Fugacity

.....a culinary twist on an environmental concept

Fugacity is a word you may not know, though it comes from the Latin word fugit, meaning to leave or move on, as in tempus fugit....time flies.

Here, it will be used as a way of determining the distribution of flavour compounds in a cooked dish, for example, where spice flavours are likely to be concentrated. The theory is quite well proven and accepted in environmental work, where it is used to determine the distribution of one or more (polluting) chemicals throughout the region/s of interest. I am applying the same rationale to one pot cooking.

In environmental work, one first needs to define something which is called the unit world. The unit world (that to be considered) may include soil, water, sediment, air, vegetation and other biota, such as fish. The theory predicts, after suitable data manipulation, how a pollutant is likely to be distributed between the various parts of the defined 'unit world'. It is assumed that the pollutant is in equilibrium with its environment, that is, there has been time to exchange from, and to, each and every part of the unit world.

In culinary terms, the unit world is defined by the dish/es that are cooking. It is necessary to define the parts of the 'unit world', and estimate the volume of each part.
So, if we consider cooking a one pot dish such as a curry, the unit world may comprise: oil/fat, water, vegetables, meat, bones, the air above the ingredients, and maybe one or two other things which may be discussed later. We can estimate the volume of all the ingredients and the cooking vessel, and we could consider whether the pot needs a lid!
Next, we must consider which flavours we are interested in, and how much there is going to be of each. Then we need to find out a few things about each flavour compound, such as the molecular weight, solubility in water, vapour pressure and the octanol water partition coefficient. Have I lost you yet?
The molecular mass is a way of expressing the size (and therefore mass) of the flavour molecule, all flavour chemicals are very small molecules (<300 Dalton) compared to some other biochemicals such as proteins, starches, DNA and the like.

The solubility in water is self explanatary, but it will be temperature dependent. The vapour pressure is the pressure of the vapour phase of the chemical above its surface. It is also temperature dependent, and when a chemical's vapour pressure is equal to atmospheric pressure at the point on the earth where the chemical is, it is said to have reached its boiling point. The octanol water partition coefficient has been discussed above, but it is less affected by temperature.

So, we have a pot containing our ingredients, say a joint of meat on the bone, some fat/oil, some water, a little vegetable puree, and we must not forget the air above the cooking pot, and whether the pot will have a lid on (effectively producing a closed system) or lid off, meaning the flavour chemicals are free to disperse into the oven or the whole kitchen space! After cooking for an hour, we may assume that all phases (parts of our unit world) are in equilibrium, which means the flavours have had time to partition into every part of the dish, and the air around it.

So how do we work out where the flavour chemicals are? Well, it works the same as the octanol water partition coefficient (Kow) experiment above except, not only do we have a partition between the oil and the water (the Kow) but also between everything else as well. Relatively simple equations enable us to work out how much of each flavour compound there is in each part of the dish (the unit world). If we know how much flavour compound we put in and the volumes of our unit world, we can calculate where it will end up and the proportions of each. And the answers may surprise you.

Here is an example.

Firstly, we must define our unit world.
I will start with a one pot dish (a 10 litre pot with a lid on), containing water, oil, meat and vegetable puree. So the unit world, with appropriate volumes, is as follows:

pot (air space): 9 litres
water: 200ml
oil: 100ml
meat: 500ml
veg. 200ml

Next we must add some flavourings, say spices, which contain certain chemicals, say:

cloves containing eugenol
cardamom containing cineol
cassia containing cinnamaldehyde
pepper containing limonene, linalool, alpha phellandrene and 3-carene, among others.

We will assume we put in the same amount of each spice chemical (never true in practice, but see later)

Then we need to find the relevant physico-chemical data we require, put it all into a spreadsheet and carry out the calculations. We assume that ever part of the unit world (in our pot) is in contact with every other part, and that the dish is cooked for long enough for everything to come to a steady state (equilibrium). We also have to guess at the level of fat in the meat and the vegetable puree (I guessed 10% for the meat, and 0.2% for the vegetables).

to be continued......