Marangoni Flow in Freely Suspended Liquid Films

We demonstrate controlled material transport driven by temperature differences in thin freely suspended smectic films. Films with submicrometer thicknesses and lateral extensions of several millimeters were studied in microgravity during suborbital rocket flights. In-plane temperature differences cause two specific Marangoni effects, directed flow and convection patterns. At low gradients, practically thresholdless, flow transports material with a normal (negative) temperature coefficient of the surface tension $d\sigma /dT<0$ from the hot to the cold film edge, it accumulates at the cold film edge. In materials with $d\sigma /dT>0$, the reverse transport from the cold to the hot edge is observed. We present a model that describes the effect quantitatively. It predicts that not the temperature gradient in the film plane but the temperature difference between the thermopads is relevant for the effect.

Figure 1

The experimental geometry is sketched in the top part. Front and rear edges of the frame are omitted. The film area is $13\times 10{\mathrm{mm}}^2$, the field of view is $7\times 5{\mathrm{mm}}^2$. Two pads with rectangular cross sections, in contact with the film, separated by $d=2.5\mathrm{mm}$, generate linear temperature gradients. These pads are set to temperatures $T_0\pm \mathrm{\Delta }T/2$, the film holder is kept at $T_0$. The bottom drawing depicts the molecular structure of the $\mathrm{Sm}\text{−}C$ film, and the definition of the $c$ director. The bar sketches the optical reflectivity under crossed polarizers $(P,A)$ for different $c$-director orientations.

Figure 2

Temperature protocol during the first 300 s of microgravity (TEXUS 55), and the velocity component $v_x$ determined from the texture displacement. Different colors represent different positions in the film. The accuracy is $\pm 20\mu \mathrm{m}/\mathrm{s}$. Accurate velocity data could be obtained only when the textures contained sufficient structure. Even though the hot pad was heated to a temperature slightly above the bulk transition to $\mathrm{Sm}\text{−}A$, the film remained completely in $\mathrm{Sm}\text{−}C$ throughout the experiment.

Figure 3

10PP8 textures (TEXUS 55) in the region between the pads: (a)–(d) Texture transported by flow from the hot pad (top) to the cold pad (bottom), (e) reverse flow after reversal of $\mathrm{\Delta }T$, thicker film is transported away from the former cold plate (bottom), (f) film after second reversal of $\mathrm{\Delta }T$ and flow direction.

Figure 4

Flow profile and heat flow in and around the freely suspended film. At the sides, the meniscus is sketched with dislocations that are related to the film thickness gradients.

Figure 5

Film of 5O.6 in the region between the pads: (a) initial uniform film, (b), (c) accumulation of thick film at the hot pad (top) and (d) after reversal of the temperature gradient. The material is in the smectic-$A$ phase, thus no textures are visible. Bright regions represent thicker film, interference fringes in (b), (c) evidence thickness gradients. Because air convection could not be completely avoided, the accumulated thicker region at the hot pad tends to wobble (b), (c).