Electrokinetic (DC)

The electro-kinetic solution, also called 'DC Conduction Steady State', describes the distribution of static electric current in conductors.

Features

2D, 3D or axisymmetric Solution, static
Plot: Scalarpotential, Electric Fieldstrength, Current Density, Eddy Current Losses Density.
Table: Ohm Resistance, Electrode Voltage, Electrode Current, Eddy Current Losses.
Coupled Thermal: Temperature.

The basis equations:
(1)        rot e = 0
(2)        div j = 0
(3)        j = σ e

Boundary conditions:
(4) n x e | Γ_0e = 0
(5) n * j | Γ_0j = 0

Electric scalar potential formulation for the conducting region:
(6) div σ grad v = 0 with
(7) e = -grad v

Electrokinetic weak v-formulation:
(8) (σ grad v, grad v’ )_Ω = 0
for all v’ element of Ω

In this example we analyze for the ohm resistance in a circular plate. The simulated electric current density is shown in the following picture.

Analytic and numerical Results

Mesh:
    Elements: 5406
    Nodes: 11074

Analytic Result:
    R = 1.08108e-5 Ohm

Numerical Result
    R = 1.069698e-5 Ohm

Deviation: 0.089%