Fluids: Kistler contact angle model

[member 428835]

Hi PF!

I keep seeing Kistler's contact angle model wrote like this $$ \theta_d = f(Ca+f^{-1}(\theta_e)) : f = \arccos\left( 1-2\tanh\left( 5.15 \left( \frac{x}{1+1.31x^{0.99}} \right)^{0.706} \right) \right) $$, where the plot then has a sort of break, something like this:

But this is not the above function, as it only works for advancing contact lines (right half of plot). How is the left side generated?

 

[Achy47]

Hi there!

The left side of the plot is generated using the receding contact angle, which is the angle formed between the liquid and the solid surface when the liquid is receding from the solid surface. This angle is typically smaller than the advancing contact angle, as the liquid is pulling away from the surface instead of advancing towards it.

In Kistler's contact angle model, the function f represents the advancing contact angle, while the function f^-1 represents the receding contact angle. This is why the left side of the plot has a different shape than the right side. To generate the left side of the plot, you would need to use the receding contact angle function instead of the advancing contact angle function.

I hope this helps clarify the plot for you. Let me know if you have any other questions!