Fig. 3

Role of the injection velocity \(U\). a The average density gradient, defined as the density difference between the bottom and the top of the mixture relative to the mixture height \(H\), as a function of \(U\). b The Rayleigh number \(\rm{Ra}\), defined based on the minimum density gradient and the maximum temperature difference in the mixture, vs. \(U\). The hollow, half-solid and solid symbols refer to the observations, where, respectively, multiple layers are never, sometimes and always observed in the mixture. The squares, circles and triangles refer to different inner diameters of the injection needles \(d =\) 1.2, 1.8 and 2.4 \({\mathrm{mm}}\), respectively. The insets show a zoomed-in view around the transition region. The horizontal dashed line in (b) at \({\mathrm{Ra}}_{\mathrm{c}} = 1.5 \times 10^4\) indicates the critical Rayleigh number reported in the literature¹⁸. Error bars correspond to standard derivations with \(n\) experiments with \(n = 3 - 5\)