Calculate forces acting on liquid film

[MarcGyongyosi]

Dear all fellow physicists,

I am struggling with the following fluid mechanics problem: considering a liquid film in an "equilibrium" position between two plane walls, I am trying to define the forces acting on the liquid.

Most importantly, gravity is pulling down on the liquid with Fg = m* g. Since the shape of the film is not uniform, this force's magnitude (slightly) varies across the film.

Furthermore, we have an adhesive force component which acts upward, sort of holding the liquid film at the walls and we have surface tension at the liquid-air interface.

My problem is with regard to the forces acting against gravity. How can I calculate them? Knowing surface tension and the wetting angle, can I define them in some way or another, based on the curvatures of the top and bottom surface of the liquid film? Like, what would the individual force vectors' magnitudes be, based on liquid properties and curvatures of the surfaces?

Looking forward to your replies,

Marc

 

[Simon Bridge]

What is available to push on the particles of the film?
i.e. what is it sitting on? Is there anything above or below the film or is it in vacuum?

 

[Andy Resnick]

I am struggling with the following fluid mechanics problem: considering a liquid film in an "equilibrium" position between two plane walls, I am trying to define the forces acting on the liquid.

<snip>

I am having trouble understanding the geometry- what is the orientation of the film with respect to gravity? For now, I'll assume the walls are vertical (the film is horizontal) and the film is something like a soap film with air reserviours on either side, so the film forms a shape like a catenary in cross-section.

First- this problem is not trivial. There are two free surfaces and at least three relevant forces- gravity, any pressure difference between the reservoirs, and wetting at the three-phase contact line. Lots of different things can happen- even if gravity is 'off' and the pressure difference is zero, if the soapy water completely wets the wall, the film will thin and break. In the opposite case- complete hydrophobic interactions, the film will detach from the wall. In general, the evolution and equilibrium shape can be obtained by the 'shooting method':

ftp://orthodox-hub.ru/books/_%D4%E8%E7%E8%EA%E0_%CC%E0%F2%E5%EC%E0%F2%E8%EA%E0/RevModPhys/RevModPhys%201984-2008/root/data/RevModPhys%201984-2008/pdf/RMP/v069/RMP_v069_p0931.pdf (starting at pg. 957)

Good luck...

 

[Simon Bridge]

... and that's just assuming the film in question is a soap film.
The type of film has not been stated - it could be oil on water with air above for all we know.

 

[PJC01]

Dear Marc,

Thank you for reaching out to your fellow physicists for help with your fluid mechanics problem. Calculating forces acting on a liquid film can be a complex task, but I will do my best to provide some guidance.

Firstly, you are correct in stating that gravity is pulling down on the liquid film with a force of Fg = m*g. This force can be calculated by multiplying the mass of the liquid film by the acceleration due to gravity.

In order to calculate the forces acting against gravity, we need to consider the other forces at play. As you mentioned, there is an adhesive force acting upward, which is holding the liquid film at the walls. This force can be calculated by considering the strength of the adhesive bond between the liquid and the walls.

Additionally, there is surface tension at the liquid-air interface. This force is caused by the cohesive forces between the molecules in the liquid. The magnitude of this force can be calculated using the equation for surface tension: F = γL, where γ is the surface tension coefficient and L is the length of the liquid-air interface.

To calculate the individual force vectors' magnitudes, you will need to consider the curvatures of the top and bottom surfaces of the liquid film. The curvature of these surfaces can be related to the surface tension, wetting angle, and liquid properties using the Young-Laplace equation: ΔP = γ(1/R1 + 1/R2), where ΔP is the pressure difference between the two surfaces and R1 and R2 are the radii of curvature of the top and bottom surfaces, respectively.

I hope this helps guide you in your calculations. Best of luck with your research.

Sincerely,