Sorption

Sorption is a general term for the mechanisms of adsorption and absorption. Adsorption describes the process of molecules being bound to a surface by means of adhesion. Absorption refers to molecules which enter a bulk volume—in electrochemical applications, this is most commonly an electrolyte that is modelled as a solid in Simcenter STAR-CCM+.

The sorption process can be written in the form of a reaction. For the example of water and steam/vapour at an interface, this sorption process can be written as:

where $r_{surf,0}$ is the sorption rate constant, $c_{fluid}$ is the concentration of the reactant, $a_{sorbed}$ is the activity of the sorbed species, and $K_{\mathrm{eq}}$ is an equilibrium constant, which allows for discontinuous concentrations at interfaces—as in Henry's law.

where $v_i$ is the stoichiometric coefficient of species $i$ .

Different methods can be used to parameterize Eqn. (4165).

Springer

To allow for the most general representation, Simcenter STAR-CCM+ models the reaction rate in terms of chemical activities rather than concentrations to account for deviations from ideal solution behavior. As a consequence, Eqn. (4165) becomes:

$$r_{surf}=r_{surf,0}\left({{\displaystyle C}}_{\mathrm{eq}}-a_{sorbed}\right)$$

(4167)

where $C_{\mathrm{eq}}$ is an equilibrium-related term.

The equilibrium concentration term for the fluid species is computed as:

$${{\displaystyle C}}_{\mathrm{eq}}=\xi {\lambda }_{\mathrm{eq}}$$

(4168)

where $\xi$ is the equilibrium concentration constant of the reaction.

${\lambda }_{\mathrm{eq}}$ is the dimensionless solute content at equilibrium and is usually computed in terms of chemical activities $a$ :

$$a=\{\begin{array}{cc}\left(\frac{c\text{R}T}{P_{\mathrm{sat}}}\right)& \text{for gas}\text{phase}\\ c& \text{\hspace{0.17em}for liquid/intercalated}\text{phase}\end{array}$$

(4169)

where $P_{sat}$ is the saturation pressure.

The Springer reaction formulation [836] is tailored to model water transport in Polymer Electrolyte Membrane (PEM) fuel cells. The dimensionless solute content at equilibrium ${\lambda }_{\mathrm{eq}}$ becomes a dimensionless water content at equilibrium, and is expressed as:

$${\lambda }_{\mathrm{eq}}=A{a}^{3\gamma }+B{a}^{2\gamma }+C{a}^{\gamma }+Da\le 1$$

(4170)

where $\gamma$ is the rate exponent. For a Multi-Component Gas continuum in Simcenter STAR-CCM+, the dimensionless water content at equilibrium is cropped at $a=1$ , which corresponds to a saturated gas (for example, water vapour). $A$ , $B$ , $C$ , and $D$ are coefficients that you specify. The default coefficient values in Simcenter STAR-CCM+ are from Springer [836] at 30°C for water.

Wu Li Berg

Similar to the Springer formulation, the Wu Li Berg reaction formulation [838] is tailored to model water transport in PEM fuel cells. The dimensionless water content at equilibrium is defined as:

$${\lambda }_{\mathrm{eq}}=0.3+6a^{\gamma }(1-\tanh (a^{\gamma }-0.5))+3.9\sqrt{a^{\gamma }}\left(1+\tanh \left(\frac{a^{\gamma }-0.89}{0.23}\right)\right)$$

(4171)

If the reactant activity $a$ exceeds 1.0, the activity is limited to a value of 1.0.

Henry

Unlike the above fuel cell related expressions, Henry's law is not formulated in terms of reference concentrations and dimensionless solute contents—the surface sorption rate is expressed directly as:

$$r_{surf}=r_{surf,0}\left(He{a}_r^{\gamma }-a_p^{\gamma }\right)$$

(4172)

where $He$ is Henry's constant, $a_r$ is the activity of the reactant species, and $a_p$ is the activity of the product species, calculated as:

$$a=\{\begin{array}{cc}\left(\frac{c\text{R}T}{P_{ref}}\right)& \text{for gas}\text{phase}\\ c& \text{\hspace{0.17em}for liquid/intercalated}\text{phase}\end{array}$$

(4173)

where $P_{ref}$ is the reference pressure ([1.0 atm]).

Sorption: Electrochemical Reaction Heating

The Electrochemical Reaction Heating model accounts for heat contributions which are due to the sorption process (for heat contributions due to reversible and irreversible electrochemical processes, see Eqn. (4143)).