Abstract.
A phase-field model that takes into account the bending energy of fluid vesicles is presented. The Canham-Helfrich model is derived in the sharp-interface limit. A dynamic equation for the phase-field has been solved numerically to find stationary shapes of vesicles with different topologies and the dynamic evolution towards them. The results are in agreement with those found by minimization of the Canham-Helfrich free energy. This fact shows that our phase-field model could be applied to more complex problems of instabilities.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Edidin, Nature Rev. Mol. Cell Biol. 4, 414 (2003).
B. Alberts, Molecular Biology of the Cell, 4th ed. (Garland Science, 2002).
J. Zimmerberg, M.M. Kozlov, Nature Rev. Mol. Cell Biol. 7, 9 (2006).
U. Seifert, Adv. Phys. 46, 13 (1997).
S.A. Safran, Adv. Phys. 48, 395 (1999).
R. Lipowsky, E. Sackmann (Editors), Structure and Dynamics of Membranes, Handbook of Biological Physics (Elsevier Science, 1995).
I. Tsafrir, Phys. Rev. Lett. 86, 1138 (2001).
I. Tsafrir, Shape Instabilities of Membranes with Anchored Polymers under Geometric Constraints, PhD Thesis, Weizmann Institute of Science (2003).
I. Tsafrir, Y. Caspi, M.A. Guedeau-Boudeville, T. Arzi, J. Stavans, Phys. Rev. Lett. 91, 138102 (2003).
H. Ringsdorf, B. Schlarb, J. Venzmer, Angew. Chem. Int. Ed. Engl. 27, 113 (1988).
M. Kraus, W. Wintz, U. Seifert, R. Lipowsky, Phys. Rev. Lett. 77, 3685 (1996).
T. Biben, C. Misbah, Phys. Rev. E 67, 031908 (2003).
H. Noguchi, G. Gompper, Phys. Rev. Lett. 93, 258102 (2004).
H. Noguchi, G. Gompper, Phys. Rev. E 72, 011901 (2005).
T. Taniguchi, Phys. Rev. Lett. 76, 4444 (1996).
P.B. Sunil Kumar, G. Gompper, R. Lipowsky, Phys. Rev. Lett. 86, 3911 (2001).
M. Laradji, P.B. Sunil Kumar, Phys. Rev. Lett. 93, 198105 (2004).
P. Sens, Phys. Rev. Lett. 93, 108103 (2004).
R. Goldstein, P. Nelson, T. Powers, U. Seifert, J. Phys. II 6, 767 (1996).
J. Prost, R. Bruinsma, Europhys. Lett. 33, 321 (1996).
J.-M. Allain, M. Ben Amar, Physica A 337, 531 (2004).
J. Langer, in Directions in Condensed Matter Physics, edited by G. Grinstein, G. Mazenko (World Scientific, 1986).
R. González-Cinca, in Advances in Condensed Matter and Statistical Physics, edited by E. Korutcheva, R. Cuerno (Nova Science Publishers, 2004) pp. 203-236, http://arxiv.org/abs/cond-mat/0305058.
M. Alava, M. Dubé, M. Rost, Adv. Phys. 53, 83 (2004).
Q. Du, C. Liu, X. Wang, J. Comput. Phys. 198, 450 (2004).
Q. Du, C. Liu, X. Wang, J. Comput. Phys. 121, 757 (2006).
G. Gompper, M. Schick, Phys. Rev. Lett. 65, 1116 (1990).
G. Gompper, M. Schick, Self-assembling amphiphilic system, Phase Transitions and Critical Phenomena, No. 16 (Academic Press, London, 1994).
P. Canham, J. Theor. Biol. 26, 61 (1970).
W. Helfrich, Z. Naturforsch. C 28, 693 (1973).
J. Cahn, J. Hilliard, J. Chem. Phys. 28, 258 (1958).
M. do Carmo, Differential Geometry of Curves and Surfaces (Prentince-Hall, 1976).
S.A. Safran, Statistical Thermodynamics of Surfaces, Interfaces, and Membranes, Frontiers in Physics, No. 90 (Addison-Wesley, 1994).
J.C. Strikwerda, Finite Difference Schemes and Partial Differential Equations (Wadsworth & Brooks, 1989).
D.P. Bertsekas, Nonlinear Programming, 2nd ed. (Athena Scientific, 1999).
E. Evans, W. Rawicz, Phys. Rev. Lett. 64, 2094 (1990).
U. Seifert, K. Berndl, R. Lipowsky, Phys. Rev. A 44, 1182 (1991).
U. Seifert, Phys. Rev. Lett. 66, 2404 (1991).
F. Jülicher, U. Seifert, R. Lipowsky, J. Phys. II 3, 1681 (1993).
U. Seifert, S. Langer, Europhys. Lett. 23, 71 (1993).
A. Yeung, E. Evans, J. Phys. II 5, 1501 (1995).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Campelo, F., Hernández-Machado, A. Dynamic model and stationary shapes of fluid vesicles. Eur. Phys. J. E 20, 37–45 (2006). https://doi.org/10.1140/epje/i2005-10079-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epje/i2005-10079-5