(Written Jan 2014)
This is a culmination of 10 years of my life! I am 26, so that is 39% of my life. Therefore, I have to give some backstory.
My dad’s dissertation was analyzing stability of other peoples’ solutions of this thing called the “Dusty-Gas Model (DGM)” applied to Chemical Vapor Infiltration (CVI). He was trained in scientific computing, so his advisor had no interest in doing experiments. Thus, the first 4 years post-PhD he was struggling to find someone to either fund or work with him to get some experiments done to verify a stable model. He succeeded in finding funding, getting people to work with him, only to have his contract yanked from under him by the university (it was more of a congressional line item contract, that he got with the university lobbyist, so they could do that). All this time, I was tasked with discovering the chemistry behind carbon-carbon CVI.
I hate chemistry. You wouldn’t get that from my CV, but people keep putting chemistry/chemical engineering projects in front of my face and the fluid dynamics stands out.
I found every hydrocarbon or radical gas phase reaction from every source I could get my hands on and typed them up in an Excel spreadsheet. Think Alfred Kinsey’s studies on crickets and sex but a lot less cool. I did connectedness graphs of these chemical reactions in my head to find a set of reduced reaction pathways that could be coded up with the DGM. I got an Honors thesis out of this, but after the grant disappeared we were out in the cold for verification.
A year later, I was refusing to have anything to do with chemistry. I went to MIT, and had an internship for the gov’t coding up everything I got my hands on. People kept handing me a recursive processes they did by hand, that is why we created computers. The next year I had the option to work for a potentially cooler gov’t body (ie not coding) when my dad showed me cost-benefit analysis that proved DC<<Oak Ridge where I could live with my grandparents and bike to work. So much for living the dream.
Picture by Danielle, http://journalitico.com
At Oak Ridge I spent my first 8 weeks banging my head on a desk, translating code from FORTRAN 77 into MATLAB and trying to figure out why my code kept giving me nonsense. To ease the headache, I added excessive complexity into the model, computing the viscosity of a mixture, diffusivities from Lenard-Jones collision integrals; I stuck in a temperature gradient for good measure. My advisor (dad) suggested I model the step function inlet conditions with an exponential function. I was doing this at the same place where the Dusty-Gas Model was postulated. Somehow, in my last 2 weeks I got the code to work. The result: a bunch of pretty pictures, that were dead wrong!
How do I know they were wrong, because the following fall, I took a class where I did stability analysis on my algorithm and proved it was unstable.
The following spring I went through another class where I started running faster away from chemistry. I thought I might reach escape velocity. I took a class where I got to model and experiment flow over a leaf. It was great! The summer, I took 2 classes so I could graduate on time, including a course in security studies. I was looking to get back to the gov’t.
Senior spring, I am sitting in a class on Topology. The professor is trailing off in every way imaginable. His handwriting followed his voice in a successfully over-damped situation towards an amplitude of zero. I tried asking questions. You know, that the thing you do to let the professor know he is not just talking himself and people that want a grade. That thing you do to get a professor to say, “Wait, you really want to know why I spent my life learning and working with this, well…”
After 3 days, he did not bite and I walked out. Called my dad and asked him if I could work on the project as my senior thesis. He had gotten some people to run some experiments with him at NIST. On Atomic Layer Deposition, but all deposition is ALD if you look close enough. Seriously, though, the derivation of the DGM does not rule out looking at flow through 1 tube or 200 or tortuous sponges. That first one is the first example in the book, literally! My BS thesis looked at the development of ALD, its challenges, a proper development of the DGM, and some dimensional analysis on the combined problem. The coolest thing about ALD as opposed to CVI is that there is only 1 reaction at a time. No more chemistry! Through another class I was taking that semester, I learned to apply an IMPES scheme to the model that are unconditionally stable. The seed of the idea of course coming from my dad. At the end, the MIT prof who I had roped in to be my thesis advisor, read it and told me I should publish and thus began the long road to publishing
It was rejected twice by the same journal. The first reason was they did not believe there was anything novel in the scheme, ie not “mathy” enough for their journal. While no one has done it, the solution is a simple exercise in applying a known methodology to the system so, I’ll buy that. The second was the ALD process needs Markov/random-walk style modeling. You’ll have to read the paper, but the gist is it can be approximated as a continuum, and I have enough dimensional analysis and experimental results to prove it. The journal it is published in is definitely the most appropriate. Moreover, there is little you can get as an experimentalist from a statistical model.  After submitting to a more appropriate journal, one reviewer raised the same random-walk complaint as above, another told me to continue pushing at the dimensional analysis. Ok, not really, he asked what does this mean to an experimentalist. I originally handed that question to my father, the co-author, but being the mathematician, he just explained the beauty of the physical model again. I went and started digging around the modified Damkohler number that the DGM had belched up and realized there is so much one can get from that number. If the paper still has grammatical mistakes in it, your eyes are better than 11 other peoples, and we are sorry we missed them (4 from the rejects, 4 from the accepted, and 3 from the authors and a wife).
So, in all its beauty, here is a working simulation of the nonlinear DGM applied to ALD. There is a lot of overkill in there: expressions for finding viscosity from a mixture as it changes, analytic expressions to find diffusivities both Knudsen and Binary as a function of concentration. There is also dimensional analysis on the entire problem that results in this cool number that you can fit a bunch of data to. Sure the entire thing is in 1D but the physics is the important part.
 I don’t really hate chemistry. Its just no one told me I needed to learn Abstract Algebra and Group Theory before I took it. Or that Gibbs free energy really governed the universe.
 I hope to run more experiments this summer and finally publish that.
 I also hate statistics. Maybe there is something deep and fundamental in that subject, but until I find it…
 I took an Abstract Algebra class and at the end, I think I might have been daydreaming before hand, I asked the professor “what is this for” and he gave me the blankest look I had ever seen, silence crept across the room, and I knew I was no longer a mathematician.
 If you have seen it before let me know, otherwise, it looks like a Damkohler-Jones number to me J