The application of fractional derivatives through Riemannliouville approach to xanthan gum viscoelasticity

  • Authors

    • Ira Sumiati Universitas Padjadjaran
    • Endang Rusyaman Universitas Padjadjaran
    • Betty Subartini Universitas Padjadjaran
    • Sukono . Universitas Padjadjaran
    • Ruly Budiono Universitas Padjadjaran
    2018-09-24
    https://doi.org/10.14419/ijet.v7i4.15254
  • Fractional Derivatives, Riemann-Liouville, Viscoelasticity, Xanthan Gum.

  • Fractional derivatives are derivative with non-integer order, one of which is used for mathematical modeling of viscoelasticity. In this research, the fractional derivative was used to obtain a mathematical model of viscoelasticity. The method used was a fractional derivative through the Riemann-Liouville approach. The mathematical model of viscoelasticity obtained was a complex modulus consisting of storage and loss modulus. This model was applied to xanthan gum concentrate solution 0.5%, 1.0%, 2.0%, 3.0%, and 4.0% with simplified model parameters. The results obtained that the storage and loss modulus increased with increasing concentration of the solution. In addition, the modulus storage was always greater than the modulus loss for all concentrations of the solution. This suggests that the elastic properties of the xanthan gum solution are more dominant than their viscosity properties for all concentrations. Therefore, the viscoelasticity model using Riemann-Liouville fractional derivatives has a good ability to investigate the viscoelasticity behavior of all xanthan gum concentrations.

     

     

  • References

    1. [1] Banks HT, Hu S, Kenz ZR, “A Brief Review of Elasticity and Viscoelasticity for Solidsâ€, Advanced in Applied Mathematics and Mechanics, Vol.3, No.1, (2011), pp:1-51, 10.4208/aamm.10-m1030 https://doi.org/10.4208/aamm.10-m1030.

      [2] Born K, Langendorff V, Boulenguer P, “Xanthan Polysaccharideâ€, Biopolymers Online, (2005).

      [3] Brigham EO, The Fast Fourier Transform and its Application, Prentice Hall: New Jersey, USA, (1988).

      [4] David SA, Pallone JLLEMJA, “Fractional order calculus: historical apologia basic concepts and some applicationsâ€, Revista Brasileira de Ensino de Física, v.33, n.4, (2011), pp: 4302(1-7).

      [5] David SA, Katayama AH, “Fractional Order for Food Gums: Modeling and Simulationâ€, Applied Mathematics, 4, (2013), pp 305-309, http://dx.doi.org/10.4236/am.2013.42046.

      [6] Debnath L, “Recent Applications of Fractional Calculus to Science and Engineeringâ€, Mathematical Problems in Engineering, IJMMS: 54, (2013), pp 3413-3442, PII. S0161171203301486

      [7] Grigoletto EC, Oliveira EC, “Fractional Versions of the Fundamental Theorem of Calculusâ€, Applied Mathematics, 4, (2013), pp 23-33, http://dx.doi.org/10.4236/am.2013.47A006.

      [8] Hilfer R, “Threefold Introduction Fractional Derivativesâ€, Anomalous Transport: Foundations and Applications, Wiley-VCH, Weinheim, (2008), pp 17, ISBN: 978-3-527-40722-4 https://doi.org/10.1002/9783527622979.ch2.

      [9] Kisela T, “Fractional Differential Equations and Their Applicationâ€, Diploma Thesis, Faculty of Mechanical Engineering Institute of Mathematics, Brno University of Technology, (2008).

      [10] Kolařík J, Pegoretti A, “Proposal of the Boltzmann-like superposition principle for nonlinear tensile creep of thermoplasticsâ€, Polymer Testing 27, (2008), pp:596-606 https://doi.org/10.1016/j.polymertesting.2008.03.002.

      [11] Rahimy M, “Application of Fractional Differential Equationsâ€, Applied Mathematics Sciences, Vol.4, no.50, pp:2453-2461

      [12] Rusyaman E, Parmikanti K, Irianingsih I, “Kekonvergenan Barisan Fungsi Turunan Berorde Fraksionalâ€, Prosiding Seminar Nasional Statistika (Sequence Convergence of Fractional Derivation Function. Proceedings of the National Seminar on Statistics), Vol.2, (2011), pp: 253-257, ISSN: 2087-5290.

      [13] Salih A, “Delta Function and Heaviside Functionâ€, Department of Aerospace Engineering, Indian Institute of Space Science and Technology, Thiruvananthapuram, (2015).

      [14] Sharma BR, Naresh L, Dhuldhoya NC, Merchant SU, Merchant UC, “Xanthan Gum – A Boon to Food Industryâ€, Food Promotion Chronicle, Vol.1 (5), (2006), pp: 27-30.

      [15] Song KW, Kuk HY, Chang GS, “Rheology of concentrated xanthan gum solutions: Oscillatory shear flow behaviorâ€, Korea-Australia Rheology Journal, Vol.18, No.2, (2006), pp 67-81.

  • Downloads

  • How to Cite

    Sumiati, I., Rusyaman, E., Subartini, B., ., S., & Budiono, R. (2018). The application of fractional derivatives through Riemannliouville approach to xanthan gum viscoelasticity. International Journal of Engineering & Technology, 7(4), 2633-2637. https://doi.org/10.14419/ijet.v7i4.15254