Energy required for expansion into viscous environment

[motorfreak]

Hi all,

I am new here, but in my (chemistry) research I have struck upon a problem that one of you might be able to help me with.

I am interested to find an expression for the energy that it would require for an object to expand in a medium of known (dynamic macro-) viscosity. In other words, how much energy is required to push back a volume V (m3) of a medium of viscosity n (Pa*s)? Or, if there is no precooked expression, how to derive this?

Background: the actual problem is situated on the molecular level, and involves the power output of a molecule when changing shape with concommitant volume expansion in a highly viscous environment.

I hope one of you will be able to help me out here, if so thanks a lot!

 

[Andy Resnick]

Interesting question...

Let me try to simplify it, to a simple expanding/contracting bubble. The bubble changes it's radius from r to r+dr, and so work is done on the fluid.

A quick literature search pulls up this paper:

"Viscosity in an Expanding Bubble", Everett C. Westerfield and W. B. Pietenpol, Phys. Rev. 55, 306 - 307 (1939)

Which I am now looking through. It seems to be concerned with an expanding bubble of viscous material, but maybe it is still of use.

 

[motorfreak]

Hi there

Thanks a lot. I am usually not very literate when it concerns papers like this, but it seems to me very close to my problem. There are 2 main problems associated with this approach in relation to my problem.
First of all, my structure is no sphere, but more like a blob which changes shape. I could use the (known) volumes to derive a spherical approximation, but that takes us further away from the real thing.
Secondly, the dependence on the viscosity of the material itself is very strong in this approach, and as I am talking about a solid in solution this should be infinite, or at least unknown... ;-) . Apart form that it seems to unneccesarily complicate matters; the volume change of the object is known, as is the viscosity. From there we would only have to know the energy required for displacement of a certain volume of medium of viscosity n. I'll continue the search, and hope anything else pops up!

Thx
Martin Klok

 

[chemisttree]

Are you asking what will be the energy required for uniform dilution of one fluid in another with differing viscosities? If so, this would seem to be the energy of mixing you are asking about.

 

[motorfreak]

No, that's not the question. The question concerns a solid object that increases its solvent-free volume against the resistance of viscosity, and what energy that would require as a function of viscosity and volume change. There is no mixing involved.

 

[chemisttree]

When you add the second liquid to the first, the level of the first liquid will increase to a new level. Find the energy required to lift that liquid to the new level and you will have your energy. If there is joule heating involved, you can do the calorimetry and add it to the above for the total energy.

 

[motorfreak]

That sounds very reasonable indeed. Just one question remaining: How to proceed? Are there textbooks or related that would cover this?

 

[chemisttree]

In this case potential energy (PE) is equal to the mass of the fluid times the gravitational constant (g) times the change in height. PE=mgh or $$\Delta PE\ = mg \Delta h\$$. In this case the mass, m, refers to the mass of the fluid being displaced.