多孔介质中颗粒迁移细观理论与数值研究

Mesoscopic theoretical and numerical study of particle migration in porous media

多孔介质中的颗粒迁移广泛存在于各种工程问题中,对土体结构变化以及土壤中污染物的传播有重要影响。目前,颗粒在多孔介质中的迁移规律研究较少从颗粒运动及孔隙结构细观层面进行理论分析。为此,采用理论与数值仿真的方法对颗粒迁移细观规律与宏观规律的联系开展研究。在理论上,将细颗粒在多孔介质中的运动处理为一个随机过程,从细观层面推导描述颗粒宏观运动的一维对流-扩散方程,并建立扩散、对流系数与反映多孔介质对细颗粒阻碍强弱的阻滞参数α,及描述细颗粒细观运动统计特征的概率参数p间的量化关系。在数值仿真上,利用逾渗理论,通过将随机游走嵌入逾渗构型中开展数值仿真试验,研究阻滞参数α与多孔介质连通性的关系。理论推导证明,在细观上随机运动的颗粒其宏观运动可以采用对流-扩散方程进行描述。数值仿真的结果表明,当连通概率P大于0.5时,由细观理论得到的对流-扩散方程能较好地描述颗粒迁移过程,阻滞参数α与连通概率P呈现二次函数的关系,而当连通概率P小于0.5时,颗粒在多孔介质中的迁移逐渐偏离理论结果,且在多孔介质中发生堵塞现象。

Particle migrations in porous media emerge in many engineering problems,and exert influence phenomena like structure changes of soil and pollutants transportation in soils.There are few theoretical analyses for these migration processes from the mesoscopic aspects of particle motion and porous media structure.Therefore,theoretical methods and simulation were implemented here to study this problem.In the theoretical aspect,the motion of the particle was treated as a random process,and the one-dimensional convection-diffusion equation was derived from the mesoscopic view.Diffusion coefficient and convection coefficient were expressed as functions of the parameters p andα,where p represents particle mesoscopic motion probability andαrepresents the blocking effect of porous media.In the aspect of simulation,the relation betweenαand connectivity of porous media gets studied by embedding random walk into percolation configuration.Theoretical results show that convection-diffusion equation can be used to describe the macroscopic transportation of particles,which mesoscopic motions are random.Simulation shows that,when connected probability P is larger than 0.5,convection-diffusion equation can well describe the process of particle migration,and there exists quadratic function relation betweenαand P.When P is less than 0.5,clogging phenomenon appears and theoretical result becomes not applicable gradually.