메뉴 건너뛰기




Volumn 85, Issue 2, 2010, Pages 565-592

Development of a generalized version of the Poisson-Nernst-Planck equations using the hybrid mixture theory: Presentation of 2D numerical examples

Author keywords

Diffusion; Gauss'law; Mixture theory; Nernst Planck equations; Porous media

Indexed keywords

CHARGED SPECIES; CLOSED SET; CONSTITUTIVE LAW; CONTINUUM MIXTURE THEORY; DEFORMATION AND STRESS; DIFFUSION EQUATIONS; ENTROPY INEQUALITY; GAUSS' LAW; INDUCED ELECTRICAL FIELD; IONIC DIFFUSION; IONIC SPECIES; MACRO SCALE; MASS CONSERVATION; MAXWELL'S EQUATIONS; MIXTURE THEORY; NERNST-PLANCK EQUATIONS; NON-LINEAR; NUMERICAL EXAMPLE; NUMERICAL SCHEME; POISSON-NERNST-PLANCK EQUATIONS; PORE SOLUTION; POROUS MEDIA; QUASI-STATIC; TRANSIENT SOLUTIONS; VELOCITY FIELD;

EID: 78149498628     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-010-9578-8     Document Type: Article
Times cited : (33)

References (30)
  • 2
    • 0018431386 scopus 로고
    • Finite element formulation and solutions of nonlinear heat transfer
    • Bathe K. J., Khoshgoftaar M.: Finite element formulation and solutions of nonlinear heat transfer. J. Nucl. Eng. Design 51, 389-401 (1979).
    • (1979) J. Nucl. Eng. Design , vol.51 , pp. 389-401
    • Bathe, K.J.1    Khoshgoftaar, M.2
  • 3
    • 0036608413 scopus 로고    scopus 로고
    • Multicomponent, multiphase thermodynamics of swelling porous media with electroquasistatics: I. Macroscale field equations
    • Bennethum L. S., Cusham J. H.: Multicomponent, multiphase thermodynamics of swelling porous media with electroquasistatics: I. Macroscale field equations. Trans. Porous Media 47, 309-336 (2002a).
    • (2002) Trans. Porous Media , vol.47 , pp. 309-336
    • Bennethum, L.S.1    Cusham, J.H.2
  • 4
    • 0036609450 scopus 로고    scopus 로고
    • Multicomponent, multiphase thermodynamics of swelling porous media with electroquasistatics: II. Constitutive theory
    • Bennethum L. S., Cusham J. H.: Multicomponent, multiphase thermodynamics of swelling porous media with electroquasistatics: II. Constitutive theory. Trans. Porous Media 47, 337-362 (2002b).
    • (2002) Trans. Porous Media , vol.47 , pp. 337-362
    • Bennethum, L.S.1    Cusham, J.H.2
  • 5
    • 0002004386 scopus 로고
    • Theory of mixtures
    • A. C. Eringen (Ed.), New York: Academic Press
    • Bowen R. M.: Theory of mixtures. In: Eringen, A. C. (eds) Continuum Physics, Academic Press, New York (1976).
    • (1976) Continuum Physics
    • Bowen, R.M.1
  • 6
    • 34250963757 scopus 로고
    • The thermodynamics of elastic materials with heat conduction and viscosity
    • Coleman B. D., Noll W.: The thermodynamics of elastic materials with heat conduction and viscosity. Arch Ration. Mech. Anal. 13, 167-178 (1969).
    • (1969) Arch Ration. Mech. Anal. , vol.13 , pp. 167-178
    • Coleman, B.D.1    Noll, W.2
  • 7
    • 0037351288 scopus 로고    scopus 로고
    • A moving finite element method for the solution of two-dimensional time-dependent models
    • Coimbra M. C., Sereno C., Rodrigues A.: A moving finite element method for the solution of two-dimensional time-dependent models. Appl. Numer. Math. 44, 449-469 (2003).
    • (2003) Appl. Numer. Math. , vol.44 , pp. 449-469
    • Coimbra, M.C.1    Sereno, C.2    Rodrigues, A.3
  • 9
    • 0032035953 scopus 로고    scopus 로고
    • A mixture theory of electromagnetism and superconductivity
    • Eringen A. C.: A mixture theory of electromagnetism and superconductivity. Int. J. Eng. Sci. 36, 525-543 (1998).
    • (1998) Int. J. Eng. Sci. , vol.36 , pp. 525-543
    • Eringen, A.C.1
  • 10
    • 0024479631 scopus 로고
    • Averaging and averaged equations for transport of interface properties in multiphase systems
    • Gray W. G., Hassanizadeh S. M.: Averaging and averaged equations for transport of interface properties in multiphase systems. Int. J. Multiph. Flow 15, 81-95 (1989).
    • (1989) Int. J. Multiph. Flow , vol.15 , pp. 81-95
    • Gray, W.G.1    Hassanizadeh, S.M.2
  • 11
    • 0032323693 scopus 로고    scopus 로고
    • Transport of multi-electrolytes in charged hydrated biological soft tissues
    • Gu W. Y., Lai W. M., Mow V. C.: Transport of multi-electrolytes in charged hydrated biological soft tissues. Trans. Porous Media 34, 143-157 (1999).
    • (1999) Trans. Porous Media , vol.34 , pp. 143-157
    • Gu, W.Y.1    Lai, W.M.2    Mow, V.C.3
  • 12
    • 0001644519 scopus 로고
    • Unconditional stable algorithms for non-linear heat conduction
    • Hughes T. J. R.: Unconditional stable algorithms for non-linear heat conduction. Comp Methods Appl. Mech. Eng. 10, 135-139 (1977).
    • (1977) Comp Methods Appl. Mech. Eng. , vol.10 , pp. 135-139
    • Hughes, T.J.R.1
  • 14
    • 0032322651 scopus 로고    scopus 로고
    • Thermo-chemo-electro-mechanical formulation of saturated porous solids
    • Huyghe J. M., Janssen J. D.: Thermo-chemo-electro-mechanical formulation of saturated porous solids. Trans. Porous Media 34, 129-141 (1999).
    • (1999) Trans. Porous Media , vol.34 , pp. 129-141
    • Huyghe, J.M.1    Janssen, J.D.2
  • 15
    • 0032684548 scopus 로고    scopus 로고
    • Diffusion of a mixture of cations and anions dissolved in water
    • Johannesson B. F.: Diffusion of a mixture of cations and anions dissolved in water. Cem. Concr. Res. 29, 1261-1270 (1999).
    • (1999) Cem. Concr. Res. , vol.29 , pp. 1261-1270
    • Johannesson, B.F.1
  • 17
    • 61449205038 scopus 로고    scopus 로고
    • Ionic diffusion and kinetic homogeneous chemical reactions in the pore solution of porous materials with moisture transport
    • Johannesson B.: Ionic diffusion and kinetic homogeneous chemical reactions in the pore solution of porous materials with moisture transport. Comp. Geotech. 36, 577-588 (2009).
    • (2009) Comp. Geotech. , vol.36 , pp. 577-588
    • Johannesson, B.1
  • 18
    • 55749088027 scopus 로고    scopus 로고
    • Numerical Calculations of the effect of moisture content and moisture flow on ionic multi-species diffusion in the pore solution of porous materials
    • Johannesson B., Hosokawa Y., Yamada K.: Numerical Calculations of the effect of moisture content and moisture flow on ionic multi-species diffusion in the pore solution of porous materials. Comp. Struct. 87, 39-46 (2009).
    • (2009) Comp. Struct. , vol.87 , pp. 39-46
    • Johannesson, B.1    Hosokawa, Y.2    Yamada, K.3
  • 19
    • 0001479630 scopus 로고
    • A reacting continuum
    • Kelly P. D.: A reacting continuum. Int. J. Eng. Sci. 2, 129-153 (1964).
    • (1964) Int. J. Eng. Sci. , vol.2 , pp. 129-153
    • Kelly, P.D.1
  • 20
    • 0019080468 scopus 로고
    • A note on anisotropic balancing dissipation in the finite element method approximation to convective-transport problems
    • Kelly D. W., Nakazawa S., Zienkiewicz O. C.: A note on anisotropic balancing dissipation in the finite element method approximation to convective-transport problems. Int. J. Numer. Methods Eng. 15, 1705-1711 (1980).
    • (1980) Int. J. Numer. Methods Eng. , vol.15 , pp. 1705-1711
    • Kelly, D.W.1    Nakazawa, S.2    Zienkiewicz, O.C.3
  • 21
    • 28444457311 scopus 로고    scopus 로고
    • Free mesh radial basis function collocation approach for the numerical solution of system of multi-ion electrolytes
    • La Rocca A., Power H.: Free mesh radial basis function collocation approach for the numerical solution of system of multi-ion electrolytes. Int. J. Numer. Methods Eng. 64, 1699-1734 (2005).
    • (2005) Int. J. Numer. Methods Eng. , vol.64 , pp. 1699-1734
    • la Rocca, A.1    Power, H.2
  • 22
    • 2142720593 scopus 로고    scopus 로고
    • Ion binding and ion specificity-the Hofmeister effect, Onsager and Lifschitz theories
    • Niham B. W., Yaminsky V.: Ion binding and ion specificity-the Hofmeister effect, Onsager and Lifschitz theories. Langmuir 13, 2097-2108 (1997).
    • (1997) Langmuir , vol.13 , pp. 2097-2108
    • Niham, B.W.1    Yaminsky, V.2
  • 24
    • 0019623320 scopus 로고
    • On thermo-elastic-plastic analysis of heat treatment processes including creep and phase changes
    • Rammerstorfer F. G., Fisher D. F., Mitter W., Bathe K. J., Snyder M. D.: On thermo-elastic-plastic analysis of heat treatment processes including creep and phase changes. Comp. Struct. 13, 771-779 (1981).
    • (1981) Comp. Struct. , vol.13 , pp. 771-779
    • Rammerstorfer, F.G.1    Fisher, D.F.2    Mitter, W.3    Bathe, K.J.4    Snyder, M.D.5
  • 25
    • 0033166961 scopus 로고    scopus 로고
    • Numerical solution of the extended Nernst-Planck model
    • Samson E., Marchand J.: Numerical solution of the extended Nernst-Planck model. J. Colloid Interface Sci. 215, 1-8 (1999).
    • (1999) J. Colloid Interface Sci. , vol.215 , pp. 1-8
    • Samson, E.1    Marchand, J.2
  • 29
    • 33750708249 scopus 로고    scopus 로고
    • On the derivation of the transport equation for swelling porous materials with finite deformation
    • Weinstein T., Bennethum L. S.: On the derivation of the transport equation for swelling porous materials with finite deformation. Int. J. Eng. Sci. 44, 1408-1422 (2006).
    • (2006) Int. J. Eng. Sci. , vol.44 , pp. 1408-1422
    • Weinstein, T.1    Bennethum, L.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.