Recipe/Theory/Ingredient evaporation
Most products are created by processing one or more ingredients. This processing can be explicit through cooking, grilling, etc. Or it can be implicit through simple storage. Many of these processes involve heat (even simple storage).
These processes will influence the water content of a product. Some products will dry out (think of nuts). Different ingredients contain different amounts of water. Different ingredients will release their water differently during drying.
The ingredients shown on a product are listed by weight as used in the product creation.
Single ingredient products give us some idea how this is handled. A product like tomato puree only has one ingredient: tomatoes. Most tomato purees also say something about the drying (double or triple concentrated). But for many other products it is not indicated how well they are dried (nuts for instance). (Cheese often shows the fat percentage in the dried product (no water left?))
One would expect that drying does not affect the nutrients: if there are x% of a nutrient in the original ingrient, there will also be x% in the dried ingredient, i.e. fat, carbohydrates, fibre, proteins and salt do not evaporate.
Evaporation formalisation
Most products do not specify how much of the ingredients (by weight) were used to create the end product, but there are exceptions. Some appelstroop products do specify this. These products boil the water out of apples to create a thick syrup. As many of these products use only one fruit happle), we can see what happpens. This product for instance states the 7 kg of apples were used to create 450 grams of syrup. So in the cooking process 6,55 kg were lost. We assume that most of this is water, but there might be some volatile components lost as well. You can smell this. But the apples were also peeled and had their core removed.
We can turn this in a loss formula for any product where the original ingredients have processed:
(1a) weightoriginal = weightprocessed + weightlost [grams] ٖ
or
(1b) weightprocessed = weightoriginal - weightlost [grams] ٖ
You can express the weight lost also in terms of fractions (expressed as percentages). Thus in creating appelstroop we lose some 95% of the original weight. As a formula:
(2) weight_fractionlost = ( weightoriginal - weightprocessed ) / weightoriginal [%]
For many products unfortunately it is not indicated how much ingredients were used to create the processed product. We have only the values in the nutritional table to go by. And this data is specified in relative terms, i.e. the weight with respect to the processed product. And the nutritional table only specifies the nutrients. Adding the nutrient percentages almost never adds up to 100%. We suppose that the difference with 100% is the water content of the product. Thus:
(3) water_fraction = 100% - Σi=1allnutrient_fractioni [%]
or more short:
(4) water_fraction = 100% - nutrient_fraction_sum [%]
Formula 4 can be expressed for the original product and the processed product, giving a water_fractionoriginal and water_fractionprocessed.
Using the approach in (4) we reformulate (1) .
(5a) weightprocessed = weight_nutrients_sumprocessed + waterprocessed [grams]
and
(5b) weightoriginal = weight_nutrients_sumoriginal + wateroriginal [grams]
Thus:
(6a) weight_nutrients_sumprocessed + waterprocessed = weight_nutrients_sumoriginal + wateroriginal - weightlost [grams]
Or
(6b) weightlost = weight_nutrients_sumoriginal + wateroriginal - weight_nutrients_sumprocessed - waterprocessed [grams]\
Now (6) must also be rewritten in terms of fractions with respect the total weight of the processed and original products. Dividing (6b) by weightoriginal we express the weight loss in terms of the original weight:
(7a) weight_fractionlost,original = weightlost / weightoriginal = (weight_nutrients_sumoriginal + wateroriginal - weight_nutrients_sumprocessed - waterprocessed) / weightoriginal = weight_nutrients_sumoriginal / weightoriginal - weight_nutrients_sumprocessed / weightoriginal + (wateroriginal - waterprocessed) / weightoriginal
(7a) (weight_nutrients_sumprocessed + waterprocessed) / weightprocessed = 100% [%]
(7b) (weight_nutrients_sumoriginal + wateroriginal - weightlost) / weightprocessed = 100% [%]
Expanding (7b):
(7c) (weight_nutrients_sumoriginal + wateroriginal) / weightprocessed - weightlost / weightprocessed = 100%
We need to normalise 7b to the total product weight of the original product, so multiplying by weightprocessed / weightprocessed and developing the terms 7b becomes:
(8b) (weight_nutrients_sumoriginal + wateroriginal) / weightprocessed * weight original / weight original - weightlost / weightprocessed = 100% [%]
(8c) ((weight_nutrients_sumoriginal + wateroriginal) / weightoriginal) / weightprocessed * weightoriginal - weightlost / weightprocessed = 100% [%]
Applying (7b) in (8c) gives (1) back again, so no errors were made:
(9a) 100% * weightoriginal / weightprocessed - weightlost / weightprocessed = 100%
(9b) weightoriginal / weightprocessed - weightlost / weightprocessed = 1
But instead of arguing the nutrients out of the equations, we like to keep them in, as we have this information available. And we will assume that no nutrients are lost during processing, so weight_nutrients_sumprocessed = weight_nutrients_sumoriginal.
Can we rewrite the formulas (7), so that we can relate the nutrient fractions for the original and processed product and find the evaporation?
This paragraph is very dense, but the application is simple. Working with fractions quickly introduces errors, as you might be comparing apples to oranges. So it was necessary. But probably it can be presented more straightforward.
Single ingredient examples
In order to check whether the final formula for evaporation makes sense we can check it for a few products. We use the CIQUAL category data for this, as it is probably consistent.