Temporal and spatial elements of thermocapillary convection in floating zones

Abstract

 We investigated experimentally spatio-temporal convective flow phenomena in cylindrical liquid bridges [floating-(half-)zones] of liquids with different Prandtl-numbers (NaNO₃?Pr=7; C₂₄H₅₀?Pr=49; C₃₆H₇₄?Pr=65). The convective flow is driven by thermocapillary forces (TC-forces) and buoyancy forces. The zones were heated from above (ΔT, Ma>0) or from below (ΔT, Ma<0) to couple both effects in different ways. Optical evaluations (view from above and view from the front) in connection with thermocouple (tc) measurements (tc-tips distributed over one half of the free surface) made it possible to get very new ideas of spatio-temporal flow structures in the considered convective system. In this article we deal with some transitionary temporal phenomena accompanying the system’s way to chaotic behaviour. We present results supplementary to well-known transitions to chaos (i.e. quasi-periodic and period-doubled flow states) and introduce some very special events. Here all considerations are based on a primarily “temporal way of thinking”. We then try to illuminate several flow situations primarily from a more “spatial point of view”. Possible spatio-temporal convective flow structures are discussed by accompanying the system from a laminar flow state up to the onset of chaotic motion. Starting with former ideas of spatio-temporal flow situations we recognize 2D- and 3D-stationary flows, “pulsating” and “rotating” modes m=1 and 2, different spatial reasons for quasi-periodic and period-doubled temporal behaviour and different spatial mechanisms that cause spatio-temporal chaotic structures in the system considered. One should realize the ambiguity of a certain time-signal with respect to various spatial structures. Additionally we find out that a revision of the interpretation of very complicated Ma/Ma _c (A)-state maps now becomes necessary. These state maps show the present flow state (e.g. a time-dependent, quasi-periodic or chaotic one) depending on the geometrical parameter aspect ratio A (i.e. the zone length) and the TC-force (i.e. the Marangoni-number).