Solution space of axisymmetric capsules enclosed by elastic membranes

European Journal of Mechanics, A/Solids

Volumn 23, Issue 5, 2004, Pages 877-892

  Blyth, M G ^a   Pozrikidis, C ^b  

^a UNIVERSITY OF EAST ANGLIA   (United Kingdom)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Boundary value problems; Capsules; Cells; Shells

Indexed keywords

BENDING MOMENTS; BOUNDARY VALUE PROBLEMS; CELLS; DIFFERENCE EQUATIONS; HYDRODYNAMICS; NUMERICAL ANALYSIS; PRESSURE EFFECTS; PROBLEM SOLVING; PROTEINS; SOLUTIONS;

CAPSULES; ELASTIC MEMBRANES; SHELLS; SOLUTION SPACE;

MEMBRANES;

EID: 12344333701     PISSN: 09977538     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechsol.2004.05.007     Document Type: Article

References (29)

1. M. Abramowitz, and I.A. Stegun Handbook of Mathematical Functions 1965 Dover New York
2. L. Boruvka, and A.W. Neumann Generalization of the classical theory of capillarity J. Chem. Phys. 66 1977 5464 5476
3. P.B. Canham The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell J. Theor. Biol. 26 1970 61 81
4. H.J. Deuling, and W. Helfrich Red blood cell shapes as explained on the basis of curvature elasticity Biophys. J. 16 1976 861 868
5. H.J. Deuling, and W. Helfrich The curvature elasticity of fluid membranes: a catalogue of vesicle shapes J. Phys. 37 1976 1335 1345
6. H.J. Deuling, and W. Helfrich A theoretical explanation for the myelin shapes of red blood cells, elasticity Blood Cells 3 1977 713 720
7. E.A. Evans, and R. Skalak Mechanics and Thermodynamics of Biomembranes 1980 CRC Press Boca Raton
8. E.A. Evans, and A. Yeung Hidden dynamics in rapid changes of bilayer shape Chemistry and Physics of Lipids 73 1994 39 56
9. J.E. Flaherty, J.B. Keller, and S.I. Rubinow Post-buckling behaviour of elastic tubes and rings with opposite sides in contact SIAM J. Appl. Math. 23 1972 446 455
10. W. Helfrich Elastic properties of lipid bilayers: theory and possible experiments Z. Naturforsch. C 28 1973 693 703
11. W. Helfrich, and H.J. Deuling Some theoretical shapes of red blood cells J. Phys. 36 C1 1975 327 329
12. J.-G. Hu, and Z.-C. Ou-Yang Shape equations of the axisymmetric vesicles Phys. Rev. E 47 1993 461 467
13. J.T Jenkins Static equilibrium configurations of a model red blood cell J. Math. Biol. 4 1977 149 169
14. F. Jülicher, and U. Seifert Shape equations for axisymmetric vesicles: a clarification Phys. Rev. E 49 1994 4728 4731
15. P.A. Kralchevsky, J.C. Eriksson, and S. Ljunggren Theory of curved interfaces and membranes: mechanical and thermodynamic approaches Adv. Colloid. Interface Sci. 48 1994 19 59
16. R. Lipowsky The conformation of membranes Nature 349 1991 475 481
17. R.S. Millman, and G.D. Parker Elements of Differential Geometry 1977 Prentice-Hall New Jersey
18. H. Møllmann Introduction to the Theory of Thin Shells 1981 Wiley New Jersey
19. H. Naito, M. Okuda, and Z.-C. Ou-Yang Counter-example to some shape equations for axisymmetric vesicles Phys. Rev. E 48 1993 2304 2307
20. Z.-C. Ou-Yang, and W. Helfrich Bending energy of vesicle membranes: general expressions for the first, second, and third variation of the shape energy and applications to spheres and cylinders Phys. Rev. A 39 1989 5280 5288
21. C. Pozrikidis Effect of bending stiffness on the deformation of liquid capsules in simple shear flow J. Fluid. Mech. 440 2001 269 291
22. C. Pozrikidis Buckling and collapse of open and closed cylindrical shells J. Engrg. Math. 42 2002 157 180
23. C. Pozrikidis Deformed shapes of axisymmetric capsules enclosed by elastic membranes J. Engrg. Math. 45 2003 169 182
24. C. Pozrikidis Modeling and Simulation of Capsules and Biological Cells 2003 Chapman & Hall/CRC Boca Raton
25. U. Seifert Configurations of fluid membranes and vesicles Adv. Phys. 46 1997 13 137
26. U. Seifert, K. Berndl, and R. Lipowsky Shape transformations of vesicles: phase diagrams for spontaneous-curvature and bilayer-coupling models Phys. Rev. A 44 1991 1182 1202
27. R.E. Waugh, and R.M. Hochmuth Mechanical equilibrium of thick, hollow, liquid membrane cylinders Biophys. J. 52 1987 391 400
28. P.R. Zarda, S. Chien, and R. Skalak Elastic deformations of red blood cells J. Biomech. 10 1977 211 221
29. W.-M. Zheng, and J. Liu Helfrich shape equation for axisymmetric vessels as a first integral Phys. Rev. E 48 1993 2856 2860