Thermal radiation and thickness fluctuations in freely suspended liquid films

Thermal convection in a vertically suspended soap film subjected to a vertical temperature gradient is marked by intense density fluctuations δρ2, uncommon to laboratory Rayleigh-Bénard convection (RBC). Such large fluctuations result from stratification in the film under the influence of gravity. Herein we present the first direct measurement of two-dimensional density fluctuations in a free-standing soap film using a single-point infrared detector. The radiation densitometer is nonintrusive and responds instantaneously to local density variations. Measurements of the power spectrum Γ(f) of δρ2 are carried out using a variety of sample geometries of the aspect ratio of unity. In all cases, Γ(f) scales with the frequency as f−1.4±0.1 in the low frequency regime, which is in good agreement with the Bolgiano’s theoretical prediction for a stably stratified fluid. Combining thermal imaging and particle tracking, we also show that it is feasible to measure the full-field density flux j(x,y)=ρ2(x,y)v(x,y) in the film. Despite that individual snapshots of j(x,y) appear random, the time-averaged flux forms a close loop similar to the large-scale circulation commonly seen in RBC, when a sufficiently large temperature gradient is present.