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Surface fluctuations of complex media

Christian Frétigny, François Lequeux, Basile Pottier,Laurence Talini and Emilie Verneuil

The free surface of a liquid is flat at a macroscopic scale but is distorted at a microscopic scale under the action of thermal motion. The propagation of the thermally excited waves depends on the medium properties, and in particular on its mechanical properties. We have developped an optical technique that probes the thermally excited waves on free surfaces or interfaces and that we named Surface Fluctuation Specular Reflection (SFSR) spectroscopy. Its principle consiste in measuring the fluctuations in the position of a laser beam that reflects on a free surface or interface.

The beam is focused on the probed surface. Its reflected part is centered on two quadrants of a photodiode. The fluctuations in the position of the beam are therefore measured through the fluctuations in the voltage difference delivered by the photodiode. With a beam size close to 50µm at the focussing point, it is possible to measure surface roughnesses of a few Angströms, which correspond to the free surface roughness of water, for instance.

The contributions of several spatial modes are taken into account instead of considering only one spatial mode as in a scattering technique. The measured signal includes no spatial information but it is much more intense than the one in a scattering experiment.
The noise measured through the fluctuations in the position of the reflected beam can be characterized by its power spectrum density (PSD, squared modulus of its Fourier transform) that provides a measurement of the mean squared value of the noise.

PSD’s of the noise measured at the free surface of silicon oils of viscosity 20 times (red), 100 times (blue), 350 times (orange) and 1000 times (green) the viscosity of water (top figure), and at the interface air/rubber (bottom figure). The black lines represent the computed PSD’s, using the values of the elastic and loss moduli measured with a rheometer (insert) for rubber.

We have measured the thermal capillary waves propagating at the free surface of viscous fluids (figure on the left), as well as the elastic waves propagating at the surface of a viscoelastic solid (a rubber sample, figure on the right), both in a very wide frequency range. The measured signals are related to the properties of the probed media. In the case of viscous fluids, the signal depends on the fluid viscosity, density and surface tension. In the case of viscoelastic materials of known surface tension and density, the frequency dependent elastic and loss moduli can be deduced from the fluctuation spectrum. We have thus measured the linear viscoelastic properties of soft solids (cross-linked PDMS) and complex fluids (supramolecular polymer solutions) in a wide frequency range.

Elastic and loss moduli of a soft solid (cross-linked PDMS, top figure) and a complex fluid (supramolecular polymer solution, bottom figure) measured using SFSR measurements (full and dotted lines) and compared to rheometric measurements (symbols).

More recently, we have studied the surface fluctuations of liquid films supported by solid substrates, either plane or structured. For film of very small thickness (i.e. smaller than 100 nm), measurement of surface flucutuations provides a determination of the hydrdynamic boundary condition at the solid wall. Nous avons ainsi mis en évidence qu’avec certaines huiles il existait une longueur de glissement négative à la paroi solide, correspondant à la formation d’un couche de molécules immobiles au voisinage de cette paroi. L’épaisseur de la couche immobile est de quelques nanomètres, et elle dépend de la nature des molécules du liquide. Ces résultats permettent de mieux comprendre comment sont modifiées les propriétés d’un liquide près d’une paroi solide.


Silicon oil thin layer spread on a liquid substrate. The coloured fringes result from the non uniform thickness of the film.


  • Boundary condition in liquid thin films revealed through the thermal fluctuations of their free surface, B. Pottier, C. Frétigny, L. Talini, Phys. Rev. Lett. 114, 227801 (2015).
  • Surface fluctuations of liquids confined on flat and patterned substrates, B. Pottier, E. Verneuil, L, Talini and O. Pierre-Louis, Phys. Rev. E 89, 052403 (2014).
  • High frequency linear rheology of complex fluids measured from their surface thermal fluctuations. B. Pottier, A. Raudsepp, C. Frétigny, F. Lequeux, J.F. Palierne, L. Talini, J. Rheol. 57, 441 (2013).
  • Two beam surface fluctuation specular reflection spectroscopy. A. Raudsepp, C. Frétigny, F. Lequeux, L. Talini, Rev. Sci. Instrum. 83, 013111 (2012).
  • High bandwith linear viscoelastic properties of complex fluids from the measurement of their free surface fluctuations. B. Pottier, G. Ducouret, C. Frétigny, F. Lequeux, L. Talini, Soft Matter 7, 7843 (2011).
  • Probing thermal waves on the free surface of various media : Surface Fluctuation Specular Reflection Spectroscopy.
    A. Tay, C. Thibierge, D. Fournier, C. Frétigny, F. Lequeux, C. Monteux, J.-P. Roger and L. Talini, Rev. Sci. Instrument 79, 103107 (2008).