Skip to content

Potential Jump Condition

The potential jump condition defines a discontinuous electric potential \(\phi\) with a given step across the boundary between two contacting regions:

\[ \left. \phi \right|_{\partial\Omega_0} - \left. \phi \right|_{\partial\Omega_1} = \phi_0, \]

where \(\partial\Omega_0\) and \(\partial\Omega_1\) are the touching boundaries of the two regions and \(\phi_0\) is the prescribed potential jump.

Both bodies need their own boundary markers on the shared interface. Then the two sides carry independent DOFs, and \(\phi_0\) can offset them.

When to use this

  • Contact potential / work-function differences at metal-metal or metal-semiconductor junctions.
  • Surface-charge double layers that produce a known potential step (electrochemical, biological membranes).
  • Idealised thin-film batteries with a prescribed open-circuit voltage modelled as a jump across the cell.

Usage

from mufem.electromagnetics.electrostatics import PotentialJumpCondition

jump_bc = PotentialJumpCondition(
    name="Contact Potential",
    marker0="Metal_A::Interface" @ Bnd,
    marker1="Metal_B::Interface" @ Bnd,
    jump=0.5,  # volts
)

electrostatics_model.add_condition(jump_bc)