Refine
Has Fulltext
- no (2)
Year of publication
- 2022 (2)
Document Type
- Article (2)
Language
- English (2)
Is part of the Bibliography
- yes (2)
Keywords
- fractal derivative (2)
- anomalous diffusion (1)
- fractional brownian motion (1)
- material coordinate (1)
- mean squared displacement (1)
- nonlinear clock (1)
- swelling soil (1)
- variable order (1)
- water adsorption (1)
Institute
The diffusion process of water in swelling (expansive) soil often deviates from normal Fick diffusion and belongs to anomalous diffusion.
The process of water adsorption by swelling soil often changes with time, in which the microstructure evolves with time and the absorption rate changes along a fractal dimension gradient function.
Thus, based on the material coordinate theory, this paper proposes a variable order derivative fractal model to describe the cumulative adsorption of water in the expansive soil, and the variable order is time dependent linearly.
The cumulative adsorption is a power law function of the anomalous sorptivity, and patterns of the variable order.
The variable-order fractal derivative model is tested to describe the cumulative adsorption in chernozemic surface soil, Wunnamurra clay and sandy loam.
The results show that the fractal derivative model with linearly time dependent variable-order has much better accuracy than the fractal derivative model with a constant derivative order and the integer order model in the application cases.
The derivative order can be used to distinguish the evolution of the anomalous adsorption process. The variable-order fractal derivative model can serve as an alternative approach to describe water anomalous adsorption in swelling soil.
In this paper, we propose a revised fractional Brownian motion run with a nonlinear clock (fBm-nlc) model and utilize it to illustrate the microscopic mechanism analysis of the fractal derivative diffusion model with variable coefficient (VC-FDM).
The power-law mean squared displacement (MSD) links the fBm-nlc model and the VC-FDM via the two-parameter power law clock and the Hurst exponent is 0.5.
The MSD is verified by using the experimental points of the chloride ions diffusion in concrete.
When compared to the linear Brownian motion, the results show that the power law MSD of the fBm-nlc is much better in fitting the experimental points of chloride ions in concrete.
The fBm-nlc clearly interprets the VC-FDM and provides a microscopic strategy in characterizing different types of non-Fickian diffusion processes with more different nonlinear functions.