Fig. 1: Marangoni natural convection within the liquids.

a Sketch of the typical oil-water two-layer Marangoni convection system, where the subscripts “o” and “w” represent oil and water, and “c” and “b” represent center and boundary, respectively. T refers to the temperature. d refers to the length of the side. h refers to the height. Red and blue colors indicate high and low temperatures, respectively. Red and blue dots indicate the center and boundary, respectively. b Instantaneous pathline cloud map of the flow field at 13 °C in the deionized water cooling test. Axes denote flow field geometric dimensions. Three dotted lines indicate monitoring lines at different depths. White lines are particle motion trajectories. Arrows denote flow direction. The gradient color bar denotes the velocity magnitude distribution. c Velocity magnitude distribution corresponding to the three monitoring lines in Fig. 1b. d Instantaneous cloud maps with different temperatures during oil-water cooling. The gradient color bar reflects the distribution of velocity magnitude. The lengths of vectors represent the relative magnitude of the velocity, and their direction indicates the flow orientation. Scale bar: 5 mm. Refer to the Methods section for detailed calculations.