Time-dependent behaviour and regularity of dissipative structures of interfacial dynamic instabilities

Abstract

Interfacial dynamic instabilities with self-amplifying and self-organizing convections driven by interfacial tension in a non-equilibrium two-phase fluid system show a surprising variety of dissipative structures. A complete investigation and description of them has to take into consideration at least four aspects. (1) First are the kinetic features of the convection behaviour and the deformation of the interface concerning stationary basic units of flow systems (b.u.f.) with the related deformations of the interface and different time-dependent behaviour (travelling quasi-stationary b.u.f. driven by long-range driving forces, relaxing oscillations with related autowave behaviour and classical mechanical waves). (2) The topological features include different spatial patterns, e.g. parallel, concentrically circular or spiral stripes, polygonal networks and hierarchically ordered structures. (3) The order–disorder features concern the size, shape and packing of the b.u.f. with respect to spatial regularity or spatial chaos. The time-dependent behaviour can be distinguished for harmonic, anharmonic and chaotic oscillations. (4) The driving faces (d.f.) and conditions for Marangoni instability I are heat-and/or mass-transfer and/or chemical reaction at the fluid interface. The resulting b.u.f., an interface-renewing flow, can behave (a) as stationary or quasistationary in travelling substructures, (b) as relaxing oscillations, e.g. travelling or spiral-shaped autowaves and (c) as classical longitudinal capillary waves. Marangoni instability II, with the same d.f. as instability I, induces in thin-layer amplification of the differences in the thickness of the layer. Marangoni instability III, with shear stress as the d.f. at a tenside-covered fluid interface, shows stationary or oscillatory hair needle-like or elliptical eddies in the plane of the interface itself. Meniscus instability, resulting from the viscous pressure as the d.f. at a travelling meniscus, is an excellent example of amplification as well as of stationary spatial deformations of the meniscus-shaped interface in a determinate way and travelling spatial deformations of substructures, which are caused by a repeated stochastic process.