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