论文标题
反应和扩散引起的局部胶体进化的同质化
Homogenisation of local colloid evolution induced by reaction and diffusion
论文作者
论文摘要
我们考虑在具有不断发展的微观结构的多孔介质中耦合反应扩散过程的均匀化。与固体基质的孔界面处的浓度依赖性反应速率可诱导域的浓度依赖性进化。因此，进化与反应扩散过程完全结合。为了传递均质限制，我们采用了两尺度的转化方法。因此，我们将高度非线性问题统一在周期性和时间圆柱形结构域中。均质结果是一个反应扩散方程，该方程与内部变量相结合，代表孔结构的局部演化。
We consider the homogenisation of a coupled reaction-diffusion process in a porous medium with evolving microstructure. A concentration-dependent reaction rate at the interface of the pores with the solid matrix induces a concentration-dependent evolution of the domain. Hence, the evolution is fully coupled with the reaction-diffusion process. In order to pass to the homogenisation limit, we employ the two-scale-transformation method. Thus, we homogenise a highly non-linear problem in a periodic and in time cylindrical domain instead. The homogenisation result is a reaction-diffusion equation, which is coupled with an internal variable, representing the local evolution of the pore structure.
