗粒加速迁移问题控制方程，通过Laplace变换和Fourier变换求出颗粒瞬时和周期性注入情况下点源和面源问题的解析解。同时，开展点源瞬时注入方式下颗粒迁移试验，并将试验和理论计算结果进行对比分析，两者较为吻合，从而验证了解析解的正确性。点源瞬时注入方式下颗粒迁移参数的分析进一步表明：吸附系数越大，颗粒的浓度峰值越小。解吸系数对浓度峰值左侧曲线影响较小，而对浓度峰值右侧曲线来说，解吸系数不仅影响颗粒浓度，也影响颗粒迁移时间；浓度等值线在x-y平面上的形状近似为椭圆形，解吸系数越大，相应的浓度等值线的范围越大；随着y方向弥散系数增大，浓度峰值上、下两侧的等值线梯度逐渐减小。研究成果可为地下污染物治理、地下水开采、核废料处置以及城市固体废弃物填埋等工程提供理论基础。

Analytical solutions for accelerated transport of particles in porous media with considering adsorption-desorption effect

The governing equation for particle accelerated transport is developed with considering adsorption-desorption effects, and then analytical solutions for particle instantaneous injection and periodic injection with point and surface sources are obtained using Laplace and Fourier transforms. Experiments on the particle instantaneous injection for point source are carried out. Comparisons between the experimental and theoretical results show that the proposed procedure can simulate the particle transport reasonably well. In addition, the transport parameters are analyzed for the case of particle instantaneous injection for the point source. It is shown that the peak concentration of particles decreases with the increase of adsorption coefficient. The effect of desorption coefficient on the curve part on the right of peak concentration is trivial; however, for the curve part on the left of the peak concentration, desorption coefficient affects both the particle concentration and the particle transport time. Furthermore, the shapes of the concentration contours in the x-y plane are approximately elliptic, and the range of the concentration contours increases with the increase of desorption coefficient. The contour gradients at upper and lower sides of the peak concentration decrease with the increase of dispersion coefficient. The study results provide a theoretical basis for various engineering items such as the underground pollutant treatment, exploration of groundwater, nuclear waste disposal and land filling of municipal solid wastes, and so on.