Heterodyn interferometry to unravel capillary interactions in particle laden interfaces

Sub-millimetric particles are found to adsorb quasi-irreversibly at fluid interfaces [1]. This trapping causes a local modification of the energy landscape [2], which in turn gives rise to capillary lateral interactions. These interactions govern the dynamics of particle self-assembling and the cohesion of resulting rafts [3]. More particularly, unavoidable undulations of the contact line and their aging are expected to have critical effects on the mechanical properties of macroscopic assemblies [4-5]. Yet, to date, the experimental exploration of these characteristics mostly relies on optically trapped particles or shock freezing of the liquid(s), and remains therefore limited to quasi-static regimes and isolated particles. In this work, we propose a new approach, based on heterodyne interferometry that enables to resolve interfacial deflections with unequalled combination of temporal and spatial resolutions [6]. Typically, vertical and lateral resolutions of about 20nm and 5μm can be reached at kHz frequencies. The principle relies on the imprint at the fluid interface of a periodic modulation of the light intensity. Digital image analysis can thus be advantageously used to filter low and high frequencies noise. The light modulation is obtained via classical interferometry, for example, with a Mach-Zehnder interferometer, and the interferogram filtration is performed on the frequency domain, for instance, using FFT (Fast Fourier Transformation).
This method is tested on several types of particles covering small (50μm), medium (130μm) and large diameters (330μm); heavy (2500kg/m3) and light (400kg/m3) materials; smooth (silanized glass) and rough (nanoparticle coated) surfaces; as well as spherical and non-spherical shapes. Our results show strong deviations from regular multipoles theoretically derived for ideal particles [7]. The application of a rough coating to a medium particle does not significantly modify the magnitude or number of the main extremum but causes the emergence of higher frequency modulations, in agreement with the promotion of higher modes by local pinning [8]. The effect of buoyancy follows expected trend with large particles approaching monopoles. Finally, dynamic observations made during particle self-assembling suggest strong coupling of the deflections caused by individual particles, see figure 1 for illustration. The consequences of this phenomenon on the behaviours of particle assemblies remain to be elucidated.