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. 2021 Nov 6;21(21):7380. doi: 10.3390/s21217380
Symbol Name Unit
ω Angular frequency rad/s
Di Bubble diameter m
σb Bubble surface tension N/m
R Bubble radius m
τe Charge-relaxation time s
N Data number -
Xi Data obtained -
Δρ Density difference between oil and gas kg/m3
VDBV Dielectric breakdown voltage V
I˜d Displacement electric current A
l Domain characteristic length m
S˜i,S˜j Dual faces m2
Qf Electric charge in dual volumes C
σ Electric conductivity S/m
Mσ Electric conductivity constitutive matrix S
I˜f Conductive electric current A
E Electric field strength V/C
ψ˜ Electric flow C
ψ˜0 Electric flow in vacuum C
Mϵ Electrical permittivity constitutive matrix F
ε0 Electrical permittivity in vacuum F/m
Mε0 Electrical permittivity in vacuum constitutive matrix F
ε Electrical permittivity of the medium F/m
U Electric potential difference V
f Frequency Hz
g Gravity acceleration m/s2
Ic Incidence vector of relative cohomology between oil volume and electrode surface. -
C, C˜=Ct Incidence matrix faces–edges in primal and dual mesh -
D, D˜ Incidence matrix faces–volumes in primal and dual mesh -
G Incidence matrix edges–nodes of primal mesh -
j Imaginary unit -
Fe Kelvin polarization force N
Φ Magnetic flow Wb
F˜ Magnetomotive force A
ρoil Oil density kg/m3
μoil Oil dynamic viscosity Ns/m2
hoil Oil height m
ϵoil Oil relative permittivity -
ψ˜P Polarization electric flow C
MχP Polarization electrical permittivity constitutive matrix F
Yi Reference data -
Y¯ Reference data mean
εr Relative electrical permittivity -
φ Scalar electric potential V
r Spherical particle radius m
τ Sinusoidal signal period s
c Speed of light m/s
T Temperature °C
VT Terminal velocity of the bubble in the oil m/s
ν Tetrahedron volume m3
τem Time electromagnetic constant s
τm Time magnetic constant s
I˜t Total current A
J Volumetric density current A/m2
Jd Volumetric density of conductive current A/m2