Fractal diffusion of silver ions in hollow cylinders with unsmooth inner surface

Li, Gang; Yao, Shao-Wen

doi:10.1177/1558925019895643

Cited by 9 publications

(7 citation statements)

References 43 publications

(55 reference statements)

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“…Although the mathematical model seems to be rigorous, the assumptions can be made to fix the real conditions, and a fractal modification might be very much needed. Recently, a fractal model was suggested 12,13,39 to study the release property of ions from a hollow fiber, and the fractal calculus and fractional calculus [50][51][52][53] can predict more accurately the antibacterial activity.…”

Section: Discussionmentioning

confidence: 99%

“…Silver ion release from hollow fibers has been caught much attention, [9][10][11][12][13] and its antibacterial ratio plays an important role in practical applications, especially in food packing systems. Recently, an intelligent packaging system was designed successfully by cellulose-polypyrrole-ZnO films, 14 which sheds a new light on new packing systems by advanced nanotechnology.…”

Section: Introductionmentioning

confidence: 99%

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Silver ion release from Ag/PET hollow fibers: Mathematical model and its application to food packing

Yao

2020

Journal of Engineered Fibers and Fabrics

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A food packing system requires an antimicrobial environment with high air permeability to guarantee absolutely both food safety and long and reliable durability. A hollow fiber membrane containing silver ions is the best candidate for this purpose. However, a safe and controllable release process has become a pressing issue in the practical application. Here, we use the predator–prey model to predict the antimicrobial activity of silver ions released from a hollow fiber, and Staphylococcus aureus was applied to the antibacterial experiment. Both theoretical and experimental results show that there are an optimal concentration of the silver ions and an optimal release time. This article sheds a bright light on the design of a new kind of food packing systems using the hollow fiber membrane.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Silver ion release from Ag/PET hollow fibers: Mathematical model and its application to food packing

Yao

2020

Journal of Engineered Fibers and Fabrics

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“…This transform makes the fractal calculus extremely simple in view of traditional calculus. Now the fractal calculus has been applied to non-linear vibration [62], biomechanics [63][64][65], electrochemical arsenic sensor [66], tsunami model [67], thermal insulation [68], fractal rate model [69], biomimic design [70,71], fractal diffusion [72], fractal filtration [73], and nanotechnology [74][75][76][77][78].…”

Section: Dimension Is Everything and Two Scale Fractal Geometrymentioning

confidence: 99%

New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle

2020

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Any physical laws are scale-dependent, the same phenomenon might lead to debating theories if observed using different scales. The two-scale thermodynamics observes the same phenomenon using two different scales, one scale is generally used in the conventional continuum mechanics, and the other scale can reveal the hidden truth beyond the continuum assumption, and fractal calculus has to be adopted to establish governing equations. Here basic properties of fractal calculus are elucidated, and the relationship between the fractal calculus and traditional calculus is revealed using the two-scale transform, fractal variational principles are discussed for 1-D fluid mechanics. Additionally planet distribution in the fractal solar system, dark energy in the fractal space, and a fractal ageing model are also discussed.

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“…The fractal derivative models have been widely applied to various discontinuous problems, for example tsunami travelling over an unsmooth boundary (Wang and Deng, 2019), snow’s thermal insulation property (Wang et al , 2019), fractal adsorption (Liu et al , 2019), fractal diffusion (Lin and Yao, 2019) and vibration in a porous medium (He, 2019b; Ji et al , 2020).…”

Section: Fractal Calculus and Two-scale Transformmentioning

confidence: 99%

A short review on analytical methods for a fully fourth-order nonlinear integral boundary value problem with fractal derivatives

2020

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Purpose This paper aims to review some effective methods for fully fourth-order nonlinear integral boundary value problems with fractal derivatives. Design/methodology/approach Boundary value problems arise everywhere in engineering, hence two-scale thermodynamics and fractal calculus have been introduced. Some analytical methods are reviewed, mainly including the variational iteration method, the Ritz method, the homotopy perturbation method, the variational principle and the Taylor series method. An example is given to show the simple solution process and the high accuracy of the solution. Findings An elemental and heuristic explanation of fractal calculus is given, and the main solution process and merits of each reviewed method are elucidated. The fractal boundary value problem in a fractal space can be approximately converted into a classical one by the two-scale transform. Originality/value This paper can be served as a paradigm for various practical applications.

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Fractal diffusion of silver ions in hollow cylinders with unsmooth inner surface

Cited by 9 publications

References 43 publications

Silver ion release from Ag/PET hollow fibers: Mathematical model and its application to food packing

Silver ion release from Ag/PET hollow fibers: Mathematical model and its application to food packing

New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle

A short review on analytical methods for a fully fourth-order nonlinear integral boundary value problem with fractal derivatives

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