Discharges in Liquids
Governing Equations
The Electric Discharge interface provides built-in charge transport models in liquids. The default model consists of a group of transport equations for each modeled charge carrier (Ref. 3):
where
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e, p, and n denote electrons, positive ions, and negative ions
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ni is the number density of the charge carrier (SI unit: 1/m3)
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E is the electric field (SI unit: V/m)
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zi denotes the carrier charge (SI unit: 1)
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μi denotes the carrier mobility (SI unit: m2/(V·s))
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wi is the drift velocity in the electric field (SI unit: m/s)
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Di is the diffusion coefficient (SI unit: m2/s)
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Ri is the reaction rate (SI unit: 1/(m3·s))
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τa is the attachment time constant (SI unit: s)
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βep is the electron–ion recombination coefficient (SI unit: m3/s)
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βpn is the ion–ion recombination coefficient (SI unit: m3/s)
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SF is the field ionization (SI unit: 1/(m3·s))
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e is the electric charge (SI unit: C)
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nioni is the number density of ionizable species (SI unit: 1/m3)
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a denotes the molecular separation distance (SI unit: m)
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m* denotes the effective electron mass (SI unit: kg)
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φΔ and φγ are ionization potential parameters (SI unit: V)
The above transport equations are fully coupled with Poisson’s equation through the electric field and the space charge:
Dissociation
Under a high electric field, dielectric liquids undergo dissociation, commonly referred to as the Wien effect, as described by the following equations (Ref. 9):
where
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Sd denotes dissociation rate (generating free ions, SI unit: 1/(m3·s))
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βpn is the ion–ion recombination coefficient (SI unit: m3/s)
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n0 is the zero-field number density (SI unit: 1/m3)
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σ0 is the zero-field electric conductivity (SI unit: S/m)
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μp is the positive ion mobility (SI unit: m2/(V·s))
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μn is the positive ion mobility (SI unit: m2/(V·s))
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F is the Onsager function
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I1 is the modified Bessel function of the first kind and order 1
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lB is the Bjerrum length (SI unit: m)
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lO is the Onsager length (SI unit: m)