Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-19T06:33:22.309Z Has data issue: false hasContentIssue false
  • English
  • Français

Interface Stability Analysis of a Gel Material Surrounded by Air

Published online by Cambridge University Press:  24 February 2015

Carlos A. Garavito Garzon ,
M. Carme. Calderer  and
Satish Kumar
Carlos A. Garavito Garzon
Affiliation:
School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, MN 55455, USA.
M. Carme. Calderer
Affiliation:
School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, MN 55455, USA.
Satish Kumar
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
Get access

Abstract

We study the stability of small amplitude harmonic perturbation at the interface of a gel material surrounded by air. The equations describing the system's dynamics are solved using classical perturbation methods. Assuming that the amplitude decays over time, we establish conditions for the system to return to its equilibrium state. The proposed model includes the effect of the boundary conditions and can be extended to more general situation in which the material is surrounded by an arbitrary fluid.

Keywords

sol-gelpolymerfluid
Type
Articles
Information
MRS Online Proceedings Library (OPL) , Volume 1753: Symposium NN – Mathematical and Computational Aspects of Materials Science , 2015 , mrsf14-1753-nn06-06
Copyright
Copyright © Materials Research Society 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Calvert, P, Mater. Res. Soc. Bull. 33, 207–212, (2008).CrossRefGoogle Scholar
Peppas, N.A., Hilt, J.Z., Khademhosseini, A., Langer, R., Adv. Mater. 18, 1345–1360 (2006).CrossRefGoogle Scholar
Misra, G.P. and Siegel, R.A., J. Controlled Release. 81, 1–6 (2002).CrossRefGoogle Scholar
Dhanarajan, A. P., Urban, J.; Siegel, R. A., ACS Symposium Series. 869, 44–57 (2004).CrossRefGoogle Scholar
Rognes, M. E. Calderer, M. C, Micek, C. A, SIAM J. Applied Math. 70, 1305–1329, (2009).CrossRefGoogle Scholar
Tanaka, H., Tomita, H., Takasu, A., Hayashi, T., Nishi, T., Phys. Rev. Lett. 68, 2794–2797 (1992).CrossRefGoogle Scholar
Tanaka, T., Sun, S.-T., Hirokawa, Y., Katayama, S., Kucera, J., Hirose, Y., Amiya, T., Nature. 325, 796–198 (1987).CrossRefGoogle Scholar
Zhang, Y., Matsumoto, E.A., Peter, A., Lin, P.-C., Kamien, R.D., Yang, S. Nano Lett. 8, 1192–1196 (2008).CrossRefGoogle Scholar
Mori, Yoichiro; Chen, Haoran; Micek, Catherine; Calderer, Maria-Carme, SIAM J. App. Math. 73(1), 104–133 (2013).CrossRefGoogle Scholar
Calderer, M.C.; Chabaud, B., Mathematical Methods in applied Sciences (unpublished).Google Scholar
Rayleigh, Lord, Proc. London Math. Soc. S1–14(1), 170–177 (1882).CrossRefGoogle Scholar
Taylor, Geoffrey, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. 201, 192–196 (1950).Google Scholar
Oron, A., Bankoff, S.G., Davis, S.H., Rev. Mod. Phys. 69, 931–980, (1997).CrossRefGoogle Scholar
Kumar, S., Matar, O.K., J. Colloidal Interface Sci. 273(2), May 15, 581–588 (2004).CrossRefGoogle Scholar
Matar, O.K., Gkanis, V., Kumar, S., J. Colloidal Interface Sci. 286(1), Jun 1, 319–332 (2005).CrossRefGoogle Scholar
Kang, M.K. and Huang, R., J. Mech. Phys. Solids. 58, 1582–1598 (2010).CrossRefGoogle Scholar
Garavito-Garzon, Carlos A., Calderer, M. Carme, Kumar, S.. Stability of gel material interfaces (unpublished).Google Scholar
Gurtin, M. E., Fried, E., Anand, L., The Mechanics and Thermodynamics of Continua Cambridge University Press, 2009.Google Scholar
Flory, P.J., J. Chem. Phys. 10, 51–61 (1942).CrossRefGoogle Scholar
Huggins, M. L., J. Chem. Phys. 9(5), 440 (1941).CrossRefGoogle Scholar