Mathematical models for the deformation of electrolyte droplets

Discrete and Continuous Dynamical Systems - Series B

Volumn 8, Issue 3, 2007, Pages 649-661

  Ryham, Rolf ^a   Liu, Chun ^b   Zikatanov, Ludmil ^b  

^a RICE UNIVERSITY   (United States)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Energetic variational method; Phase field; Poisson Nernst Plank

Indexed keywords

EID: 35348967424     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2007.8.649     Document Type: Conference Paper

References (30)

1. Douglas N. Arnold, Franco Brezzi, and Michel Fortin, A stable finite element for the Stokes equations, Calcolo, 21 (1984), 338-344.
2. Y. Ben and H.-C. Chang, Nonlinear Smoluchowski slip velocity and vortex generation, J. Fluid Mech., 461 (2002) 229-238.
3. F. Brezzi and M. Fortin, "Mixed and Hybrid Finite Element Methods," Springer Series in Computational Mathematics, 1991.
4. L. Evans, "Partial Differential Equations," Graduate Studies in Mathematics, 19, AMS, Providence, RI, 1998.
5. V. Barcilon, Ion flow through narrow membrane channels: Part I & II, SIAM J. Appl. Math., 52 (1992).
6. I. Borukhov, D. Andelman and H. Orland, Steric effects in electrolytes: a modified Poisson-Boltzmann equation, Physical Review Letters, 79 (1997).
7. + Conduction and selectivity, Science, 280 (1998).
8. Q. Du, C. Liu, and X. Wang A phase field approach in the numerical study of the elastic bending energy for vesicle membranes, Journal of Computational Physics, 198 (1994), 450-468.
9. Q. Du, C. Liu, R. Ryham and X. Wang, Phase field modeling of the spontaneous curvature effect in cell membranes, Communications in Pure and Applied Analysis, 4 (2005), 537-548.
10. F.H. Lin and C. Liu, Nonparabolic dissipative systems, modeling the flow Of liquid crystals, Comm. Pure Appl. Math., XLVIII (1995), 501-537.
11. C. Liu and J. Shen, A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method, Physica D, 179 (2003), 211-228.
12. Hang Lu, Martin A. Schmidt and Klavs F. Jensen, A microfluidic electroporation device for cell lysis, Lab on a Chip, 5 (2005), 23-29.
13. K. Mustafa, M. Bazant, and A. Ajdari, Steric effects of double layer charging, preprint, (2006).
14. Boaz Nadler, "Mathematical Models of Ionic Flow Through Open Protien Channels," Ph.D Thesis, School of Mathematical Sciences, Telaviv Univ., 2002.
15. F. Oosawa, "Polyelectrolytes," Marcel Dekker, New York, 1971.
16. R. F. Probstein, "Physicochemical Hydrodynamics, An Introduction," John Wiley and Sons, INC., 1994.
17. I. Rubinstein, "Electro-Diffusion of Ions," SIAM, Philadelphia, 1990.
18. I. Rubinstein and B. Zaltzmann, "Surface Chemistry and Electrochemistry of Membranes," Marcel Deckker, New York, 1998.
19. I. Rubinstein and B. Zaltzmann, Electro-osmotically induced convection at a permselective membrane, Physical Review E., 62 (2000).
20. R. Ryham and C. Liu, On well posedness of mathematical models of electrolytes, in preparation.
21. R. Ryham, C. Liu and Z.Q. Wang, Electro-kinetic fluids: analysis and simulation, Nonlinearity, 6 (2006).
22. Z. Shuss, B. Nadler and B. Eisenberg, Derivation of PNP equations in bath and channel from a molecular model, Physical Review E, 64 (2001).
23. T. Squires and M. Bazant, Induced-charge electro-osmosis, J. Fluid Mech., 509 (2004), 217-252.
24. Roger Temam, "Navier Stokes Equations, Theory and Numerical Analysis," AMS Chelsea Publishing, Providence, Rhode Island, 2000.
25. "Electrorheological Fluids," ed. R. Tao, 81-91, World Scientific, Singapore, 1992.
26. Jonathan Richard Shewchuk, Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator, in Applied Computational Geometry: "Towards Geometric Engineering", Volume 1148 of Lecture Notes in Computer Science, pages 203-222, Springer-Verlag, Berlin, 1996.
27. W. Wen et. al., The giant electrorheological effect in suspensions of nanoparticles, Nature: Materials, 2 (2003).
28. J. Xu and L. Zikatanov, A monotone finite element scheme for convection-diffusion equations, Mathematics of Computation, 68 (1999), 1429-1446.
29. R. Zhou, P. Wang and H.C. Chang, Bacteria capture, concentration and detection by AC dielectrophoresis and self-assembly of dispersed single-wall carbon nanotubes, Electrophoresis, 27 (2006).
30. L. Yeo, D. Lastochkin, S.C. Wang, H.C. and Chang, A New ac electrospray Mechanism by Maxwell-Wagner Polarization and Capillary Resonance, Phys. Rev. Lett., 92 (2004), 133902-133904.