In this letter, we provide an experimental study highlighting a relation between the anomalous diffusion and the fractal dimension of the environment using the methanol anomalous transport through the porous solid pellets with various pores geometries and different chemical compositions. The anomalous diffusion exponent was derived from the non-integer order of the time-fractional diffusion equation that describes the methanol anomalous transport through the solid media. The surface fractal dimension was estimated from the nitrogen adsorption isotherms using the Frenkel-Halsey-Hill method. Our study shows that decreasing the fractal dimension leads to increasing the anomalous diffusion exponent, whereas the anomalous diffusion constant is independent on the fractal dimension. We show that the obtained results are in a good agreement with the anomalous diffusion model on a fractal mesh.

在这封信中，我们提供了一项实验研究，着重说明了甲醇的异常扩散通过具有各种孔几何形状和不同化学成分的多孔固体颗粒的异常扩散与环境的分形维数之间的关系。异常扩散指数是根据时间分数扩散方程的非整数阶数得出的，该时间分数扩散方程描述了甲醇通过固体介质的异常传输。使用Frenkel-Halsey-Hill方法根据氮吸附等温线估算表面分形维数。我们的研究表明，减小分形维数会导致异常扩散指数的增加，而异常扩散常数则与分形维数无关。