Multi-Frequency Ultrasonic Shear Waves Rheology for Soft Materials Monitoring in Cosmetics

摘要

Cosmetic products can be considered as complex fluids, like polymers and colloidal suspensions. To describe their mechanical structures, it is possible to monitor the complex shear modulus, a rheological quantity representative of the material elasticity and viscosity. Among others, Rouse and Zimm settled a model in which, at short times, these kinds of materials presents a complex shear modulus that follow a power law over the frequencies. When one look to the state of the art, it seems that the power law coefficient is linked to the intrinsic structure of the product: from zero for an elastic solid, to one for a viscous fluid. This article tries to explain this phenomenon using the fractional derivative theory, and to get an estimation of the coefficient relying on micro-rheology. The first experiments have been performed on water, gels and cosmetic emulsions. The results show that for structures closed to Newtonian fluid the coefficient is around one and it decreases when the fluid differs from this ideal case. The coefficient evolution over the time for gels is linked to the gelation phenomenon. As a consequence we can ensure that this quantity is correlated to the material microscopic structure.