modelGasSolubility
Extends from Icons.GasSolubility, Interfaces.ConditionalHeatPort (Partial model to include a conditional HeatPort in order to describe the power loss via a thermal network).
Information
ConcentrationLiquid = kH · ConcentrationGas
Henry's law: The concentration of the gas in the liquid is proportional to the partial pressure of the gas during equilibrium.
Relations
kd·A·cgas |
dissolution rate |
kv·A·cliquid |
volatility rate |
kH = kd/kv = cliquid/cgas |
equilibrium |
van't Hoff's equation |
|
ΔrG0= ΔH - T·ΔS = -R·T·log(KH) |
Gibb's energy |
entropy |
Notations
cgas |
gaseous molar concentration of the substance |
cliquid |
liquid molar concentration of the substance |
KH |
Henry's coeficient at current temperature T |
kd |
dissolution rate coefficient in liquid at current temperature T |
kv |
volatility rate coefficient at current temperature T |
A |
surface area between gas and liquid |
ΔH |
enthalpy of dissolution |
TheatPort |
current temperature T |
KH0 |
tabulated Henry's constant at base temperature TK |
TK |
base temperature of tabulated coefficients |
Ω |
change of number of ways of arranging molecules |
ΔS |
entropy of the dissolution |
ΔsG0 |
Gibb's energy of the dissolution |
Henry's coefficient kH depends on temperature and on the identities of all substances present in solution.
Water fraction (W_solution, plasma 0.94, RBC 0.65 => blood 0.81 ml/ml) in solution can change the solubility of gases in water [1] as c_pure=c_solution/W_solution.
References
[1] Dash RK, Bassingthwaighte JB. Erratum to: Blood HbO2 and HbCO2 dissociation curves at varied O2, CO2, pH, 2, 3-DPG and temperature levels. Ann Biomed Eng 2010;38:1683-701.
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| Types.DiffusionPermeability | solubilityRateCoef | 0.01 | The rate constant of incoming gas to solution (default 10 liter per second) |
| Types.GasSolubility | kH_T0 | Henry's law coefficient at base temperature (i.e. in (mmol/l)/kPa at 25degC: aO2=0.011, aCO2=0.245, ..) | |
| Types.Fraction | solventFraction | 1 | Free solvent fraction in liquid (i.e. 'mol/mol' ratio between current solution and pure solvent in one liter; e.g. in plasma=0.96, in RBC=0.717) |
| External inputs/outputs | |||
| Boolean | useHeatPort (from ConditionalHeatPort) | false | =true, if HeatPort is enabled |
| Temperature dependence | |||
| Types.Temperature | T (from ConditionalHeatPort) | 310.15 | Fixed device temperature if useHeatPort = false |
| Types.Temperature | T0 | 298.15 | Base temperature for kH_T0 |
| Types.Temperature | C | Gas-liquid specific constant for Van't Hoff's change of kH (i.e.: O2..1700K,CO2..2400K,N2..1300K,CO..1300K,..) | |
Connectors
| Type | Name | Default | Description |
|---|---|---|---|
| Thermal.Interfaces.HeatPort_a | heatPort (from ConditionalHeatPort) | ||
| Interfaces.ChemicalPort_b | q_out | Gaseous solution | |
| Interfaces.ChemicalPort_a | q_in | Dissolved in liquid solution |
Components
| Type | Name | Default | Description |
|---|---|---|---|
| Types.Temperature | T_heatPort (from ConditionalHeatPort) | Temperature of HeatPort | |
| Types.HeatFlowRate | lossHeat (from ConditionalHeatPort) | Loss heat leaving component via HeatPort | |
| Types.GasSolubility | kH | Henry's law coefficient such as liquid-gas concentration ratio |
Revisions
2009-2015 by Marek Matejak, Charles University, Prague, Czech Republic