- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2024-01-11 18:03:04+13:00
- Desc:
- Initial documentation to use in making an exposure
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/af4/rawfile/ca0ee1a16a2b93fbefe9ea6de72d5d0a6b254eed/FAIRDO BG example 3.9.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="BG6" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<!-- The Nernst-Planck equation-->
<units name="dim">
<unit units="dimensionless"/>
</units>
<units name="mol_per_s">
<unit units="mole"/>
<unit exponent="-1" units="second"/>
</units>
<units name="per_mol">
<unit exponent="-1" units="mole"/>
</units>
<units name="C_per_mol">
<unit units="coulomb"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="J_per_mol">
<unit units="joule"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="J_per_C">
<unit units="joule"/>
<unit exponent="-1" units="coulomb"/>
</units>
<component name="main">
<variable initial_value="0" name="t" units="second"/>
<variable initial_value="9.64853321e4" name="F" units="C_per_mol"/>
<variable initial_value="2578.73058" name="RT" units="J_per_mol"/>
<!-- R=8.31446262 J/mol/K, T=310.15 K, -->
<!-- State variables-->
<variable initial_value="3" name="q_i_1" units="mole"/>
<variable initial_value="0" name="q_i_2" units="mole"/>
<variable initial_value="0" name="q_e_m" units="coulomb"/>
<variable name="v_i_m" units="mol_per_s"/>
<variable name="u_i_1" units="J_per_mol"/>
<variable name="u_i_2" units="J_per_mol"/>
<variable initial_value="-0.080" name="u_e_m" units="J_per_C"/>
<variable name="u_f_m" units="J_per_mol"/>
<variable name="u_r_m" units="J_per_mol"/>
<variable name="u_nernst" units="J_per_C"/>
<variable initial_value="1" name="z_q" units="dim"/>
<!-- Constitutive parameters-->
<variable initial_value="20" name="K_q_i_1" units="per_mol"/>
<variable initial_value="20" name="K_q_i_2" units="per_mol"/>
<variable initial_value="10" name="kappa_i_m" units="mol_per_s"/>
<!-- Conservation laws-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_i_1</ci>
</apply>
<apply>
<minus/>
<ci>v_i_m</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_i_2</ci>
</apply>
<ci>v_i_m</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_e_m</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>z_q</ci>
</apply>
<ci>F</ci>
<ci>v_i_m</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_f_m</ci>
<apply>
<plus/>
<ci>u_i_1</ci>
<apply>
<times/>
<ci>z_q</ci>
<ci>F</ci>
<ci>u_e_m</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_r_m</ci>
<ci>u_i_2</ci>
</apply>
<!-- Constitutive relations-->
<apply>
<eq/>
<ci>u_i_1</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_q_i_1</ci>
<ci>q_i_1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_i_2</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_q_i_2</ci>
<ci>q_i_2</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_i_m</ci>
<apply>
<times/>
<ci>kappa_i_m</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_f_m</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_r_m</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_nernst</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>RT</ci>
<apply>
<times/>
<ci>z_q</ci>
<ci>F</ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_q_i_2</ci>
<ci>q_i_2</ci>
</apply>
<apply>
<times/>
<ci>K_q_i_1</ci>
<ci>q_i_1</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
</model>
