- Author:
- Soroush Safaei <ssaf006@aucklanduni.ac.nz>
- Date:
- 2018-01-11 17:25:06+13:00
- Desc:
- fixing cellml equations
- Permanent Source URI:
- https://models.cellml.org/workspace/297/rawfile/bb2ab4e8c78a4e0d03fb97a2f43d3de151c711a7/BG/New - Boron NH4Cl expts - original eqns--ro.cellml
<?xml version='1.0'?>
<model name="Boron_CO2_expts_original_eqns" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<units name="per_s">
<unit exponent="-1" units="second"/>
</units>
<units name="per_m">
<unit exponent="-1" units="metre"/>
</units>
<units name="m_per_s">
<unit units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="mol_per_m3">
<unit units="mole"/>
<unit exponent="-3" units="metre"/>
</units>
<units name="mol_per_m2_s">
<unit exponent="1" units="mole"/>
<unit exponent="-2" units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="mol_per_m3_s">
<unit exponent="1" units="mole"/>
<unit exponent="-3" units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="J_per_C">
<unit units="joule"/>
<unit exponent="-1" units="coulomb"/>
</units>
<units name="C_per_mol">
<unit units="coulomb"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="J_per_mol_K">
<unit units="joule"/>
<unit exponent="-1" units="mole"/>
<unit exponent="-1" units="kelvin"/>
</units>
<units name="m3_per_mol">
<unit exponent="3" units="metre"/>
<unit exponent="-1" units="mole"/>
</units>
<component name="main">
<!-- var u_E: J_per_C {init: -0.05, pub: out}; -->
<variable initial_value="-0.055" name="V_m" public_interface="out" units="J_per_C"/>
<!---55 mV in WFB code....for consistency with the code for the CO2 model, I would use V_m and not u_E-->
<variable initial_value="0.0" name="TB_i" units="mol_per_m3"/>
<variable name="NH3_i" units="mol_per_m3"/>
<variable name="NH3_o" units="mol_per_m3"/>
<variable name="NH4_i" units="mol_per_m3"/>
<variable name="NH4_o" units="mol_per_m3"/>
<variable name="TB_o" units="mol_per_m3"/>
<!-- new variable for TB_o. This variable is needed for calculating the initial concentrations for NH4_o and NH3_o-->
<variable initial_value="4.786300923226380e-05" name="H_i" units="mol_per_m3"/>
<!--4.786300923226380e-05 corresponds to pHi = 7.32, value used by WFB in his code
var H_i_ref: mol_per_m3 {init: 1e-6}; -->
<variable initial_value="3.981071705534970e-05" name="H_Lim" units="mol_per_m3"/>
<!--for consistency with the code for the CO2 model, I am using H_Lim and not H_i_ref....also, since k = 0 for all NH3 simulations J_H doesn't affect the ode-->
<variable initial_value="1.995262314968879e-05" name="H_o" units="mol_per_m3"/>
<variable name="t" units="second"/>
<variable name="pH_i" units="dimensionless"/>
<variable name="pH_o" units="dimensionless"/>
<variable name="pH_Lim" units="dimensionless"/>
<!--RO added this variable-->
<variable initial_value="8000" name="rho" units="per_m"/>
<!--cell is cylindrical and not spherical, thus rho = 2/radius-->
<variable name="epsilon" units="dimensionless"/>
<variable name="alpha_i" units="dimensionless"/>
<!--var alpha_o: dimensionless; there is no need for alpha_o-->
<variable initial_value="6e-5" name="P_NH3" units="m_per_s"/>
<!--P_NH3 is fixed-->
<variable initial_value="1e-6" name="P_NH4" units="m_per_s"/>
<!--P_NH4 varies: 0, 1e-8, 1e-7, 1e-6 m_per_s-->
<variable initial_value="0" name="k" units="per_s"/>
<!-- k is always zero. Also RO changed units here. RO & WFB would like to keep the units of k per_s to avoid confusion with permeability-->
<variable initial_value="0.0256796" name="RTF" units="J_per_C"/>
<variable initial_value="3.162277660168379e-07" name="K_B" units="mol_per_m3"/>
<variable initial_value="-9" name="beta" units="mol_per_m3"/>
<variable name="J_H" units="mol_per_m2_s"/>
<!--RO says that if we define J_H in units of "per_m2" then we should explain in the text that J_H has already been divided by rho in the equation below...flux versus pseudoflux . -->
<variable name="J_NH4" units="mol_per_m2_s"/>
<variable name="J_NH3" units="mol_per_m2_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>epsilon</ci>
<apply>
<exp/>
<apply>
<divide/>
<ci>V_m</ci>
<ci>RTF</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>pH_i</ci>
<apply>
<minus/>
<apply>
<log/>
<apply>
<times/>
<cn cellml:units="m3_per_mol" type="e-notation">1<sep/>-3</cn>
<ci>H_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>pH_o</ci>
<apply>
<minus/>
<apply>
<log/>
<apply>
<times/>
<cn cellml:units="m3_per_mol" type="e-notation">1<sep/>-3</cn>
<ci>H_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>pH_Lim</ci>
<apply>
<minus/>
<apply>
<log/>
<apply>
<times/>
<cn cellml:units="m3_per_mol" type="e-notation">1<sep/>-3</cn>
<ci>H_Lim</ci>
</apply>
</apply>
</apply>
</apply>
<!--RO added this-->
<!-- NH4_o = sel
case t < 100{second}:
0{mol_per_m3};
case t < 700{second}:
10{mol_per_m3};
otherwise:
0{mol_per_m3};
endsel;-->
<!-- RO changed to TB_o....see below-->
<!-- WFB may have used 9 mM for TB in his simulations and not 10 mM as stated in the legend of fig 6 of the ms :(. -->
<apply>
<eq/>
<ci>TB_o</ci>
<piecewise>
<piece>
<cn cellml:units="mol_per_m3">0</cn>
<apply>
<lt/>
<ci>t</ci>
<cn cellml:units="second">100</cn>
</apply>
</piece>
<piece>
<cn cellml:units="mol_per_m3">9</cn>
<apply>
<lt/>
<ci>t</ci>
<cn cellml:units="second">1500</cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="mol_per_m3">0</cn>
</otherwise>
</piecewise>
</apply>
<!--alpha_o = H_o/(H_o+K_B); ....not correct :(
NH3_o = (1{dimensionless}-alpha_o)/alpha_o*NH4_o;...not correct :(-->
<!--New by RO-->
<apply>
<eq/>
<ci>NH4_o</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>H_o</ci>
<ci>TB_o</ci>
</apply>
<apply>
<plus/>
<ci>H_o</ci>
<ci>K_B</ci>
</apply>
</apply>
</apply>
<!--Based on the equilibrium in the bulk solution (outside the cell)-->
<!--New by RO-->
<apply>
<eq/>
<ci>NH3_o</ci>
<apply>
<minus/>
<ci>TB_o</ci>
<ci>NH4_o</ci>
</apply>
</apply>
<!--J_H = k*(H_i-H_Lim);
For consistency with the CO2 model, J_H is now defined aas below-->
<apply>
<eq/>
<ci>J_H</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>k</ci>
<apply>
<minus/>
<ci>H_i</ci>
<ci>H_Lim</ci>
</apply>
</apply>
<apply>
<lt/>
<ci>pH_i</ci>
<ci>pH_Lim</ci>
</apply>
</piece>
<otherwise>
<cn cellml:units="mol_per_m2_s">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>J_NH3</ci>
<apply>
<times/>
<ci>P_NH3</ci>
<apply>
<minus/>
<ci>NH3_o</ci>
<ci>NH3_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_NH4</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>P_NH4</ci>
<ci>V_m</ci>
</apply>
<ci>RTF</ci>
</apply>
<apply>
<minus/>
<ci>NH4_o</ci>
<apply>
<times/>
<ci>NH4_i</ci>
<ci>epsilon</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>epsilon</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>TB_i</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<apply>
<plus/>
<ci>J_NH3</ci>
<ci>J_NH4</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_i</ci>
<apply>
<divide/>
<ci>H_i</ci>
<apply>
<plus/>
<ci>H_i</ci>
<ci>K_B</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>H_i</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2.303</cn>
</apply>
<ci>H_i</ci>
</apply>
<ci>beta</ci>
</apply>
<ci>rho</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>alpha_i</ci>
</apply>
<ci>J_NH4</ci>
</apply>
<apply>
<times/>
<ci>alpha_i</ci>
<ci>J_NH3</ci>
</apply>
</apply>
<ci>J_H</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>NH4_i</ci>
<apply>
<times/>
<ci>alpha_i</ci>
<ci>TB_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>NH3_i</ci>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>alpha_i</ci>
</apply>
<ci>TB_i</ci>
</apply>
</apply>
</math>
</component>
</model>
