Fig. 3
Modeling of mixing and heat transport mechanisms. Snapshots of mixing of a patch of fluorescent dye (passive scalar) released in a classical thermal turbulence system and b active biphasic turbulence, at time instants (left to right) 0, 10, and 24 s after injection. In classical thermal turbulence a, the spreading occurs primarily along path of the large-scale circulation (LSC), while in the active biphasic case b, the mixing is fast and occurs across a wide range of scales (see Supplementary Movie 10 and 11 for the comparison). False coloring was adopted based on the intensity of the dye. c Collective LSC velocity Vc in the active regime vs. Jakob number Jab of the bottom plate. The LSC velocity for classical thermal turbulence (black dashed line) is also shown for comparison. d Differential heat flux δNu—Nul vs. theoretical estimate of liquid agitation39 \(u\prime = V_{\mathrm{c}}\sqrt \alpha\). Here, δNu is the total heat transfer enhancement, Nul is heat transfer enhancement contributed by biphasic kinematics, and u′ is the theoretically estimated liquid velocity fluctuation (r.m.s) based on the measured Vc and volume fraction α. e Nusselt number for increasing Jakob number Jab (see also Suppl. Mat.). The shaded areas show different contributions to the total heat transfer enhancement, namely thermal turbulence (gray), biphasic particle kinematics (blue) and induced liquid agitation (green). The inset compares active particle induced heat transport with the Nu vs. Ra scaling of classical thermal turbulence. Scale bar: 22 mm
