Du Nouy Method for Measurement of Surface Tension

[Dario56]

This method calculates surface tension based on force balance acting on the ring placed on the liquid surface: $$ F = G + \gamma L $$
where ##G## is weight of the ring, ##L## is wetted length of the ring which is equal to its circumference, ##F## is outer force of tensiometer acting on the ring

So, when force balance is reached by changing outer force, ring is ripped off from the surface and surface tension can be calculated.

However, if this is so, what does surface tension of liquid have to do with force acting on the ring since adhesion between ring and liquid is what resists ring being ripped of from the surface not surface tension of the liquid?

 

[Chestermiller]

Please articulate your understanding of the term surface tension.

 

[Dario56]

Please articulate your understanding of the term surface tension.

Work needed to expand surface of the liquid per unit area. In most general terms, surface energy can be defined for any surface and interphase, but here we determine surface tension of interphase liquid/air.

This is not ideal as we would want to determine surface energy in a vacuum because any medium (in our case air) stabilizes the surface of the liquid by adhesion and adsorption.

 

[Chestermiller]

Work needed to expand surface of the liquid per unit area.

This is somewhat consistent with the definition of surface tension I am accustomed to be working with: in-plane normal tensile force per unit length along any contour within the surface. Are you comfortable with this definition?

 

[Dario56]

This is somewhat consistent with the definition of surface tension I am accustomed to be working with: in-plane normal force per unit length along any contour within the surface. Are you comfortable with this definition?

Well, I do know that surface tension can be defined as force per unit of length where length is some constant dimension connected to change in area. This can be seen in example on wikipedia. I am not completely comfortable with definition you used, where can I study it more?

 

[Chestermiller]

I don't have any book references. I learned this a long time ago in course work, and it has never failed to deliver. I strongly encourage you to learn about it. It is very simple to apply, as in the example of the Du Nuoy ring that you cited.

 

[hutchphd]

My way into thinking about it was the Laplace-Young equation

 

[Chestermiller]

My way into thinking about it was the Laplace-Young equation

The Laplace-Young equation can be derived from the definition I gave for the case of a curved surface.

 

[hutchphd]

I am not completely comfortable with definition you used, where can I study it more?

I was recommending it and its derivation as a means of understanding tensile strength as force per length. It helped me.

 

[Dario56]

I was recommending it and its derivation as a means of understanding tensile strength as force per length. It helped me.

I do understand N/m interpretation which is usually tought (there is example on wikipedia), that interpretation is equivalent to J/m2 since length in N/m is really only parameter of the surface area.

Isn't tensile strength measured in [Pa] = [N/m2]?

 

[Lord Jestocost]

Surface energy, the potential energy resulting from the surface tension. The surface tension opposes an increase in the surface area. In order to enlarge the surface by an amount ##\Delta A##, an amount of work ##\Delta W## is required. The ratio of the work ##\Delta W## to the surface increase ##\Delta A##, is called the surface tension ##\sigma##:

##\sigma = \frac { \Delta W } {\Delta A }##

 

[Dario56]

Surface energy, the potential energy resulting from the surface tension. The surface tension opposes an increase in the surface area. In order to enlarge the surface by an amount ##\Delta A##, an amount of work ##\Delta W## is required. The ratio of the work ##\Delta W## to the surface increase ##\Delta A##, is called the surface tension ##\sigma##:

##\sigma = \frac { Delta W } {\Delta A }##

It doesn't really answer my question.

 

[Chestermiller]

I would like to see what your sketch looks like for the water and ring when the upward force has been applied to the ring.

 

[Lord Jestocost]

Isn't tensile strength measured in [Pa] = [N/m2]?

Yes. But what has "tensile strenght" to do with "surface tension"?

 

[Dario56]

I would like to see what your sketch looks like for the water and ring when the upward force has been applied to the ring.

We have stemmed away from my original question which is that adhesion between ring and the liquid is what keeps the ring on the surface not surface tension of the liquid.

If there were no adhesive forces between the ring and the liquid, outer force (no matter how small) would immediatelly torn it from the surface regardless of surface tension of the liquid.

 

[hutchphd]

It will be the weakest link in the chain...could be adhesion or it could be tensile strength of the liquid surface I think. If the ring comes off "wet" I think it is probably not the adhesion.

 

[Lord Jestocost]

Of course, one needs adhesion between the liquid and the ring in order to be able to enlarge the liquid’s surface when pulling out the ring. The work done to pull out the ring is related to the corresponding increase in the liquid's surface energy.

Du Noüy ring method | KRÜSS Scientific - Kruss​

 

[Dario56]

Of course, one needs adhesion between the liquid and the ring in order to be able to enlarge the liquid’s surface when pulling out the ring. The work done to pull out the ring is related to the corresponding increase in the liquid's surface energy.

Du Noüy ring method | KRÜSS Scientific - Kruss​

Yes, however force balance is written for the ring not the liquid. Adhesion is the force acting on the ring not surface tension. Surface tension acts on the liquid to minimize its surface area.

 

[Chestermiller]

It will be the weakest link in the chain...could be adhesion or it could be tensile strength of the liquid surface I think. If the ring comes off "wet" I think it is probably not the adhesion.

I think the point is that the air water interfaces at the inner and outer radii of the ring are essentially vertical when the failure occurs. I don't think that the upward force applied to the ring is varying substantially as this point is approached.

 

[Lord Jestocost]

Yes, however force balance is written for the ring not the liquid.

If adhesion is the mere force acting on the ring, why does the force which you have to apply to pull the wetted ring out of the liquid increases with distance between the ring and the liquid?

Surface tension measurement by Du Noüy ring method​

 

[Chestermiller]

It's definitely not adhesion that causes the ring to break loose. It is a hydrodynamic instability caused by the liquid film breaking apart. We know this because there is residual water on the ring after the failure of the film.

 

[Dario56]

It's definitely not adhesion that causes the ring to break loose. It is a hydrodynamic instability caused by the liquid film breaking apart. We know this because there is residual water on the ring after the failure of the film.

Interesting. This isn't mentioned anywhere where this method is described. What does hydrodynamic instability have to do with surface tension?

 

[Lord Jestocost]

It is a hydrodynamic instability caused by the liquid film breaking apart.

I think you wanted to point out to the Plateau–Rayleigh instability.

 

[Chestermiller]

Interesting. This isn't mentioned anywhere where this method is described. What does hydrodynamic instability have to do with surface tension?

You are dealing with a fluid bounded by a free surface, right? Small perturbations to the shape of the surface and to the film itself (due to any type of fluctuation, such as a tiny vibration of the room or an air current) can either be damped out (by the viscous nature of the fluid) or amplify, depending on how much the film has been thinned out. If they amplify, the film will break apart. This is what happens when soap bubbles break apart.