7.5 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Continuous foam separation | 2/3 | https://en.wikipedia.org/wiki/Continuous_foam_separation | reference | science, encyclopedia | 2026-05-05T10:46:52.712893+00:00 | kb-cron |
Δ
P
=
γ
∘
(
1
R
1
+
1
R
2
)
{\displaystyle \Delta P=\gamma ^{\circ }({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}})}
As pressure grows inside the bubbles, the liquid lamellae shown in the figure above will forced to move toward plateau borders causing a collapse of the lamellae.
==== Gibbs adsorption isotherm ==== The Gibbs adsorption isotherm can be used to determine the change in surface tension with changing concentration. Since chemical potential varies with a change in concentration, the following equation can be used to estimate the change in surface tension where dγ is the change in surface tension of the interface, Γ1 is the surface excess of the solvent, Γ2 is the surface excess of the solute (surfactant), dμ1 is the change in chemical potential of the solvent, and dμ2 is the change in chemical potential of the solute:
d
γ
=
Γ
1
d
μ
1
+
Γ
2
d
μ
2
{\displaystyle \mathrm {d} \gamma =\Gamma _{1}\mathrm {d} \mu _{1}+\Gamma _{2}\mathrm {d} \mu _{2}}
For ideal cases, Γ1 = 0 and the created foam is dependent on the change in chemical potential of the solute. During foaming, the solute experiences a change in chemical potential as it goes from the bulk solution to the foam surface. In this case, the following equation can be applied where a is the activity of the surfactant, R is the gas constant, and T is the absolute temperature:
Γ
2
=
−
a
R
T
(
∂
γ
∂
a
)
T
{\displaystyle \Gamma _{2}=-{\frac {{a}\,}{RT}}\,\left({\frac {\partial \gamma }{\partial a}}\right)_{T}\,}
In order solve for the area on the foam surface occupied by one adsorbed molecule, As, the following equation can be used where NA is the Avogadro constant.
A
s
=
1
N
A
Γ
2
{\displaystyle A_{\text{s}}={\frac {{1}\,}{N_{\text{A}}\Gamma _{2}}}}
== Applications ==
=== Wastewater treatment ===
Continuous foam separation is used in wastewater treatment to remove detergent-derived foaming agents such as ABS, which became common in wastewater by the 1950s. In 1959 it was shown that by adding 2-octane to foamed wastewater, 94% of ABS could be removed from the activated sludge through using foam separation techniques. The foam produced during wastewater treatment can either be recycled back into the activated sludge tank within a waste treatment plant, the bacterial organisms that live there have been found to break down ABS when allowed enough time, or extracted and collapsed for disposal. Foam separation has also been found to decrease the chemical oxygen demand when used as secondary treatment technique for wastewater.
==== Heavy metal removal ==== The removal of heavy metal ions from wastewater is important because they accumulate easily in the food chain, ending in animals such as swordfish that humans eat. Foam separation can be used to remove heavy metal ions from wastewater at low costs, especially when used in multistage systems. When performing ion foam separation there are three operational conditions that must be met for optimal production of foam for ion removal: foam formation, flooding, and weeping/dumping.
=== Protein extraction === Foam separation can be used for the extraction of proteins from a solution especially to concentrate the protein from a dilute solution. When purifying proteins from solution on an industrial scale, the most cost efficient method is desired. As such, foam separation offers a method with low capital and maintenance costs due to the simple mechanical design; this design also allows for easy operation. However, there are two reasons why using foam separation to extract protein from solution has not been widespread: firstly some proteins denature when going through the foaming process and secondly, control and prediction of foaming is typically difficult to calculate. In order to determine the success of protein extraction through foaming three calculations are used.
Enrichment ratio
=
(
Protein concentration in the foam
Protein concentration in the initial feed
)
{\displaystyle {\text{ Enrichment ratio}}=\left({\frac {\text{Protein concentration in the foam}}{\text{Protein concentration in the initial feed}}}\right)}
The Enrichment ratio demonstrates how effective the foaming is in extracting the protein from the solution into the foam, the higher the number the better the affinity the protein has for the foam state.
Separation ratio
=
(
Protein concentration in the foam
Protein concentration in the outlet stream
)
{\displaystyle {\text{ Separation ratio}}=\left({\frac {\text{Protein concentration in the foam}}{\text{Protein concentration in the outlet stream}}}\right)}
The Separation ratio is similar to the enrichment ratio in that the more effective the extraction of protein from the solution into the foam, the higher the number will be.
Recovery
=
(
Mass of protein in the foam
Mass of protein in the initial feed
)
×
100
%
{\displaystyle {\text{ Recovery}}=\left({\frac {\text{Mass of protein in the foam}}{\text{Mass of protein in the initial feed}}}\right)\times 100\%}