Thickeners: Thickeners commonly used in skin moisturizers are water-dispersible polymers and fatty alcohols. Normally, they are used simultaneously in skincare emulsions, as these formulations are more prone to destabilization.60 The list of the thickeners used in this study is on Table C-3 in the Supplementary Material.

Thickeners influence the product’s perception, particularly what is called the primary and secondary skin feelings.54,61The primary feeling is correlated to the viscosity perceived at the onset of the flow of the product (\(\eta_{1}\), viscosity at low shear stresses), while the secondary feeling corresponds to a much lower final viscosity, perceived during the product’s application (\(\eta_{2}\), viscosity at high shear stresses). Under such circumstances, the ideal value of \(\eta_{1}\) is between 1350 and 3500 Pa·s for creams and between 120 and 500 Pa·s for lotions. In contrast, \(\eta_{2}\) should be between 0.023 and 0.500 Pa·s for both types of product. This last viscosity interval corresponds to a shear rate of around 500 s-1 if the application is over small areas (e.g. face), or 5000 s-1 if the application is over large areas of the body.54
Composition-viscosity data for polymer thickened aqueous solutions,62 together with reliable theoretical models to predict the effect of the dispersed phase,63 were used to construct equations of the type \(log(\eta)=a+bx_{n}+c\phi\) (average relative error of 22%), for each polymer, and for both \(\eta_{1}\ \)and \(\eta_{2}\) (\(\phi\) is the mass fraction of oil phase). Since only one polymer is used, mixing rules are not needed. Fatty alcohols were used at a 2-4% concentration. As indicated above, all the formulations also included a fixed amount of mandatory ingredients, namely water, humectant (3% Glycerol) and preservative (0.7% Cosgard®).
Optimization problem : Product design variables and short formulation of the optimization problem for both case studies - in the form of (3) - are shown in Table 2.
Table 2. Product design variables and initial problem formulation