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We experimentally investigate the extensional flow of a sheet – or curtain – of viscoelastic liquid falling freely from a slot at constant flow rate under gravity. Extruded liquids are aqueous solutions of flexible polyethylene oxide (PEO) and of semi-rigid partially hydrolysed polyacrylamide (HPAM) with low shear viscosities. Velocimetry measurements reveal that the mean velocity field $U(z)$ (where $z$ is the distance from the slot exit) does not reduce to a free fall. More precisely, we show that the liquid falls initially with sub-gravitational accelerations up to a distance from the slot which scales as $g\unicode[STIX]{x1D70F}_{fil}^{2}$ (where $g$ is gravity and $\unicode[STIX]{x1D70F}_{fil}$ is the extensional relaxation time of the liquid) due to the stretching of polymer molecules. Beyond this elastic length, inertia dominates and the local acceleration reaches the asymptotic free-fall value $g$. The length of the sub-gravitational part of the curtain is shown to be much larger than the equivalent viscous length $((4\unicode[STIX]{x1D702}/\unicode[STIX]{x1D70C})^{2}/g)^{1/3}$ for Newtonian liquids of density $\unicode[STIX]{x1D70C}$ and dynamic viscosity $\unicode[STIX]{x1D702}$ which is usually small compared to the curtain length. By analogy with Newtonian curtains, we show that the velocity field $U(z)$ rescales on a master curve. Besides, the flow is shown to be only weakly affected by the history of polymer deformations in the die upstream of the curtain. Furthermore, investigations on the curtain stability reveal that polymer addition reduces the minimum flow rate required to maintain a continuous sheet of liquid.

We propose a simple model for the chevron structure observed in recent experiments by cooling a smectic A liquid crystal. We discuss the influence of the cell thickness and of the anchoring conditions on the temperature dependence of the layer tilt angle, and the formation of this structure in the vicinity of a smectic A—nematic transition. Below this critical point, a transition between a bookshelf structure and a chevron one appears. This transition is second order, with continuity of the tilt angle, the threshold being a function of the cell thickness. In addition to a classical layer thinning mechanism, we discuss another possibly based on the temperature dependence of the elastic moduli. We also propose an explanation for the existence of a critical thickness below which the chevrons do not appear.

In this communication, we report some recent results1,2 obtained in the study of the Rayleigh-Taylor instability of a thin layer. This interfacial instability exhibits interesting “growth and form” effects, in which the non-linearities play an essential role: formation of two-dimensional patterns of different symmetries, transition between patterns (sometimes involving front propagation phenomena), secondary instabilities...