An Investigation of Methanol Anomalous Diffusion in Mesoporous Silica
DOI:
https://doi.org/10.15330/pcss.17.3.426-429Keywords:
diffusion, anomalous diffusion, fractional diffusion, super-diffusion, silica, methanolAbstract
Methanol transport in mesoporous silica is investigated. It is demonstrated that usual approach based on the second Fick’s law fails describing the experimental kinetic data. Contrary, the solution of the time-fractional diffusion equation fits the experimental data in a fairly good manner. Obtained value of the fractional order reveals the presence of fast super-diffusive regime of transport.
References
[1] R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000).
[2] I. Podlubny, Fract. Calc. Appl. Anal. 5, 367 (2002).
[3] P. Paradisi, R. Cesari, F. Mainardi, F. Tampieri, Physica A 293, 130 (2001).
[4] M. Ciesielski, J. Leszczynski, Comput. Methods Mech. June (3-6), 1 (2003).
[5] B. O’Shaughnessy, I. Procaccia, Phys. Rev. A 32, 3073 (1985).
[6] F. Höfling, T. Franosch, Reports Prog. Phys. 76, 046602 (2013).
[7] A. Bovet, M. Gamarino, I. Furno, P. Ricci, A. Fasoli, K. Gustafson, D.E. Newman, R. Sanchez, Nucl. Fusion 54, 104009 (2014).
[8] F. Mainardi, Y. Luchko, G. Pagnini, Fract. Calc. Appl. Anal. 4, 153 (2001).
[9] C. Atkinson, A. Osseiran, SIAM J. Appl. Math. 71, 92 (2011).
[10] J. Crank, The Mathematics of Diffusion (Clarendon Press, Oxford, 1975).
[11] B.G. Trewyn, I.I. Slowing, S. Giri, H. Chen, V.S. Lin, Acc. Chem. Res. 40, 846 (2007).
[12] P.Ye. Stryzhak, A.I. Trypol's'kyy, O.O. Zhokh, patent UA 103312, opublikovano10.12.2015, byul. # 23/2015.
[13] N. Su, J. Hydrol. 519, 1792 (2014).
[14] S. Hapca, J.W. Crawford, K. Macmillan, M.J. Wilson, I.M. Young, J. Theor. Biol. 248, 212 (2007).
[15] R. Hilfer, J. Phys. Chem. B. 104, 3914 (2000).
[16] M.I. Cruz, W.E.E. Stone, J.J. Fripiat, J. Phys. Chem. 76, 3078 (1972).
[2] I. Podlubny, Fract. Calc. Appl. Anal. 5, 367 (2002).
[3] P. Paradisi, R. Cesari, F. Mainardi, F. Tampieri, Physica A 293, 130 (2001).
[4] M. Ciesielski, J. Leszczynski, Comput. Methods Mech. June (3-6), 1 (2003).
[5] B. O’Shaughnessy, I. Procaccia, Phys. Rev. A 32, 3073 (1985).
[6] F. Höfling, T. Franosch, Reports Prog. Phys. 76, 046602 (2013).
[7] A. Bovet, M. Gamarino, I. Furno, P. Ricci, A. Fasoli, K. Gustafson, D.E. Newman, R. Sanchez, Nucl. Fusion 54, 104009 (2014).
[8] F. Mainardi, Y. Luchko, G. Pagnini, Fract. Calc. Appl. Anal. 4, 153 (2001).
[9] C. Atkinson, A. Osseiran, SIAM J. Appl. Math. 71, 92 (2011).
[10] J. Crank, The Mathematics of Diffusion (Clarendon Press, Oxford, 1975).
[11] B.G. Trewyn, I.I. Slowing, S. Giri, H. Chen, V.S. Lin, Acc. Chem. Res. 40, 846 (2007).
[12] P.Ye. Stryzhak, A.I. Trypol's'kyy, O.O. Zhokh, patent UA 103312, opublikovano10.12.2015, byul. # 23/2015.
[13] N. Su, J. Hydrol. 519, 1792 (2014).
[14] S. Hapca, J.W. Crawford, K. Macmillan, M.J. Wilson, I.M. Young, J. Theor. Biol. 248, 212 (2007).
[15] R. Hilfer, J. Phys. Chem. B. 104, 3914 (2000).
[16] M.I. Cruz, W.E.E. Stone, J.J. Fripiat, J. Phys. Chem. 76, 3078 (1972).
Downloads
Published
2016-09-15
How to Cite
Zhokh, A., & Strizhak, P. (2016). An Investigation of Methanol Anomalous Diffusion in Mesoporous Silica. Physics and Chemistry of Solid State, 17(3), 426–429. https://doi.org/10.15330/pcss.17.3.426-429
Issue
Section
Scientific articles
