Szyszkowski equation

${\displaystyle \sigma _{m}=\sigma _{w}\left(1-0.411\log \left(1+{\frac {x}{a}}\right)\right)}$

with:

• σ_m is surface tension of the mixture
• σ_w is surface tension of pure water
• a is component specific constant (see table below)
• x is mole fraction of the solvated component

The equation can be rearranged to be explicit in a:

${\displaystyle {\begin{aligned}a&={\frac {x}{10^{\left(-1+{\frac {{\frac {\sigma _{m}}{\sigma _{w}}}-1}{-0.411}}\right)}}}\\&=x10^{\left(1+{\frac {{\frac {\sigma _{m}}{\sigma _{w}}}-1}{0.411}}\right)}\end{aligned}}}$

This allows the direct calculation of that component specific parameter a from experimental data.

The equation can also be written as:

${\displaystyle \gamma =\gamma _{0}-{\frac {RT}{\omega }}\ln(1+K_{ad}c)}$

with:

• γ is surface tension of the mixture
• γ₀ is surface tension of pure water
• R is ideal gas constant 8.31 J/(mol*K)
• T is temperature in K
• ω is cross-sectional area of the surfactant molecules at the surface

The surface tension of pure water is dependent on temperature. At room temperature (298 K), it is equal to 71.97 mN/m [4]

Meissner and Michaels published the following a constants:

The following table and diagram show experimentally determined surface tensions in the mixture of water and propionic acid.

This example shows a good agreement between the published value a=2.6*10⁻³ and the calculated value a=2.59*10⁻³ at the smallest given mole fraction of 0.00861 but at higher concentrations of propionic acid the value of an increases considerably, showing deviations from the predicted value.

• Bohdan Szyszkowski