[jorgensd]

Temperature as a UFL expression

• Electrolyte(temperature=...) now takes either:

  • a number, the default of the parameter "<name>.T", as before, so it acts as a known coefficient;
  • a UFL expression, used as given. This can be a known coefficient, such as a parameter shared with another model or a prescribed profile, or an unknown field, e.g. the temperature of a heat equation. The electrolyte's equations are then coupled to it.

  density and viscosity already worked this way.

• Electrolyte.T returns a UFL expression instead of a Parameter.

• Where the temperature enters:

  • Nernst-Planck migration, through F/(RT);
  • the ionic conductivity;
  • the Butler-Volmer factor nF/(RT);
  • the membrane conductivity.

  With a temperature field, all of these, and their Jacobians, depend on it.

• ProtonExchangeMembrane(temperature=...) accepts an expression too and passes it to its electrolyte.

• Not yet temperature-dependent: the diffusivities and rate constants. An Arrhenius law would be the next step for full thermal coupling.

Tests

• test_conduction_and_transport_at_the_temperature_of_a_heat_equation (test_electrochemistry_from_ufl.py) compares the model with plain UFL on five cell types, residuals and Jacobians.
  • The model is electrolyte conduction and Nernst-Planck transport of V²⁺, V³⁺ and H⁺, with SO₄²⁻ by electroneutrality.
  • The temperature is the unknown of a heat equation.
  • The plain residual is written one equation at a time: charge, each ion, heat.
• test_the_temperature_can_be_the_field_of_a_heat_equation (test_electrolyte.py) checks three things for a temperature field in kelvin:
  • the units are consistent;
  • "e.T" is no longer a parameter;
  • the temperature is an unknown of the system.

Other changes to the electrolyte

• The Electrolyte docstring is restructured. It first says what an electrolyte is: a dilute, electroneutral solution whose ions move independently, with their concentrations and the temperature as its state. It then gives what the class computes, before the parameters it creates.
• New labelled displays: electroneutrality ($\sum_k z_k c_k = 0$) and electrolyte-current, which states $\mathbf{i}_l = F \sum_k z_k \mathbf{N}_k = -\kappa \nabla \phi - F \sum_k z_k t D_k \nabla c_k$, with the conductivity $\kappa$.
  • electrolyte-current moves from ElectrolyteConduction to Electrolyte, which computes it. Its label is unchanged.
  • ElectrolyteConduction now states only charge conservation, $\nabla \cdot \mathbf{i}_l = 0$, and refers to it.
• conductivity, diffusion_current and current_density refer to these displays instead of repeating the formulas in plain text.
• The 1D vanadium demo renames its electroneutrality label to vanadium-electroneutrality, since it is the vanadium instance of the general law, and refers to the general one.