THERMAL SCIENCE

International Scientific Journal

A FRACTAL MODEL FOR PRESSURE DROP THROUGH A CIGARETTE FILTER

ABSTRACT
A fractal model for pressure drop through a cigarette filter is suggested, the fractal dimensions of both a single fiber and the filter's cross-sections are calculated, which are two main factors affecting the pressure drop. The two-scale transform is made to convert the fractal derivative model on a smaller scale to an approximate continuous model on a larger scale, so that the model can be easily solved. An optimal filter structure is suggested for minimal pressure drop.
KEYWORDS
PAPER SUBMITTED: 2019-05-01
PAPER REVISED: 2019-10-28
PAPER ACCEPTED: 2019-10-28
PUBLISHED ONLINE: 2020-06-21
DOI REFERENCE: https://doi.org/10.2298/TSCI2004653Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2020, VOLUME 24, ISSUE Issue 4, PAGES [2653 - 2659]
REFERENCES
  1. Keith, C. H., Pressure-Drop-Flow Relationships in Cigarette Filter Rods and Tobacco Columns, Beitrage zur Tabakforschung International, 11 (1982), 3, pp. 115-121
  2. Huang, J. X., et al., Transverse Vibration of an Axially Moving Slender Fiber of Viscoelastic Fluid in Bubbfil Spinning and Stuffer Box crimping, Thermal Science, 19 (2015), 4, pp. 1437-1441
  3. Zhang, L., et al., Vibration of an Axially Moving Jet in a Dry Spinning Process, Journal of Low Frequency Noise, Vibration and Active Control, 38 (2019), 3-4, pp. 1125-1131
  4. Chen, R. X., et al., Mechanism of Nanofiber Crimp, Thermal Science, 17 (2013), 5, pp. 1473-1477
  5. Yang, Z. P., et al., On the Cross-Section of Shaped Fibers in the Dry Spinning Process: Physical Explanation by the Geometric Potential Theory, Results in Physics, 14 (2019), Sept., 102347
  6. Fan, J., et al., Explanation of the Cell Orientation in a Nanofiber Membrane by the Geometric Potential Theory, Results in Physics, 15 (2019), Dec., 102537
  7. 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 (2019), 3-4, pp. 1676-1680
  8. Li, X. X., He, J. H. Nanoscale Adhesion and Attachment Oscillation Under the Geometric Potential Part 1: The Formation Mechanism of Nanofiber Membrane in the Electrospinning, Results in Physics, 12 (2019), Mar., pp. 1405-1410
  9. Liu, P., He, J. H., Geometrical Potential: An Explanation on of Nanofibers Wettability, Thermal Science 22 (2018), 1A, pp. 33-38
  10. Zhou, C. J., et al., What Factors Affect Lotus Effect? Thermal Science, 22 (2018), 4, pp. 1737-1743
  11. Tian, D., et al., Geometrical Potential and Nanofiber Membrane's Highly Selective Adsorption Property. Adsorption Science & Technology, 37 (2019), 5-6, pp. 367-388
  12. Tian, D., et al., Hall-Petch Effect and Inverse Hall-Petch Effect: A fractal Unification, Fractals, 26 (2018), 6, 1850083
  13. He, J. H. From Micro to Nano and from Science to Technology: Nano Age Makes the Impossible Possible, Micro and Nanosystems, 12 (2020) 1, pp. 1-2
  14. Fan, J., et al., A Model for Allometric Permeation in Fractal Branching Channel Net Driven by Capillary pressUre, International Journal of Numerical Methods for Heat & Fluid Flow, 25 (2015), 8, pp. 1886-1895
  15. Fan, J. Shang, X. M. Fractal Heat Transfer in Wool Fiber Hierarchy, Heat Transfer Research, 44 (2013), 5, pp. 399-40
  16. Li, X. X., et al., A Fractal Modification of the Surface Coverage Model for an Electrochemical Arsenic Sensor, Electrochimica Acta, 296 (2019), Feb., pp. 491-493
  17. Fan, J., et al., Model of Moisture Diffusion in Fractal Media, Thermal Science, 19 (2015), 4, pp. 1161-1166
  18. He, J. H., et al., A New Fractional Derivative And Its Application To Explanation Of Polar Bear Hairs, Journal of King Saud University Science, 28 (2016), 2, pp. 190-192
  19. Wang, Q. L., et al., Fractal Analysis of Polar Bear Hairs, Thermal Science, 19 (2015), Suppl., pp. S143-S144
  20. Wang, Q. L., et al., Fractal Calculus and Its Application to Explanation of Biomechanism of Polar Bear Hairs, Fractals, 26 (2018), 6, ID 1850086
  21. Chen, R. X., et al., Silk Cocoon: "Emperor's New Clothes" for Pupa: FractalNano-hydrodynamical Approach, Journal of Nano Research, 22 (2013), May, pp. 65-70
  22. Liu, F. J., et al., A Delayed Fractional Model for Cocoon Heat-Proof Property, Thermal Science, 21 (2017), 4, pp. 1867-1871
  23. Majumder, M., et al., Nanoscale Hydrodynamics - Enhanced Flow in Carbon Nanotubes, Nature, 438 (2005), 7064, pp. 44-44
  24. Liu, Y. Q., et al., Air Permeability of Nanofiber Membrane with Hierarchical Structure, Thermal Science, 22 (2018), 4, pp. 1637-1643
  25. Wang, F. Y., et al., Improvement of Air Permeability of Bubbfil Nanofiber Membrane, Thermal Science, 22 (2018), 1A, pp. 17-21
  26. Tian, D., et al., Self-Assembly of Macromolecules in a Long and Narrow Tube, Thermal Science, 22 (2018), 4, pp. 1659-1664
  27. Tian, D., et al., Macromolecule Orientation in Nanofibers, Nanomaterials, 8 (2018), 11, 918
  28. Tian, D., He, J. H. Macromolecular Electrospinning: Basic Concept & Preliminary Experiment, Results in Physics, 11 (2018), Dec., pp. 740-742
  29. Liu, Q., et al., Silk Fibroin/Polyethylene Glycol Nanofibrous Membranes Loaded with Curcumin, Thermal Science, 21 (2017), 4, pp. 1587-1594
  30. Zhao, L., et al., Fractal Approach to Flow through Porous Material, Int. J. Nonlin. Sci. Num., 10 (2009), 7, pp. 897-901
  31. 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, 854 (2019), 113565
  32. He, J. H., Ji, F. Y., Two-Scale Mathematics and Fractional Calculus for Thermodynamics, Thermal Science, 23 (2019), 4, pp. 2131-2133
  33. He, J. H. Fractal Calculus and Its Geometrical Explanation, Results in Physics, 10 (2018), Sept., pp. 272-276
  34. He, J. H., Ain, Q. T., New Promises and Future Challenges of Fractal Calculus: from Two-Scale Thermodynamics to Fractal Variational Principle, Thermal Science, 24 (2020), 2A, pp. 659-681
  35. He, J. H., A Short Review on Analytical Methods for to a Fully Fourth-Order Nonlinear Integral Boundary Value Problem with Fractal Derivatives, International Journal of Numerical Methods for Heat and Fluid Flow, On-line first, doi.org/10.1108/HFF-01-2020-0060, 2020

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence