Simulation Results. Still Undergoing validation
I've finally managed to produce an aggregate simulator that agreed with two of de larrard's simple cases. The code is awful and has to be recompiled for every run as it's still very much a work in progress. The cunning old badger fails to give you a couple of the constants you need to duplicate his work probably because he'd like to sell you his simulator.
For my first run not using canned data, I tried an analysis of of Walter's mixture from <A href="http://www.cnczone.com/forums/showpost.php?p=312253&postcount=1639">Post 1639 </A>
Using the upper value each size range walter gave in the post and assuming .03mm for zeospheres, I asked the simulator what the packing density should be.
Since it works by volume, I assumed that 25% by volume of the solid fraction was taken up by the zeospheres and that 15% each were taken up by the other quartz fractions.
The model thinks that the mixture contains about 29% voids if poured into a container with no epoxy. If vibrated, it is expected to compact to 27% voids. If vibrated under pressure, the model expects it to compact down to 20%. The book indicates that vibration under pressure is the most effective method.
It also says that the hypothetical best compaction this mixture will achieve is about 15% voids.
As a result, I think this mixture suffers from the problem described recently of using a small quantity of epoxy but not enough to fill the voids. This mixture will be too dry if if less than 20% epoxy by volume is used but 30 percent is the conservative figure to ensure no voids.
Walter hypothesized about the zeospheres making the mix dry. I ran another model calculation evening out the volume percentages of the various components to 16.6 percent of each. 29% 27% 19% and 13% were the void percentages for poured, vibrated, vibrated under pressure, and hypothetical maximum compaction. I further ran the model asking it to optimize the density by changing the amount of zeospheres. It said that when vibrated under pressure that 16% zeospheres by volume would have been optimal yielding 20% voids.
It must be stated that I haven't fully got this validated yet and I was forced to assume values for some constants based on literature values. As far as I know however, this does give a rather fair relative notion of what is and isn't going to work well although it may be off a few percent in the absolute density.
--Cameron
Explanations of compaction and my untested E/G manufacturing process
Quote:
Originally Posted by
lgalla
I don't understand vibration under pressure or vacuum.I thought these were separate processes.If you press,in theory the aggregates will lock together and vibration cannot occur or be useful.If you vibrate to success the aggregates are aligned and further pressing will only compress entrapped air as aggregates and epoxy are not compressable.
Larry,
The model I am working with does not take into account the epoxy directly. Aggregates will pack together greatly increasing their densities as they are given the energy to overcome the friction that makes them site where they are. Based on de Larrard's lab work, "de Larryard" 's theory of vibration efficacy is flawed. Vibration causes the aggregates to oscillate in place and the oscillation transforms the system from one govenerned by static friction to one that is goverend by dynamic fricition. In non-engineering english: "A moving object is easier to keep moving with friction losses that a non moving object is to get moving under the influence of friction."
In essence, vibration causes the mass of aggregate to behave more like a fluid than no vibration but it is a fluid with a high "viscosity". It will flow but pressure will encourage it to flow faster and farther. When this solid fluid flows, the particles pack together as densely as the energy input can force them. If you simply vibrate a mixture, it will flow and compact under the influence of gravity. If you vibrate the mixture under pressure, it will flow and compact more.
While it is true that a bit of compression with a weight could in theory trap a tiny bit of air at the boundary between the lid and the mold, I'm not thinking this is a huge problem although lining the mold with some RTM release paper probably would solve this.
Quote:
Originally Posted by
lgalla
Mixing under vacuum is probably the most useful starting point with enough epoxy to fill the voids.Tamping as walter has done is probably a good method as a previous post I made on Ramed earth.
Good concrete has 7%voids.Does anyone remember the claimed density of commercial E/G?From this we will be able to calculate the void content assuming 93% aggregate.
Tamping is probably a good method of compacting but I don't have a number for the model to predict what it does so unless a whole bunch of measurements are made, I can't tell you anything about it other than it sounds good which is why I haven't discussed it today. If it's similar to rodding of concrete or aggregate, it's not as good as it sounds however.
The model and studying that I have done explain what happens to a box of rocks when it is compacted by pouring it, vibrating it, rodding it, and vibrating it under pressure. When the epoxy enters, the system gets more complicated. I'll explain my reasoning about what happens but I'm not sure that there is a wide body of published literature about anybody really knowing what happens.
The first problem is that the amount of epoxy needed to fill all voids in the "box of rocks" is dependent on how much the box of rocks has been compacted together.
Let's do a thought experiment with a big box of marbles. If this were in the geometrically regular face centered lattice pattern, it would have a packing density of 74% (percentage of the box volume). If any less than 26% epoxy was used (also by volume), there would be either internal voids or the top layer of marbles would not be embedded in epoxy.
If marbles are randomly dumped in the box, literature values show that the density is generally between 61% and 64% (percentage of box volume) and it depends how the marbles were treated after they were dumped in the box. In short, the actual percentage of the box volume depends both on what is put in the box and how it was put there. Even though it is the same box and the same marbles, in this case between 36% and 39% epoxy will be needed to fill all of the voids. Whether it's 36% or 39% depends on how and how much much the box is perturbed during and after the addition of the marbles.
You can think of it as the marbles wanting to pack together with as high a density as possible but that requires energy. They marbles get energy from gravity and pressure and vibration but energy is used up by friction between the marbles themselves, friction between the marbles and the box and drag if the marbles are in the box with a fluid like say epoxy.
Without knowing the amount the marbles would pack together if beaten on mercilessly (theoretical value), the size(s) of the marbles, and the amount of beating they've taken, it can't be predicted from theory what the density will be.
So in short, if you randomly distribute less epoxy into the mixture than the volume of the voids, even under vacuum, you will still have voids. These will just be voids that are filled with vacuum or epoxy vapors or something and they will likely end up filled with air when the system equilibriates after coming back to atmospheric pressure. The better the system is compacted however, the less epoxy will be required to fill the voids.
According to the theory Binder Skin Theory of Gamski as put forward by Gupta, the maximum strength actually occurs at a point with slightly more epoxy that the de Larrard model predicts. Gamski postulates that a 30um layer of epoxy must surround every particle for the mixture to be maximally effective. Thus, the epoxy required will never be less than the amount in the de Larrard model but it could be more depending on the veracity of the Gamski model in light of accurate predictions of the packing density.
In short, vacuum will remove the layer of adsorbed air, water vapor and other bad things surrounding the aggregate and keep them away such that the epoxy has a chance to fill the voids. The epoxy however still requires energy to flow into the voids. The energy that the epoxy can use to flow into the voids comes either from its weight, external pressure, and in some cases its temperature. The epoxy is opposed by the surface energy of the aggregate. When the surface energy of the epoxy becomes higher than the surface energy of the aggregate as happens near the end of the cure cycle, the epoxy has insufficient energy to penetrate voids and will stop trying.
The surfactants that Walter and I have acquired drastically lower the surface energy of the epoxy making it as easy as possible for it to smoothy flow around and between aggregate particles. Unfortunately however, if the epoxy runs out of energy before it fills all of the voids, then you will be left with voids even if they are filled with vacuum! It is not true that Nature abhors a vacuum: it only true that checkbooks abhor vacuum pumps though it's not pertinent.
In summary, deairing additives and surfactants are added to the system to make sure that the epoxy has enough energy to go where it needs to go and to minimize the amount of energy required (aka trouble on our part required) to get the epoxy to go there.
Vacuum ensures that adsorbed air and other adsorbed chemicals don't cause bubble voids. Air removal additives help to ensure that bubbles that are filled with air break and rise to the surface. Surfactants make sure that it takes the epoxy as little energy as possible to flow into the spaces between aggregates. Coupling agents form either hydrogen (weak) or covalent (stronger) chemical bonds between the aggregate and the epoxy increasing the strength of the bond between the epoxy matrix and the aggregate.
The additives except for coupling agents do little to alter the fundamentals of the system: they just make it easier and more forgiving. The fundamental problem is still that to get a mixture of maximum modulus, a mixture of maximum possible density must be created. To create such a mixture requires picking the aggregate sizes and percentages in such a way that the mixture can be compacted to a maximum box fill percentage.
Quote:
Originally Posted by
lgalla
Another pitfall I see is:if I take a block of granite 12X12X12 and brush on epoxy I may acheive 99% granite/epoxy mix or better.John said before "jigsaw puzzles in the dark"If you took little square granite pieces and glued them to gether you would have very low epoxy demand,but questionable strength????
Surfactants&wetting agents:Epoxy's are a difficult mix,.05% surfactant is very difficult indeed.The present problem is aggregate packing ratios,epoxy viscosity etc.Surfacants will not help a void.I have developed A-void and have to retire.
Larry
I respond to your pitfall thusly:
The engineering models used to describe the phenomena in these types of composite materials require that the materials in question have bulk properties based on random distribution of the components. Your granite jigsaw puzzle and epoxy countertop paint both violate the assumptions of the models for continuous composites. These two cases can however be modeled as blocks of granite glued together and epoxy paint on a countertop respectively and their properties can be easily predicted: much easier than E/G.
You can avoid a void with a surfactant if the problem at hand is the epoxy not flowing where you need it to go. Only more epoxy will avoid the issue of the vacuum void as described above. If you use any less epoxy than required by the de Larrard model, then you have an ill performing dry mix regardless. It may still require more according to Gamski but every exact epoxy mixes are likely going to be fruitless unless you know the packing density of your mixture after it is compacted either from models or trial and error.
This does however bring up another problem. Neither the theory or the practice work correctly if the aggregate sizes aren't randomly distributed. Under these circumstances, in direct opposition to Walter's theory, I'd have to say that a great deal of care needs to be taken to thoroughly mix the aggregates beforehand. Mixtures without similar proportions for all size ranges may separate when compacted and thus the properties will not be as desired.
According to the above constraints, I'd mix the aggregates thoroughly in a separate box than the storage container of the individual aggregates. I'd treat the aggregate with the appropriate coupling agent and then allow the mixture to dry for sufficient time preferably at elevated temperature and under vacuum.
I'd then mix the epoxy and add the deairing agents and the surfactants mixing thoroughly knowing exactly how much epoxy I had. I'd then pour the mixed epoxy into a fresh cup to avoid unmixed residues. I would then weigh out the exact amount of mixed aggregates required for the proper mixture and convert to volume using the specific gravity(checking to make sure that the epoxy quantity was greater than or equal to the de Larrard voids; also remembering that the actual mix properties are governed by volume not weight).
I'd then add the mixed treated aggregate slowly to the epoxy mixture until all of it was added. Curiously in this case the right amount of aggregate will probably look as though it is way too much since the whole thing will take up more volume than it will in the final product. I'd then place this mixed batch under vaccum to get the air out. Finally, I'd place the mixture into the mold, even if there seemed to be some sand or rocks sticking out. Finally, I'd put the lid on the mold followed by a couple of heavy cinder blocks and activate a vibrator attached to the bottom and vibrate the bejesus out of it until a few minutes before the mixture gels. (This assumes using one of the equally proportioned mixes that won't segregate under vibration). I'd also put a few heat lamps on the mold to increase the crosslink count in the epoxy to help keep the stiffness up at temperature.
There you have it, as close as I can bring you to a deluxe recipe for E/G without having made any myself yet. Just a bit of electrical conduit and 16 sheets of concrete board and I'll have a laboratory and be able to get cracking! I imagine my coupling agents will be here from dow Monday or Tuesday. It's been an interesting day in E/G land.
Walter,
Good work on the new mix. Seeing the cups however, I think you have way too many zeospheres. From what I've learned lately, you only want a couple percent more by volume of them than the other stuff. If you have the list of grades you're using and the weight percentages of each and the model number on your zeospheres, I'll tell you what I predict the packing density as.
Graybeard,
That looks like a heck of a spin casting contraption. It's very different that the concept that I had but I suspect that it will work pretty well. It will make tubes with the very interesting and good property than the highest strength materials are to the outside and any excess epoxy will end up on the inside where it doesn't matter. I'd suggest starting the spin out at low RPM's to make sure everything is coated and then gradually increase the speed to blazing fast while the epoxy is still liquid. This reminds me of the Rheometer apparatus used for determining the properties of concrete that I read about!
Peace all,
I've been writing this message for way too long.