Mathematical modelling for better cosmetics – L’Oréal

Mathematical modelling for better cosmetics – L’Oréal


My name is Eva Bessac I am responsible for scientific calculation for the hair business. I have been working for L’Oréal for 13 years. I discover the wealth of potential
in mathematics and statistics via relations with other more traditional expertise in this environment. For shampoo for example,
we had a formula that was slightly cloudy. It not as obvious as all that, but this is unacceptable
for a finished product to be put on the market. Experts in the physical-chemical department
gave us a way of solving this problem. Their advice was to change the balances between
two surfactants used in the formula. Surfactants are molecules enabling the shampoo
to wash and also to lather. We drew up an experiment plan. It consisted of exploring a field
concerning the concentrations of these surfactants. We evaluated a wide variety
of concentrations of one of the surfactants and then very variable concentrations of the other one. Each point became a formula that was manufactured.
From this formula, we measured the limpidity. We could have just kept
the most limpid formula out of all those we studied. But we went a step further by modeling the results.
In particular, we can examine the most optimal area. By drawing up another mathematical model we can represent the results of
our experiment plan in the form of this graph Here, we calculate a ratio between the two surfactants.
This is the indicator for the formula’s composition. And we represent the limpidity result according to the ratios. We can see an equation appearing.
Based on this model, we made additional formulas. They are the pink dots on this graph. One of these formulas is what we call really limpid. Here, I am taking you into the world of color. Color is represented in a 3-dimensional space. The first dimension, L,
gives an indication of the clarity. Lower down is dark and higher up is lighter. The second dimension, A
shows the quantity of red in the products. The third dimension, B
shows the quantity of yellow in the products. Natural hair occupies
a very narrow space in this colorimetric area. Here is black hair, and blond hair is here. This whole cloud of dots represents colors
we know how to make, we master and sell. As part of a project on new hair dyes,
we decided to widen this pallet of colors. These new dyes will give
greater richness to our pallet of colors because by mixing them,
they will add to our existing colors, make them deeper and in some cases for those interested,
give flashy colors, even these colors here directly. When we measure the color of the new dyes,
we can add more dots to this representation. We can see that they bring points that are very different
from the colors we usually see on the market. This is where the model can help. The model is calculation time,
but it is very short compared to the experimentation time and it instantly gives us
the potential colors achievable using these new dyes. For example, here we can see that we can be
a little more neutral than a natural color. Above all though,
we will examine going further in highlights. The model has completed its role
when it has provided the basis for the recipe. The final stages, fine tuning the color,
the color experts will do. Before working at L’Oréal,
I had no idea that we could use mathematical models and statistics to develop cosmetic products. I contribute to L’Oréal Research by using tools that I like.

About the Author: Earl Hamill

Leave a Reply

Your email address will not be published. Required fields are marked *