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# Electrical Conductivity Simulation

### with VGSTUDIO MAX

Simulate electrical conductivity directly on CT scans of different materials using the Transport Phenomena Simulation Module for VGSTUDIO MAX.

## Simulation of Electrical Conductivity

Electrical conductivity measures a material's ability to allow the transport of an electric charge.

The Transport Phenomena Simulation Module for VGSTUDIO MAX:

• Simulates the stationary electric potential and current fields in a two-component material, where each material has a different electrical conductivity, with the boundary condition that inlet and outlet are each clamped to a different constant electric potential.
• Works directly on voxel data and makes use of the sub-voxel accurate, local adaptive surface determination in VGSTUDIO MAX.
• Has "experiment mode" for performing a virtual experiment for the transport of electrical charge, as well as a "tensor mode" for calculating the electrical conductivity tensor.

The electrical conductivity module is based on following differential equations for stationary voltage and current density fields in a two-component material:

where Ω is the entire simulation domain and Ωₐ is the domain of component a (with a = 1, 2). It is assumed that Ω₁  and Ω₂ do not overlap and their union equals Ω. U is the electric potential (in volts), J is the current density, σₐ is the conductivity of component a, Δ is the Laplace operator, and grad is the gradient operator.

## Experiment Mode

In experiment mode, the software performs a virtual experiment on the CT data of a structure. Use the experiment mode to simulate the transport of electrical charge through the structure from an inlet plane towards an outlet plane parallel to each other. Perpendicular to the inlet and outlet plane, you can define sealed or embedded boundary conditions. A voltage difference must be specified as driving quantity for the flow. Current density (2D view) Current density (3D view) Electric potential (2D view) Electric potential (3D view) Streamlines

## Tensor Mode

In tensor mode, the software calculates the intrinsic effective tensor-valued electrical conductivity. Calculate the electrical conductivity tensor either on the whole structure or for increments of the structure by using an integration mesh. Tensor mode Effective electrical conductivity tensor per integration mesh cell Mean effective electrical conductivity (2D view) Void fraction (2D view)

In addition to the tensors' eigenvalues and eigenvectors, the components of the effective electrical conductivity tensor with respect to the simulation coordinate system are provided in a table view.