PhD defence: Dynamic surface forces of confined ionic solutions: experimental measurements and theoretical modeling - Caroline Cramail (MODI)

This thesis focuses on the transport of ionic solutions confined at the nanoscale by dielectric solid surfaces. On an industrial level, this theme is part of the search for more efficient charged and nanostructured filtration membranes, for applications such as seawater desalination or osmotic energy recovery. Using a dynamic surface force apparatus (dSFA), we measure, near equilibrium, an overdamping effect resulting from the coupled restoration of the system's mechanical, electrical and diffusive equilibria. We model the dynamic surface force using a continuous and mean-field description, in which the dynamics are a linear perturbation of the equilibrium. Equilibrium is described by the non-linear Poisson-Boltzmann equation and the Derjaguin approximation, a theory of the electric double layer whose experimental compatibility has been verified for nearly 50 years. The fluxes (of volume, charge and solute) are also related to the (mechanical, electrical and diffusive) forces through Onsager’s matrix (1931), whose coefficients are calculated, following Smoluchowski’s approach (1903), by applying transport laws (Stokes and Nernst-Planck equations with advection) in the electric double layers. We compare our model for the dynamic surface force to our experimental measurements without any fitting parameters. The electrical boundary condition (surface charge) used in the model is indeed directly deduced from the equilibrium force, which we measure simultaneously with the dynamic force. This is the strength of our approach, made possible by the unique features of our dSFA. The model quantitatively reproduces the measurements, particularly the observed over-damping, across the entire range of parameters explored. Thus, in dynamic situations close to equilibrium, the Stokes equation may apply in the vicinity of a charged surface, and the surface charge(s) involved in electrokinetic transport may remain that of equilibrium. To our knowledge, this result is the first direct comparison between Smoluchowski’s theory of electrokinetic phenomena and experiment.