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.

The condition requires both bodies to have their own boundary markers on the shared interface so the two sides carry independent DOFs that can be offset by \(\phi_0\).

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)