Diffuse Interface Methods for Multiple Phase Materials: An Energetic Variational Approach

Brannick, James; Li, Chun; Qian, Tiezheng; Sun, Han

doi:10.4208/nmtma.2015.w12si

Cited by 12 publications

(9 citation statements)

References 24 publications

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“…It is not at all clear that Maxwell’s equations joined with constitutive equations; and boundary conditions always have steady state solutions in the sinusoidal case. The Maxwell equations joined with diffusion and convection equations (like Navier–Stokes [ 118 , 119 , 120 , 121 , 122 , 123 , 124 , 125 , 126 , 127 , 128 , 129 , 130 , 131 , 132 , 133 , 134 , 135 ] or PNP

Poisson Nernst Planck

drift diffusion [ 52 , 53 , 55 , 57 , 59 , 61 , 123 , 136 , 137 , 138 , 139 , 140 , 141 , 142 , 143 , 144 , 145 ]) certainly do not always have solutions that are linear functions of just the electric field [ 146 , 147 , 148 , 149 ].”…”

Section: Discussion: From Electrodynamics To Biophysics and Backmentioning

confidence: 99%

Maxwell Equations without a Polarization Field, Using a Paradigm from Biophysics

Eisenberg

2021

Entropy

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When forces are applied to matter, the distribution of mass changes. Similarly, when an electric field is applied to matter with charge, the distribution of charge changes. The change in the distribution of charge (when a local electric field is applied) might in general be called the induced charge. When the change in charge is simply related to the applied local electric field, the polarization field P is widely used to describe the induced charge. This approach does not allow electrical measurements (in themselves) to determine the structure of the polarization fields. Many polarization fields will produce the same electrical forces because only the divergence of polarization enters Maxwell’s first equation, relating charge and electric forces and field. The curl of any function can be added to a polarization field P without changing the electric field at all. The divergence of the curl is always zero. Additional information is needed to specify the curl and thus the structure of the P field. When the structure of charge changes substantially with the local electric field, the induced charge is a nonlinear and time dependent function of the field and P is not a useful framework to describe either the electrical or structural basis-induced charge. In the nonlinear, time dependent case, models must describe the charge distribution and how it varies as the field changes. One class of models has been used widely in biophysics to describe field dependent charge, i.e., the phenomenon of nonlinear time dependent induced charge, called ‘gating current’ in the biophysical literature. The operational definition of gating current has worked well in biophysics for fifty years, where it has been found to makes neurons respond sensitively to voltage. Theoretical estimates of polarization computed with this definition fit experimental data. I propose that the operational definition of gating current be used to define voltage and time dependent induced charge, although other definitions may be needed as well, for example if the induced charge is fundamentally current dependent. Gating currents involve substantial changes in structure and so need to be computed from a combination of electrodynamics and mechanics because everything charged interacts with everything charged as well as most things mechanical. It may be useful to separate the classical polarization field as a component of the total induced charge, as it is in biophysics. When nothing is known about polarization, it is necessary to use an approximate representation of polarization with a dielectric constant that is a single real positive number. This approximation allows important results in some cases, e.g., design of integrated circuits in silicon semiconductors, but can be seriously misleading in other cases, e.g., ionic solutions.

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Poisson Nernst Planck

Section: Discussion: From Electrodynamics To Biophysics and Backmentioning

confidence: 99%

Maxwell Equations without a Polarization Field, Using a Paradigm from Biophysics

Eisenberg

2021

Entropy

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“…If one confines oneself to sinusoidal systems (as in classical impedance or dielectric spectroscopy [11,44,54,55]), one should explicitly introduce the sinusoids into the equations and not just assume that the simplified treatment of sinusoids in elementary circuit theory [56][57][58][59][60] is correct: it is not at all clear that Maxwell's equations-combined with other field equations (like Navier Stokes [61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78] or PNP = drift diffusion [66,[79][80][81][82][83][84][85][86][87][88][89][90][91][92][93][94]); [joined] with constitutive equations; and boundary conditions-always have steady state solutions in the sinusoidal case. They certainly do not always have solutions that are linear functions of just the electric field…”

Section: Figurementioning

confidence: 99%

Maxwell Equations Without a Polarization Field, Using a Paradigm from Biophysics

Eisenberg¹

2020

Preprint

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Electrodynamics is usually written using polarization fields to describe changes in distribution of charge as electric fields change. This approach does not specify polarization fields uniquely from electrical measurements. Many polarization fields will produce the same electrodynamic forces and flows because only divergence of polarization enters Maxwell’s first equation, relating charge and electric field. The curl of any function can be added to a polarization field without changing the electric field at all. The divergence of the curl is always zero. To be unique, models must describe the charge distribution and how it varies. I propose a different paradigm to describe field dependent charge, i.e., the phenomenon of polarization. This operational definition of polarization has worked well in biophysics for fifty years, where a field dependent, time dependent polarization provides gating current that makes neurons respond sensitively to voltage. Theoretical estimates of polarization computed with this definition fit experimental data. I propose that operational definition be used to define polarization charge in general. Charge movement needs to be computed from a combination of electrodynamics and mechanics because ‘everything interacts with everything else’. The classical polarization field need not enter into that treatment at all. When nothing is known about polarization, it is necessary to use an approximate representation with a dielectric constant that is a single real positive number. This approximation allows important results in some cases, e.g., design of integrated circuits in silicon semiconductors, but can be seriously misleading in other cases, e.g., ionic solutions.

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“…Multiphase problems involving three or more fluid components have attracted a growing interest, and a number of researchers have contributed to the advance of this field; see e.g. [28,6,26,7,27,24,12,5,15,9,39,3,37], among others. Among the past studies, a handful of phase field models (e.g.…”

Section: Introductionmentioning

confidence: 99%

Multiphase flows of N immiscible incompressible fluids: A reduction-consistent and thermodynamically-consistent formulation and associated algorithm

Dong

2018

Journal of Computational Physics

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We present a reduction-consistent and thermodynamically consistent formulation and an associated numerical algorithm for simulating the dynamics of an isothermal mixture consisting of N (N 2) immiscible incompressible fluids with different physical properties (densities, viscosities, and pair-wise surface tensions). By reduction consistency we refer to the property that if only a set of M (1 M N −1) fluids are present in the system then the N-phase governing equations and boundary conditions will exactly reduce to those for the corresponding M -phase system. By theromdynamic consistency we refer to the property that the formulation honors the thermodynamic principles. Our N-phase formulation is developed based on a more general method that allows for the systematic construction of reductionconsistent formulations, and the method suggests the existence of many possible forms of reductionconsistent and thermodynamically consistent N-phase formulations. Extensive numerical experiments have been presented for flow problems involving multiple fluid components and large density ratios and large viscosity ratios, and the simulation results are compared with the physical theories or the available physical solutions. The comparisons demonstrate that our method produces physically accurate results for this class of problems.

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Diffuse Interface Methods for Multiple Phase Materials: An Energetic Variational Approach

Cited by 12 publications

References 24 publications

Maxwell Equations without a Polarization Field, Using a Paradigm from Biophysics

Maxwell Equations without a Polarization Field, Using a Paradigm from Biophysics

Maxwell Equations Without a Polarization Field, Using a Paradigm from Biophysics

Multiphase flows of N immiscible incompressible fluids: A reduction-consistent and thermodynamically-consistent formulation and associated algorithm

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