A fractal Richards’ equation to capture the non-Boltzmann scaling of water transport in unsaturated media |
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| Institution: | 1. Sun Yat-sen Business School, Sun Yat-sen University, Guangzhou 510275, PR China;2. Department of Mathematics, City University of Science and Information Technology, Peshawar, KP, Pakistan;1. Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran;2. Department of Mathematics, GC women University, Sialkot, Pakistan;3. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran;4. Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran;5. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan 430212, PR China |
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| Abstract: | The traditional Richards’ equation implies that the wetting front in unsaturated soil follows Boltzmann scaling, with travel distance growing as the square root of time. This study proposes a fractal Richards’ equation (FRE), replacing the integer-order time derivative of water content by a fractal derivative, using a power law ruler in time. FRE solutions exhibit anomalous non-Boltzmann scaling, attributed to the fractal nature of heterogeneous media. Several applications are presented, fitting the FRE to water content curves from previous literature. |
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