Anisotropic Superattenuation of Capillary Waves on Driven Glass Interfaces

Abstract

Metrological AFM measurements are performed on the silica glass interfaces of photonic band-gap fibres and hollow capillaries. The freezing of attenuated out-of-equilibrium capillary waves during the drawing process is shown to result in a reduced surface roughness. The roughness attenuation with respect to the expected thermodynamical limit is determined to vary with the drawing stress following a power law. A striking anisotropic character of the height correlation is observed: glass surfaces thus retain a structural record of the direction of the flow to which the liquid was submitted.What governs the structure of a glass surface? To very good approximation, the bulk structure of a vitreous material resembles a snapshot of the liquid before glass transition [1]. Similarly, the surface of a glass corresponds to the frozen liquid interface [2], and can reveal frozen surface modes of this interface. Over a wide range of length scales, from the nanometer up to the millimeter range, the sub-nanometer roughness of a fire-polished glass surface results from the superposition of frozen thermal equilibrium capillary waves of the liquid [3].At equilibrium, capillary fluctuations of liquid interfaces originate from the interplay between thermal noise (k B T ) and interface tension (γ), and result in a superposition of capillary waves. Height fluctuations scale as:which equals 0.3-0.4 nm for most simple liquids. Liquid interfaces are thus extremely smooth. Thermal interface fluctuations correspond to a lower bound of the interface width imposed by equilibrium thermodynamics. In this context, the application of any external field is usually expected to enhance the level of fluctuations. In the presence of a flow, amplification of capillary fluctuations typically gives rise to hydrodynamic instabilities [4]. However recent results suggest that shear flow may in fact induce a non-linear attenuation of capillary waves [5][6][7].Here we present an accurate experimental characterization of such an attenuation of capillary fluctuations on glass surfaces. In particular, we show that a glass surface retains a structural record of the direction of the flow to which the liquid was submitted. Performing high precision Atomic Force Microscopy (AFM) roughness measurements on the inner glass interfaces of photonic band-gap fibres and hollow capillaries produced by fibre drawing, we show that driven glass interfaces re-FIG. 1. Sketch of the drawing of Hollow Core Photonic Band Gap Fibres (PBGF).The two AFM measurements represent the surface topography of the inner surfaces of a PBGF before (preform) and after (fibre) the hot drawing region (in orange). While isotropic before drawing, the sub-nanometer roughness exhibits clear elongated patterns along the fibre axis after drawing. The color bar represents a height range of 1.6 nm.sult from the freezing of attenuated capillary waves. The roughness is strongly anisotropic with an overall amplitude that presents a non-linear attenuation with respect to the expected equilibrium thermodynamic...

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