NON-FICKIAN DIFFUSION IN TIME–SPACE FLUCTUATING DIFFUSIVITY LANDSCAPES: FROM SUPERFAST TO ULTRASLOW

Yingjie Liang, Peibo Tian, Shuhong Wang and Wei Xu
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Yingjie Liang: Key Laboratory of Ministry of Education for Coastal Disaster and Protection, College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu 211100, P. R. China
Peibo Tian: Key Laboratory of Ministry of Education for Coastal Disaster and Protection, College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu 211100, P. R. China
Shuhong Wang: Key Laboratory of Ministry of Education for Coastal Disaster and Protection, College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu 211100, P. R. China
Wei Xu: ��College of Science, Qingdao University of Technology, Qingdao, Shandong 266525, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 07, 1-10

Abstract: In this study, the local time and space structural derivative diffusion model is introduced to describe non-Fickian diffusion in heterogeneous media from ultraslow to superfast. Its equivalent heterogeneous diffusion process (HDP) model with time and space-dependent diffusion coefficient is also given. The connection and difference between the proposed model and the existing HDP models are compared. Different types of diffusion processes can be captured by selecting proper structural functions in the structural derivative model, which is determined based on the concentration of tracers, mean squared displacement (MSD) and diffusion coefficient of the heterogeneous media. The dynamics of the free cooling granular gases with constant restitution coefficient and velocity-dependent restitution coefficient is investigated to test the proposed model. The results show that the diffusion law of the granular particles is not uniform for the short and long-time scales, but one uniform diffusion law derived from the proposed model can well fit the data in different time scales. The patterns of the time-dependent diffusion coefficient are also simulated to deeply understand the complicated non-Fickian diffusion in complex system.

Keywords: Non-Fickian Diffusion; Structural Derivative; Heterogeneous Diffusion Process; Ultraslow Diffusion; Superfast Diffusion (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21501917

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