The destabilization of free liquid sheets is of great practical importance for aerosol dispersions. The disintegration of a sheet through the formation of holes was first mentioned by Dombrowski in the 50's and has been later reported for different types of complex fluids, including surfactant solutions, surfactant-stabilized air bubbles, and dilute emulsions. However, despite its relative ubiquity, the physical mechanisms at the origin of the perforation process have not been conclusively elucidated so far. We study the destabilization of a freely expanding sheet resulting from the impact of a single drop of fluid onto a small target, and show that dilute oil-in-water emulsion-based sheets disintegrate through the nucleation and growth of holes. We show that the velocity, v, and thickness, h, fields of the sheet are not perturbed by the presence of holes, and follow the scaling expected for a plain inviscid fluid, v∼r/t and h ∼ 1/rt, with t the time elapsed since the drop impact and r the radial position. In addition the velocity Vc of the opening of holes is constant and quantitatively follows a Taylor-Culick law, V_c=√(2γ/(ρh)), with ρ the density, and γ the surface tension of the emulsion. We demonstrate that each perforation event is preceded by a pre-hole that thins out the sheet and widens with time. The pre-hole dynamics follows a powerlaw evolution, with an exponent ¾, theoretically predicted for a liquid spreading on another liquid of higher surface tension due to Marangoni stresses. The surface tension gradient stress is counterbalanced by a viscous stress that drags the subsurface fluid, whose flow causes a local thinning of the film leading ultimately to its rupture. Quantitative comparisons between the spreading dynamics of pre-holes and that of a drop of the emulsion oil phase deposited on the emulsion aqueous phase confirm this physical picture.

The destabilization of free liquid sheets is of great practical importance for aerosol dispersions. The disintegration of a sheet through the formation of holes was first mentioned by Dombrowski in the 50's and has been later reported for different types of complex fluids, including surfactant solutions, surfactant-stabilized air bubbles, and dilute emulsions. However, despite its relative ubiquity, the physical mechanisms at the origin of the perforation process have not been conclusively elucidated so far. We study the destabilization of a freely expanding sheet resulting from the impact of a single drop of fluid onto a small target, and show that dilute oil-in-water emulsion-based sheets disintegrate through the nucleation and growth of holes. We show that the velocity, v, and thickness, h, fields of the sheet are not perturbed by the presence of holes, and follow the scaling expected for a plain inviscid fluid, v∼r/t and h ∼ 1/rt, with t the time elapsed since the drop impact and r the radial position. In addition the velocity Vc of the opening of holes is constant and quantitatively follows a Taylor-Culick law, V_c=√(2γ/(ρh)), with ρ the density, and γ the surface tension of the emulsion. We demonstrate that each perforation event is preceded by a pre-hole that thins out the sheet and widens with time. The pre-hole dynamics follows a powerlaw evolution, with an exponent ¾, theoretically predicted for a liquid spreading on another liquid of higher surface tension due to Marangoni stresses. The surface tension gradient stress is counterbalanced by a viscous stress that drags the subsurface fluid, whose flow causes a local thinning of the film leading ultimately to its rupture. Quantitative comparisons between the spreading dynamics of pre-holes and that of a drop of the emulsion oil phase deposited on the emulsion aqueous phase confirm this physical picture.

The modal method based on Gegenbauer polynomials (MMGE) is extended to the case of bidi- mensional binary gratings. A new concept of modified polynomials is introduced in order to take into account boundary conditions and also to make the method more flexible in use. In the previous versions of MMGE, an undersized matrix relation is obtained by solving Maxwells equations, and the boundary conditions complement this undersized system. In the current work, contrary to this previous version of the MMGE, boundary conditions are incorporated into the definition of a new basis of polynomial functions, which are adapted to the boundary value prob- lem of interest. Results are successfully compared for both metallic and dielectric structures to those obtained from the modal method based on Fourier expansion (MMFE) and MMFE with adaptative spatial resolution.

This will be an easy review of all kinds of surface waves, i.e.waves existing specifically at interfaces between media that are different in some respect: − water waves− acoustic waves− plasma waves (or surface polaritons)− surface states in semiconductors, topological insulators included- Dyakonov surface waves (at interfaces of transparent media differing by symmetry)− ... Existing and possible future applications will be discussed.