## Humectants

### Quick Start

We like to add humectants to coated formulation to "keep water in". But it's tricky to work out the true effects of adding a few % of a humectant.

### Credits

The theory and data are from a mix of resources.

### Humectants

RH
Saturated % water
Wt % Humectant
Humectant

% Water in Humectant
Wt % Water
Water isotherm

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### Keeping water in the surface

We have some coating or film in contact with air. You happen to know that at even when immersed in water, the water content is too low, say 0.5%. For whatever reason, you want to increase the amount of water - a typical example might be a skin cream. You add an humectant which you know likes to absorb water from the atmosphere. If you need, say, 2% water in the final product, how much, of which humectant, should you add?

One approximate way to answer this is to calculate the % water at equilibrium in the humectant at a given RH, then take the simple assumption that the total water in the system is that value, reduced by the % humectant added.

For common humectants, the equilibrium water can be calculated via the Norrish equation which tells us that for a given RH there is a molar fraction of water, xw in equilibrium with a molar fraction of the humectant, xh depending on a constant K, available in the literature

x_w=(RH)/(e^(-Kx_h^2))

The K values used (you can find them in the code) are taken from a paper by Baeza et al1 which they have shown to be valid across the wide range of RH levels of interest to us.

Via some simple arithmetic (converting mole fraction to weight%) based on your chosen RH, saturated coating content (and a simple linear RH dependence), wt % of humectant and choice of humectant, we can calculate the total wt % of water in the coating.

The default graph shows the typical plots from the Norrish isotherm world. Those of us more familiar with water isotherms can select that option.

### Use with caution

The initial beta version prompted plenty of discussion about what it means to add a humectant and what effect it has on the system. Although the default assumption is that the humectant simply adds more water, it is clear that this hardly describes the full range of effects of these additions. Some alternatives, which the app cannot cover are:

• The humectant and water have a synergistic effect on the system. This is certainly the case with skin as the humectant is interacting with the complex NMF (Natural Moisturizing Factor) in the skin.
• The humectant might be concentrated at the surface or somehow creates a strong surface effect so that things like conductivity of static electricity are increased; this is likely to be the case in hair care.
• The humectant reacts into the system, changing its structure and its water sorption capabilities.
• Because desorption isotherms show hysteresis compared to absorption ones, the humectant keeps a relatively large amount of moisture in a drying coating, allowing the structure more time to relax. We can loosely call this a "kinetic humectant effect" though purists have good grounds to disagree (isotherms are thermodynamic...).
1

Rosa Baeza et al, Evaluation of Norrish’s Equation for Correlating the Water Activity of Highly Concentrated Solutions of Sugars, Polyols, and Polyethylene Glycols, Food Bioprocess Technol (2010) 3:87–92