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Fractal diffusion-reaction model for a porous electrode

Fractal modifications of Fick's laws are discussed by taking into account the electrode's porous structure, and a fractal derivative model for diffusion-reaction process in a thin film of an amperometric enzymatic reaction is established. Particular attention is paid to giving an intuitive grasp for its fractal variational principle and its solution procedure. Extremely fast or extremely slow diffusion process can be achieved by suitable control of the electrode's surface morphology, a sponge-like surface leads to an extremely fast diffusion, while a lotus-leaf-like uneven surface predicts an extremely slow process. This paper sheds a bright light on an optimal design of an electrode's surface morphology.
PAPER REVISED: 2020-06-12
PAPER ACCEPTED: 2020-06-12
  1. Zhokh, A., et al. Relationship between the anomalous diffusion and the fractal dimension of the environment, Chem. Phys., 503(2018), pp.71-76
  2. Shanmugarajan, A., et al. Analytical solution of amperometric enzymatic reactions based on Homotopy perturbation method, Electrochimica Acta 56 (2011), pp.3345-3352.
  3. Rahamathunissa, G. & Rajendran, L. Application of He's variational iteration method in nonlinear boundary value problems in enzyme-substrate reaction diffusion processes: part 1. The steady-state amperometric response, J. Math. Chem., 44(3) (2008), pp.849-861
  4. Abukhaled, M. & Khuri, S.A. A semi-analytical solution of amperometric enzymatic reactions based on Green's functions and fixed point iterative, Journal of Electroanalytical Chemistry 792 (2017),pp. 66-71
  5. He, J.H. A simple approach to one-dimensional convection-diffusion equation and its fractional modification for E reaction arising in rotating disk electrodes, Journal of Electroanalytical Chemistry, 2019, Article Number: 113565
  6. Li, X.X, et al., A fractal modification of the surface coverage model for an electrochemical arsenic sensor, Electrochimica Acta, 296(2019), pp. 491-493
  7. He, J.-H.. Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves, J. Appl. Comput. Mech., 6(4) (2020) DOI: 10.22055/JACM.2019.14813
  8. Li, X. J. & He J.H. Variational multi-scale finite element method for the two-phase flow of polymer melt filling process, International Journal of Numerical Methods for Heat & Fluid Flow, doi:10.1108/HFF-07-2019-0599.
  9. He, J.H. A modified Li-He's variational principle for plasma, International Journal of Numerical Methods for Heat and Fluid Flow, (2019) DOI: 10.1108/HFF-06-2019-0523
  10. He, J.H. Lagrange Crisis and Generalized Variational Principle for 3D unsteady flow, International Journal of Numerical Methods for Heat and Fluid Flow, 2019, DOI: 10.1108/HFF-07-2019-0577
  11. He, J.H. & Sun, C. A variational principle for a thin film equation, Journal of Mathematical Chemistry. 57(9)(2019) pp 2075-2081
  12. He, J.H. Generalized Variational Principles for Buckling Analysis of Circular Cylinders, Acta Mechanica, 2019 DOI: 10.1007/s00707-019-02569-7
  13. He, J.H. A fractal variational theory for one-dimensional compressible flow in a microgravity space, Fractals, 2019 DOI: 10.1142/S0218348X20500243
  14. Malkovich, E.G., et al. Two-component model for catalyst deactivation, Chemical Engineering Journal, 378(2019), UNSP 122176
  15. Greiner, R., et al. Tomography based simulation of reactive flow at the micro-scale: Particulate filters with wall integrated catalyst, Chemical Engineering Journal, 378(2019), UNSP 121919
  16. Phutke, M., et al. Modelling solid-solid reactions: Contact-point approach, Chemical Engineering Journal, 377(SI)(2019), UNSP 120570
  17. Gonzalez-Casamachin, D. A., et al. Visible-light photocatalytic degradation of acid violet 7 dye in a continuous annular reactor using ZnO/PPy photocatalyst: Synthesis, characterization, mass transfer effect evaluation and kinetic analysis, Chemical Engineering Journal, 373(2019): 325-337
  18. Ain QT, He JH. On two-scale dimension and its applications, Thermal Science, 23(3B)(2019): 1707-1712
  19. He, J.H., Ji, F.Y. Two-scale mathematics and fractional calculus for thermodynamics, Therm. Sci., 23(4)(2019) 2131-2133 DOI: 10.2298/TSCI1904131H
  20. He, J.H. A Tutorial Review on Fractal Spacetime and Fractional Calculus, International Journal of Theoretical Physics, 53(11) (2014): 3698-3718
  21. He, J.H. Fractal calculus and its geometrical explanation, Results in Physics,10(2018), 272-276
  22. Wang, Q.L., et al., Fractal calculus and its application to explanation of biomechanism of polar bear, Fractals, 26(6)(2018), 1850086
  23. Wang, Q.L., et al., Fractal calculus and its application to explanation of biomechanism of polar bear (vol 26, 1850086, 2018) , Fractals, 27(5)(2019) 1992001
  24. Fan, J. et al., Explanation of the cell orientation in a nanofiber membrane by the geometric potential theory, Results in Physics, 15(2019), Article 102537
  25. Jin, X., et al. Low frequency of a deforming capillary vibration, part 1: Mathematical model, Journal of Low Frequency Noise Vibration and Active Control, 38(3-4)(2019),1676-1680
  26. Li, X.X. & He, J.H. Along the evolution process Kleiber's 3/4 law makes way for Rubner's surface law: a fractal approach, Fractals, 27(2)(2019): 1950015
  27. Tian, D. , et al. Geometrical potential and nanofiber membrane's highly selective adsorption property, Adsorption Science & Technology, 37(5-6) (2019), 367-388
  28. Wang, Y, et al. A variational formulation for anisotropic wave traveling in a porous medium, Fractals, 27(4)(2019) 19500476
  29. Wang, K.L., et al. A remark on Wang's fractal variational principle, Fractals,
  30. Yu, D.N., et al. Homotopy perturbation method with an auxiliary parameter for nonlinear oscillators, Journal of Low Frequency Noise Vibration and Active Control, 38(3-4)(2019), pp.1540-1554
  31. Ren, Z.F., et al. He's multiple scales method for nonlinear vibrations, Journal of Low Frequency Noise Vibration and Active Control, 38(3-4)(2019), pp.1708-1712
  32. Liu, Z.J., et al.. Hybridization of homotopy perturbation method and Laplace transformation for the partial differential equations, Thermal Science, 21(2017), pp.1843-1846
  33. Adamu, M.Y. & Ogenyi, P. New approach to parameterized homotopy perturbation method, Thermal Science, 22(4)(2018), pp.1865-1870
  34. Ban, T. & Cui, R.Q. He's homotopy perturbation method for solving time-fractional Swift-Hohenerg equation, Thermal Science, 22(4)(2018), pp.1601-1605
  35. Anjum, N. & He, J.H. Laplace transform: Making the variational iteration method easier, Applied Mathematics Letters, 92(2019), pp.134-138
  36. He, J.H. Some asymptotic methods for strongly nonlinear equations, International Journal of Modern Physics B, 20(2006), pp.1141-1199.
  37. He, J.H. The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators, Journal of Low Frequency Noise Vibration and Active Control, 38(3-4)(2019), pp.1252-1260
  38. He, J.H., Ji, F.Y. Taylor series solution for Lane-Emden equation, Journal of Mathematical Chemistry, 57(8)(2019), pp.1932-1934
  39. He, C.H., et al. Taylor series solution for fractal Bratu-type equation arising in electrospinning process, Fractals, 28(2020), 1, Article Number 2050011 DOI: 10.1142/S0218348X20500115