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Surface tension

In TEA, when using CAPE-OPEN version 1.0, surface tension is only available between vapor and liquid. Because two-phase qualifiers are not well defined, external objects may specify both "Liquid" and "VaporLiquid" for the phase specifier of surfaceTension. Composition derivatives are not supported for version 1.0; however, COFE's material objects will translate a call for surfaceTension.DmolFraction properly when TEA is loaded as version 1.1 property package and a PMC specifies "Liquid" as phase identifier.

For CAPE-OPEN version 1.1, surface tension is a regular two-phase property.

None of the formulas below take any of the vapor properties into account.

Mixture surface tension

All surface tension derivatives are obtained by perturbation.

Ideal

\begin{displaymath}\sigma_m = \sum^{c}_{i=1} x_i \sigma_i\end{displaymath}

Winterfeld et al.

This method by Winterfeld et al. (1978) is DIPPR 7C procedure:

\begin{displaymath}\sigma_m = {\sum^{c}_{i=1} \left( ({x_i / \rho^L_i})^2 +......) \over\left(\sum^{c}_{i=1} ({x_i / \rho^L_i}) \right)^2}\end{displaymath}

Digulio-Teja

This method evaluates the compound surface tensions at the compounds normal boiling points (σb,i) and computes the mixture critical temperature, normal boiling temperature and the mixture surface tension at normal boiling temperature with the following mixing rules:

$\displaystyle T_{c,m}$ $\textstyle =$ $\displaystyle \sum^{c}_{i=1} x_i T_{c,i}$
$\displaystyle T_{b,m}$ $\textstyle =$ $\displaystyle \sum^{c}_{i=1} x_i T_{b,i}$
$\displaystyle \sigma_{b,m}$ $\textstyle =$ $\displaystyle \sum^{c}_{i=1} x_i \sigma_{b,i}$

Then it corrects the σb,m with:

$\displaystyle T^*$ $\textstyle =$ $\displaystyle {(1/T_r -1) \over (1/T_{rb}-1)}$
$\displaystyle \sigma$ $\textstyle =$ $\displaystyle 1.002855 (T^*)^{1.118091} {T \over T_b} \sigma_r$

Pure compound surface tension

Pure compound surface tension is required by the internal mixture surface tension routines, and can only be used with these routines. If mixture surface tension is calculated by an external calculation routine, pure compound surface tension is obtained by using the same external routine and making a call for each compound in which compositions are set as to have only that compound present.

Compound surface tensions are only determined for temperatures below the compound's critical temperature, otherwise it is assumed that the compound does not contribute to the mixture surface tension (to prevent numerical difficulties, implemented as σi = 1e-10). The following methods are available.

Temperature Correlation

The parameters for the temperature correlation for liquid surface tension of pure compounds are available through TEA's PCD data files.

Brock-Bird

This is DIPPR procedure 7A:

$\displaystyle T_{br}$ $\textstyle =$ $\displaystyle T_{b,i} / T_{c,i}$
$\displaystyle Q$ $\textstyle =$ $\displaystyle 0.1207 \left( 1 + T_{br} ( \ln (P_{c,i}) - 11.526 )\over (1 - T_r) \right) - 0.281$
$\displaystyle \sigma_i$ $\textstyle =$ $\displaystyle 4.6~10^{-7} P^{2/3}_{c,i} T^{1/3}_{c,i}Q (1 - T_r)^{11/9}$

Lielmezs-Herrick

This method by Lielmezs and Herrick (1986) uses the Temperature Correlation but evaluates it at the reduced normal boiling temperature and corrects the resulting σr with:

$\displaystyle T^*$ $\textstyle =$ $\displaystyle {(1/T_r -1) \over (1/T_{rb}-1)}$
$\displaystyle \sigma$ $\textstyle =$ $\displaystyle 1.002855 (T^*)^{1.118091} {T \over T_b} \sigma_r$

Per compound

When selecting the Per Compound routine, the above methods can be selected on a per-compound basis in the compounds tab.

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