I have just been entertained by a YouTube video that explains the saga of Nikola Motors, who were at one time valued more than Ford, based upon a truck chassis that was towed up a hill and filmed rolling down: https://www.youtube.com/watch?v=88fWUZhYb04 It seems too incredible to be true, so how do such things happen? Generally (and not commenting specifically on the Nikola Motors case), I think that it is because there exist fraudsters and there exist individuals along with global corporations) who are gullible, but both are motivated by money or power (which amount to the same thing). I hear the phrase “fake it ‘til you make it” a lot, but this doesn’t explain the phenomenon, in my opinion. Instead, I think that the ‘game’ of the purported innovator is often to simply raise equity from gullible investors who are desperate to believe, and then ‘do one’. (For the benefit of non-British readers, this refers to the ‘moonlight flit’ where debtors ‘upsticked’ in the dead of night, never to be seen again.) Does anybody remember that the Republic of Ireland was, about 10-15 years ago, apparently about to become the next Qatar based upon unproven tight gas reserves on the border with the North? I was once asked to assess a technology that was, essentially, a thermodynamic power cycle that purported to draw heat at ambient temperature, create work (mechanical power) with no impact on the surroundings, and reject heat at the same ambient temperature. When I read the line that the Second Law of Thermodynamics had been busted, I stopped reading, and reported my opinion. (Believe it or not, a draft paper, seen by me, was audaciously submitted for publication to ‘Nature’. It is reassuring that it was kicked-out before being sent for peer-review.) The gullible still wanted to believe that it worked, but I persisted, and investment into this ‘ground-breaking’ power cycle ceased, but there remained some true-believers. To some people the luddite was me, long after I had failed to explain the entropy to them. If something appears to be too good to be true then it might be, but then again it might not. But, just like, say, transubstantiation, extraordinary claims require extraordinary evidence. Clever people emphatically do sometimes develop truly disruptive technologies, and there emphatically do exist ‘knockover’ commercial opportunities. If a company’s equity is largely due to management themselves, then this must tell one about their confidence in their technology; the ’game’ isn’t being played. Technological investment and adoption should surely be driven by science and verifiable data, rather than the charisma of a salesperson. Don’t trust me, but instead trust the data, and check it for yourself. Look where the equity to fund technological development has come from. Do the proponents of a particular technology have genuine ‘skin in the game’? Would, I wonder, investors post-Nikola Motors’ demonstration of the potential energy term of the First Law of Thermodynamics have proceeded had they bothered to look under the bonnet/ hood?

I’ve had a lovely year. I genuinely love talking to people about foam fractionation, and I’ve been doing a lot of talking this year because 1. The staggering efficacy of foam fractionation for the remediation of PFAS contaminated water streams has recently been demonstrated, and 2. The use of the Hydrodynamic Theory of Rising Foam for understanding the mechanism of foam fractionation (as is expanded upon in my book , jointly-authored with Bruce Li) is gaining traction amongst practitioners and academic researchers alike. This week I had an enjoyable chat with a research student who is working on foam fractionation. The student demonstrated to me excellent mechanistic understanding combined with a desire to apply the process. Great! There was a little point about dimensional (dimensionless) analysis that wasn’t fully understood however, and so I thought I’d write something about this herein. The keystone of the ‘mechanistic’ models that I developed for foam fractionation was the foam drainage law , which is an expression for the liquid superficial drainage velocity in a Lagrangian frame of reference that is moving with the bubbles. This was developed using the method of dimensionless analysis which is often misunderstood. In essence, it shows that the drainage velocity, non-dimensionalised as a ‘Stokes number’ is a function of the volumetric liquid fraction only. It doesn’t say what that function is, but merely that such a function must exist. I decided to fit a power-law relationship to drainage data because many behaviours in nature demonstrate such dependency, and it works very well. The dimensionless analysis reveals the dependency of drainage upon bubble size, liquid viscosity and density and the acceleration due to gravity; if one wants to foam fractionate on the moon, then this is the way forward! The fit is empirical, so my method isn’t completely mechanistic. Let’s call it ‘semi-mechanistic’, for the sake of argument. (It is worth noting that, during my conversation this week, I discovered that I wasn’t, in fact, the first to propose a power-law dependency of drainage upon volumetric liquid fraction; Miles et al. (1945) beat me to it. Thanks for telling me.) A better-known dimensional analysis is that leading to the Blasius relationship for the friction factor due to turbulent flow in a hydraulically smooth tube, where the friction factor is a power-law function of the Reynolds number. One can measure wall shear stress as a function of flow velocity, but correct application of Buckingham’s Pi-Theorem reveals the dependency upon liquid physical properties and internal pipe diameter too. This is long way from simply performing a curve-fit on an Excel graph. Many academic researchers dislike empiricism. Some think it is a kind of ‘cop-out’ that is employed by those who can’t develop a completely mechanistic model. I guess that, in some respects, it is. If I could develop a completely mechanistic model that can be employed in practise for foam drainage I would, but I cannot for reasons that I now describe: Leonard & Lemlich (1965) developed a foam drainage model that assumed that viscous losses were only in the Plateau borders and not the foam nodes. That is a good assumption for very dry foam, which fractionation foams generally are not. (Robert Lemlich of the University of Cincinnati was a titan of foam fractionation development but his work is often overlooked by some; when I was developing foam fractionation models I would always check if Lemlich had done it before, and often he had.) The viscous losses in the Plateau borders are a function of the surface shear viscosity, but one cannot measure this surface property to within two or three orders of magnitude (at best) and so the model doesn’t have any practical efficacy. Three decades later, Verbist & Weaire (1996) proposed ‘The Foam Drainage Equation’, but this was identical to Leonard & Lemlich save for the fact that they assumed that the gas-liquid interface was rigid. Stephan Koehler, when he was at Harvard, proposed an alternative drainage model in a series of papers that assumed that losses occurred entirely at the nodes, and then generalised his model to account for Plateau border losses. This was better, but still the problem of surface shear viscosity arose. (For wetter foams, the losses must be dependent upon surface dilatational viscosity as well, which is easier to measure in the lab.) For all the mathematical elegance of these drainage models, they are not of any practical use precisely because we do not know the surface shear viscosity. Thus, empiricism must be the way forward. My dimensionless analysis was not an attempt to combine the drainage models of Lemlich and Koehler, since Koehler had already done that. Instead, my drainage law simply offers an expression that is mathematically tractable (thereby facilitating its use in foam fractionation modelling) and works. When somebody can measure the surface shear viscosity of a gas-liquid interface with any certainty then we can talk; in the interim, I will stick with my empiricism for the purposes of practical process design. A significant proponent of the power of dimensional analysis in the process industries was the late, great, Prof John Davidson FRS who was arguably the inventor of fluidisation. I was fortunate to have him as a teacher and mentor. I know that John didn’t think that my drainage law was a ‘cop-out’! 15 years ago I spotted that a research group in Australia were ‘doing’ empiricism incorrectly with respect to some froth flotation data, in that they were proposing dimensionally-inconsistent relationships gained by curve fits on Excel. Poorly-performed empiricism can send the practitioner down the garden path, since dimensionally-inconsistent relationships only apply for the specific kit upon which the data was obtained. Thus I was prompted to write a ‘paper’ on the use of dimensional analysis in minerals processing . This is essentially just a lecture, and I discuss the development of Blasius first, before considering the foam drainage law. If you have got this far in my blog post, then you may like to take a look. The power of dimensional analysis in understanding complex process systems is immense, and foam fractionation is certainly a complex process system. It is unlikely that the performance of a foam fractionator within the Arctic Circle will replicate that operating in outback Australia, for instance. There will be a temperature dependency. Dimensional analysis has illuminated this dependency, such that we can estimate how foam fractionation will perform in extremely low temperatures, and we know how to make it work. And this was done without me trying to find my woolly hat.

I'm delighted to say that the paper 'PFAS Removal from Groundwaters using Surface-Active Foam Fractionation' that I have co-authored with colleagues Dave Burns and Pete Murphy from OPEC Systems has been published in the journal Remediation. In the paper, extensive site data are presented from the Army Aviation Centre Oakey (QLD, Australia) that demonstrate the remarkable performance of SAFF technology with respect to remediation of PFAS contaminated groundwaters.

Visualisation of the Hydrodynamic Theory of Foam in an 'app'

Steven Abbott's apps relevant to foam fractionation

Understanding how liquid fraction in a pneumatic foam changes with height