Surface Tension - Lung Alveoli

[elemis]

So, the way I understand this is as follows :

The alveoli (pretend they're bubbles) have diameters of the order of microns implying a massive pressure required to inflate them by the Young-Laplace equation.

$p_{in}-p_{out}=\frac{2\gamma}{r}$

However, the presence of pulmonary surfactant molecules (lets just pretend they're like detergents molecules in washing liquid) can effectively reduce the surface tension at the unexpanded alveoli and hence allow easy inflation.

Now this bit I don't understand :

As the alveoli expand the distance between the individual surfactant molecules on the alveoli increases and hence the surface tension rises again therefore decreasing the rate of expansion.

What is the mathematical connection between surface tension and separation between surfactant molecules ? How can I rationalise the statement in bold ?

 

[Chestermiller]

So, the way I understand this is as follows :

The alveoli (pretend they're bubbles) have diameters of the order of microns implying a massive pressure required to inflate them by the Young-Laplace equation.

$p_{in}-p_{out}=\frac{2\gamma}{r}$

However, the presence of pulmonary surfactant molecules (lets just pretend they're like detergents molecules in washing liquid) can effectively reduce the surface tension at the unexpanded alveoli and hence allow easy inflation.

Now this bit I don't understand :

As the alveoli expand the distance between the individual surfactant molecules on the alveoli increases and hence the surface tension rises again therefore decreasing the rate of expansion.

What is the mathematical connection between surface tension and separation between surfactant molecules ? How can I rationalise the statement in bold ?

The surfactant molecules separate the molecules of the alveoli, which are, apparently, highly attractive to one another. However, if the distance between the surfactant molecules increases (i.e., their concentration at the surface decreases), more molecules of alveloi are able to come into contact with one another, and this causes their attractive effect to increase. Just imagine if the concentration of the surfactant molecules was greatly reduced. It would be as if they were not even there.

Chet

 

[elemis]

The surfactant molecules separate the molecules of the alveoli, which are, apparently, highly attractive to one another. However, if the distance between the surfactant molecules increases (i.e., their concentration at the surface decreases), more molecules of alveloi are able to come into contact with one another, and this causes their attractive effect to increase. Just imagine if the concentration of the surfactant molecules was greatly reduced. It would be as if they were not even there.

Chet

Hi Chet,

So to be clear, the alveoli expansion simply results in an drop in the effective concentration (activity) of the surfactant and hence since their surface excess decreases we note an increase in surface tension ?

 

[Chestermiller]

Hi Chet,

So to be clear, the alveoli expansion simply results in an drop in the effective concentration (activity) of the surfactant and hence since their surface excess decreases we note an increase in surface tension ?

That's my understanding of what the statement is saying.

Chet

 

[PJC01]

Surface tension and surfactant molecules play a crucial role in the mechanics of lung alveoli. As a scientist, it is important to understand the relationship between these two factors in order to fully comprehend the process of alveoli inflation and deflation.

Surface tension is a physical property of liquids that arises due to the cohesive forces between molecules at the surface of the liquid. In the case of lung alveoli, the surface tension is caused by the thin layer of fluid lining the alveoli walls. This surface tension creates a force that resists the expansion of the alveoli, making it difficult for them to inflate.

However, the presence of surfactant molecules in the fluid lining of the alveoli reduces the surface tension. This is because surfactants have a hydrophobic (water-repelling) end and a hydrophilic (water-attracting) end. The hydrophobic end attaches to the surface of the alveoli, while the hydrophilic end faces towards the fluid. This creates a layer on the surface of the alveoli that effectively reduces the surface tension, making it easier for the alveoli to expand.

Now, as the alveoli expand, the distance between individual surfactant molecules also increases. This means that the hydrophobic ends of the surfactant molecules are further apart, reducing their ability to interact with the alveoli surface. As a result, the surface tension increases again, making it more difficult for the alveoli to continue expanding at the same rate.

The mathematical connection between surface tension and separation between surfactant molecules is described by the Young-Laplace equation, as mentioned in the content. This equation relates the pressure difference across a curved interface (in this case, the alveoli) to the surface tension and the radius of curvature. As the alveoli expand, the radius of curvature increases, leading to a decrease in pressure difference and an increase in surface tension.

In summary, the presence of surfactant molecules reduces the surface tension in lung alveoli, making it easier for them to inflate. However, as the alveoli expand, the distance between surfactant molecules increases, leading to an increase in surface tension and a decrease in the rate of expansion. This relationship is described by the Young-Laplace equation and is crucial in understanding the mechanics of lung alveoli.