What you need to determine is the point at which the work done by the rate of creation of the new surface area equates that done due to the shear forces in the liquid layers which are in turn depended on the surface with which the liquid is in contact , flow velocity, and temperature. I have never tested this but I would expect that the speed of sound in a medium is related to this property . But this is only my first guess

There is definitely an upper limit for stretching of solids due to the limited velocity of elastic and plastic wave propagation ( J. Appl. Phys. 21, 987 (1950); http://dx.doi.org/10.1063/1.1699544 (8 pages), The Propagation of Plastic Deformation in Solids, Theodore Von Karman and Pol Duwez). The bulk elastic properties and viscosity should lead to similar effects in liquids as in fluids. There should definitely be models available for stretching of viscous materials coming from the field of die drawing of polymer or glass fibers, but that is a bit out of my own field unfortunately.

Dear colleagues, thanks for your interesting suggestions. It would be interesting to know your thoughts about the basic ideas I discussed in the paper I linked to my question. These were based on assuming that failure of the liquid metal film would be initiated once local as opposed to global thinning occured, and then by the question of whether such a local thinning could "heal" again under the prevailing conditions, with surface tension and viscosity as parameters that would support such healing. The criterion I envisaged would then roughly be along the lines of "how fast would the metal film have to be stretched to make sure that the flow of liquid melt from within the film could not compensate the local thinning any more". Does this make any sense to you, and do you have an idea who - not only in person, but maybe in terms of research fields - might be working in such fields? Experimentally or numerically? Who might prepare thin films of liquid metal and observe their behaviour? And specifically, films in "thin air", not on substrate?

Ultra thin films are good candidates to a new kind of emulsion detection systems. It's an outstanding environment, particularly on Precise Cosmology and Particle Scattering Movies. Liquid is almost perfect under high temperatures. So, it depends on materials, pressure and temperature to acquire a balance. Check Light Meson Holography. Here.

The problem seems to be similar to that of the contraction of a water jet with subsequent formation of drops. Physical reasons can be the Rayleigh instability, the interaction with dynamic pressure waves in the gas phase or turbulences in the fuid flow if the Reynolds number is too high. These effects are treated in fluid mechanics but usually for bulk samples and not for thin films.

My experiments did not like to get oxidation thin film. Therefore, we applied vacunm conditon around Pa-4, however the film formed surface of liquid tin around 20 min. with surface flow. We never measured the speed of stretching of the film as well as rupture criteria. The film easily breached surface flow coused by surface tension difference between cold and hot disk sustaing the liquid bridge.

Regarding to viscosit sy and urface tension, please show "Thermophysical property measurements of refractory metals over 3,000 C using an electrostatic levitation furnace,Takehiko Ishikawa, Paul-Francois Paradis, Shinichi Yoda ,International Journal of Thermophysics (impact factor: 0.95). 06/2013".

International Journal of Thermophysics (impact factor: 0.95). 06/2013;

Dear Dr. Griesche, dear colleagues, thanks for your response - one comment in that respect, I may have to be a bit more concrete in may definition of "dynamic": I can't really give an exact figure, but I am not thinking of real high speed effects, it is more like, say, a few mm per second at the utmost: Basically we have bubble growth in a foam induced by an internal blowing gas source, namely titanium hydride particles under conditions of thermally or chemically (if hydrogen is removed from the substance due to its reaction with the aluminium matrix to form a titanium aluminide) decomposition.

Would this change any of the many views expressed here?

Sounds pretty much like a cavitation phenomenon in lubrication flow commonly seen in a journal bearing.

Dear Shiu-Hwa Shyu,

I am not a fluid dynamics expert, but please see my comment above, I would expect anything like cavitation to happen only in very much more dynamic environments than what I am thinking of. In my case, dynamic was meant to signify that there is a "rate of change" in effect at all, whereas other criteria for metal film stability I know from the metal foam community suggest a minimum thickness the film must have to be stable: Once drainage effects cause the films to reach this threshold, it will rupture, no matter how the limit was reached.

Now I don't believe this is the full truth, I believe that if local rather than global thinning occurs, it is a question of boundary conditions like the speed with which a lamella is stretched that determines whether the local thinning can be compensated for via metal flow within the lamella, or not: In the former case, the "neck" will disappear, in the latter it will grow till the film ruptures. I have tried to graphically illustrate this, too, in the aforementioned paper.

You can challeng this problem with Dr. Divandari. he Dr Thesis on Bubble Damage (Chapter 4 of Casting practice book by john campbell).

Email: [email protected]

Dear Dr. Lehmhus,

maybe another effect has to be taken into account. I'm not sure if you have high fluid flow velocities due to Marangoni-driven convection. Any gradient in chemical composition or, as a weaker effect due to temperature gradients, can drive this flow (provided the surface is free and not covered by e.g. oxide layers).

Regards, AG

Dear Mr. Khoshkharam,

thanks for your suggestion, indeed I have been discussing the issue with Dr. Divandari (the world is small, you know) not such a long time ago, actually in February this year, but this did not lead to any direct action at the time, the problem being that I currently don't have any resources to support work in the field, so there was no basis for a real cooperation which would have had to be based on efforts from both sides.

Unfortunately the situation on my part is not changed, this being the reason why I have been using researchgate lately to discuss the question and hopefully find someone who can address the issue out of his own interest, and based on his own resources.

Needless to say, there are other groups, too, who could contribute to this - not the least (from the experimental perspective) Francisco Garcia-Moreno's group in Berlin, who would have a near-perfect experimental basis, but like me as I understand currently no resources they could dedicate to the topic (naturally, they have their own prioritization).

Best regards,

Dirk Lehmhus

If you are thinking about a free film as in a foam, then you would expect a rough balance in the viscous forces. As there is more material in thicker parts of the film the total viscous force (at the same stetching rate) would be higher than in a thinner part of the film. This suggests a fundamental instability in which thinner parts would stretch faster, thereby thinning out more quickly than the thicker parts. So for a free film that is being extended there is a fundamental instability.

Including particles can counteract this fundamental instability, and in order to get a foam you will have to include something (i.e. particles in a metal foam) to induce a disjoining pressure that prevents this instability from taking over. (But since you are working in the area of metal foams you probably know all this already).

Best

Alexander

Dear Alexander,

if I get you rigth I think I have very crudely been discussing some of the general aspects you mention in the paper I mentioned in the initial question: I agree with your point that thinner parts must necessarily stretch faster, thinning out further in the effect.

However, imagine that such local thinning has occured. Now stop the stretching. Then effects like e.g. the minimization of surface energy should lead to disappearance of the local thinning. This will happen at a certain "rate". The level of this "rate of healing" (or material re-distribution) should depend on surface energy, viscosity etc. And thus I would expect that conditions exist under which this "healing" occurs faster than the "further thinning" induced by stretching of the film (I should mention I am indeed thinking of foams, and thus the environment you described). To turn this statement around, I would expect a "maximum stretching rate" to exist for any film characterized by a certain set of (for the moment, fix) parameters like the aforementioned viscosity, surface energy etc. Again the other way roudn, I would expect e.g. an increase in surface energy to also increase the assumed "maximum stretching rate", as the driving for compensating teh thinning would be increase by the higher surface energy.

Problem is, personally I can't proof it. Not experimentally, not by simulation. And thus I also cannot evaluate the relative influence of the parameters that might have a role in this. Nor can I be sure that I know them all. For example, Axel Griesche above already named a potential added influence of the marangoni effect in an environment where this is relevant (which is in principle the case in many types of metal foams).

Best regards,

Dirk

If you are thinking of a foam, then your argument won't work. The reason is that the boundary of each foam cell would like to be spherical, and unless the gas content is minimal (i.e. a bubble situation) this means that the foam walls are inherently unstable without disjoining pressure. So I am not sure that the following will be helpful for your project.

Now, for the sake of argument, let us assume that you have a flat interface that you want to stretch. In that case there is a Laplace pressure related to the local curvature of your interface and if the interface is not stretched you will find a flat interface. You could set up your problem first as a filament that has a curved interface. The curvature will set up a pressure gradient (you could do this with periodic boundary conditions or with a boundary at a wall where the pressure inside the filament and outside the filament have to be the same).

Next you can solve the problem of the expanding filament (where extension rate now depends of film thickness) and you have a partial differential equation that contains the film height (supposed to be symmetric), its gradient (i.e. the curvature) which you can then solve to see when the instabilities occur.

Alexander

The physics here sounds very similar to atomization. Here there are various experimental studies which have looked at the effects that you are interested. There is less on the theoretical side, at least once you have particles in the film. Co-incidentally some of the work done on this area was done in Bremen by Udo Fritsching! Who is both interested, or at least has been, in metal atomization and in atomization with particles present.

Dear Andrew,

again I have to say the world is small, indeed. I have been discussing this with Professor Fritsching quite a while ago already, but to do something more concrete, to go into detail, here as in other cases the problem of other research priorities and limited capacity came in: Though indeed he was interested, and initially we did discuss the possibility of e.g. a DFG proposal, that never materialized yet ...

This may be analogous to sheet atomization in fuel spray or liquid metal atomization. I would recommend a literature survey of "fuel spray sheet atomization", "liquid metal sheet atomization", or variations of the like. The balance between the surface tension/viscosity and inertia is defined by the dimensionless Weber number. I believe you should be able to find some empirical relationships based on the Weber number that should get you close to your goal. The addition of 2nd phase particles (ceramic inclusions) will definitely alter the surface tension (i.e. the surface tension of the solid ceramic/liquid metal interface is different than that of the liquid metal/gas interface). Now that I think of it your question didn't specify whether the sheet is surrounded by gas, water or spreading over a solid surface. It also doesn't specify the orientation (in parallel to gravitational forces or at some angle with respect to)? All of those factors will also effect the critical speed.

Dear John, thanks for your interesting suggestions, as I am not an expert in this field, I'll have to check them and may then come back to you. You are right, I did not specificy the "surroundings" - I tought this was clear from the literature reference and the statements on the "foam background" of my question: The film is in "mid-air" - well, not air, of course, as these foams are blown using TiH2 which releases hydrogen: What I am oncerned with are the cell walls of a liquid foam, the liquid being an aluminium alloy, with or without particle addition.

What I keep wondering about with respect to several of the answers I have recieved here is the question of speed: You mention processes like "fuel spray sheet atomization" - to me, this sounds very fast. When I think of aluminium foam expansion, I would imagine the maximum speed of stretching the cell walls might experience to be in the range of a few mm per second - if one mm at all.

Do you think th elaws you mentioned would over this, too?

Best regards,

Dirk

Dear John,

since you are from the US, maybe we can discuss this personally? Right at this moment I am at the MS&T conference in Montreal, any chance you are here, too?

Best regards one more,

Dirk

Dear Dr. Lehmhus,

Maybe other phenomenon appears, such as inhomogeneous of the thickness or property in small scale, which may affect the deformation in the film, it perhaps induces stress or strain concentration during deformation process. It might induce the rupture earlier than usual.

Regards

M Zheng

Dear Dr. Lehmhus,

I would expect that your colleague Volker Uhlenwinkel (IWT Uni Bremen) should be an interesting person to talk to. He is active in the spray atomization of metal passing via a thin metal film.