High bandwidth linear viscoelastic properties of complex fluids from the measurement of their free surface fluctuations

Abstract

We present a new non-invasive optical method to measure the linear viscoelastic properties of materials, ranging from complex fluids to soft solids, within a large frequency range (about 0.1–10⁴ Hz). The surface fluctuation specular reflection (SFSR) technique is based on the measurement of the thermal fluctuations of the free surfaces of materials at which a laser beam is specularly reflected. The propagation of the thermal surface waves depends on the surface tension, density, and complex viscoelastic modulus G*(ω) of the material. The SFSR signal results from the contribution of different surface modes, and we discuss the leading effect measured as a function of |G*| and frequency. For known surface tension and density, we show that the frequency dependent elastic and loss moduli can be deduced from the fluctuation spectrum. Using a viscoelastic solid (a cross-linked PDMS), which linear viscoelastic properties are known in a large frequency range from rheometric measurements and the time–temperature superposition principle, we show that there is a good agreement between the rheological characterization provided by rheometric and fluctuation measurements. We also present measurements conducted with a complex fluid: a supramolecular polymer solution, formed from H-bonded molecules. At low frequencies, the agreement with rheometric measurements is again very good. We further investigate the high frequency rheology of the supramolecular polymer solution, and show that it behaves very similarly to supramolecular polymer solutions formed by wormlike giant micelles.