List of Symbols

img specific interfacial area, m−1
img activity of species i, unitless
A area, m2
Ac cell or electrode area, m2
Ar Archimedes number, unitless
b Tafel slope, V per decade
B Debye constant for solvent, (kg/mol)½ m−1
c total concentration or salt concentration, mol m−3
c speed of light, 2.99792 × 108 m s−1
ci concentration of species i, mol m−3
C capacitance, F
Cd differential capacitance, F
CDL double layer capacitance per unit area, F m−2
Cp battery capacity offset, unitless
img distance, m
img hydraulic diameter, m
img molecular diffusivity of species i, m2·s−1
E energy for battery or double layer capacitor, J or W·h
E elastic modulus, Pa
Ea activation energy, J/mol
Eg energy gap, eV
f frequency, Hz
fi fugacity of species i, Pa
F Faraday's constant, 96485 C per equivalent
Fx component of force, N
img acceleration of gravity, m s−2
G Gibbs energy, J mol−1
G conductance, Ω−1
Gr Grashof number, unitless
h thickness, gap in electrolysis cells, m
h Planck's constant, J-s
H Enthalpy, J mol−1
i, i current density, A m−2
img current, A
img exchange current density, A·m−2
img photon flux, s−1·m−2
Ji molar flux of species i, mol m−2 s−1
ka, kc anodic and cathodic reaction rate constants
kc mass transfer coefficient, m s−1
k thermal conductivity, W·m−1·K−1
K equilibrium constant, unitless
L characteristic length, m
Lp diffusion length, m
m mass, kg
m molality, mol kg−1
img mass flow, kg s−1
Mi molecular weight, g·mol−1 or kg·mol−1
n number of electrons transferred
n number density of electrons, m−3
ni number of moles of species i, mol
ni number density of electrons in intrinsic semiconductor, m−3
NAV Avogadro's number
NA number density of acceptor atoms, m−3
ND number density of donor atoms, m−3
Ni molar flux of species i relative to stationary coordinates, mol m−2 s−1
p pressure, Pa
p number density of holes, m−3
P power, W
P perimeter, m
q fundamental charge, 1.602 × 10−19 C
q charge per unit surface area, C·m−2
img rate of heat generation, W
Q charge, C or A·h
r radius, m
R universal gas constant, 8.314 J mol−1K−1
RΩ ohmic resistance, Ω or Ω-m2
Re Reynolds number, unitless
img homogeneous reaction rate, mol m−3s−1
img stoichiometric coefficient, unitless
S electrical conductance, S
S entropy, J mol−1K−1
Sh Sherwood number, unitless
Sc Schmidt number, unitless
t time, s
img transference number of species i, unitless
T Temperature, K, or °C
U equilibrium potential, V
ui mobility of ion, m2 mol J−1s−1
v velocity, m s−1
V electric potential or voltage, V
vs superficial velocity, m s−1
img volumetric flowrate m3 s−1
img volume, m3
W work, J
W width of depletion layer, m
wimg molar flowrate, mol s−1
Wa Wagner number, unitless
xi mole fraction of species i in condensed phase, unitless
yi mole fraction of species i in gas phase, unitless
zi charge number

Greek Symbols

α Debye constant for solvent, (kg/mol)½
α relative permeability, unitless
α absorption coefficient, m−1
αa, αc transfer coefficient for anodic and cathodic reactions, unitless
β symmetry factor, unitless
img activity coefficient, unitless
ɛ porosity, unitless
ɛo permittivity of free space, 8.854 × 10−12 C V−1 m−1
ɛ permittivity, C V−1m−1or F m−1
ɛr relative permittivity, unitless
img strain, unitless
ηc current efficiency
ηcoul coulombic efficiency, unitless
ηf faradaic efficiency, unitless
img surface overpotential, V
κ electrical conductivity, S m−1
img Debye length, or wavelength, m
img absolute activity
img equivalent conductance, S m−2equivilent−1
img conductance, S m−1
img viscosity, Pa-s
img chemical potential, J mol−1
img kinematic viscosity, m2 s−1
img scan rate, V s−1
img stoichiometric coefficient, unitless
img electro-osmotic drag coefficient, unitless
img mass density, kg m−3
img charge density, C m−3
σ electrical conductivity of solid, S m−1; or surface energy, J m−2
τ characteristic time, s
τ tortuosity, dimensionless
ϕ potential, V
Φ quantum yield
img gas holdup, osmotic coefficient, unitless
img angular frequency, rad s−1

Subscripts and Superscripts

a anode
avg average value
b bubble
c charge, cathode, or cutoff frequency
cb conduction band
ct charge transfer
d discharge
e electrolyte
eff effective quantity
f formation
fb flat band
h electrical portion of hybrid system
i species
int interface
lim limiting value
M metal
o value at standard or reference conditions
ocv open circuit voltage
ph photon
Rx reaction
s solution, separator, or surface
sc space charge
vb valence band
∞ bulk value far from electrode
o initial value
θ equilibrium potential at reference conditions
* ideal gas
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