Fig. 3: Determination of the switching criterion for thermal regulator in the forward direction.

a, b Plot of the time-dependent variation of pressure drop and wall temperature under varying χ ranging from 0.133 to 0.52. When χ < 0.25, both pressure drop and wall temperature fluctuate periodically corresponding to the chaotic two-phase flow (Supplementary Fig. 6), indicating the “off” state of the thermal regulator. In contrast, when χ > 0.25, the pressure drop and wall temperature remain unchangeable, switching to an “on” state, in which two-phase backflow is completely rectified (Supplementary Fig. 7). c In the switched-on state, χ directly regulates the pressure drop and wall temperature (in orange zone, χ < 0.25, whereas in blue zone, χ > 0.25). Here \(\dot{{{{{{\rm{m}}}}}}}\) = 0.23 kg h⁻¹. d, A critical χ of 0.25 indicates the switching criterion of thermal regulator and Tesla channel. The error bars for χ are ~±1%. Source data are provided as a Source Data file.