Spiral Thermal Waves Generated by Self-Propelled Camphor Boats

Spiral thermal surface waves arising from self-propulsion of the camphor-driven objects are reported. Spiral thermal waves were registered for the dissolution and evaporation-guided self-propulsion. Soluto-capillarity is accompanied by thermo-capillarity under self-propulsion of camphor boats. The jump in the surface tension due to the soluto-capillarity is much larger than that due to the thermo-capillarity. The observed thermal effect is related to the adsorption of camphor molecules at the water/vapor interface. The observed spirals are shaped as Archimedean ones.

propulsion of camphor boats gives rise to the spiral thermal fields, resembling those inherent for the Belousov-Zhabotinsky reaction. [6][7][8][9] The experimental system is shown schematically in Figure 1a-b. Generally selfpropulsion of the camphor-driven objects is possible under two scenarios, namely under evaporation and dissolution of camphor. [19][20][21]25 Both of the regimes were studied experimentally. When the self-propulsion was guided by dissolution of camphor, the grains were placed directly on the water surfaces, as shown in Figure 1a. Special rotator depicted in Figure 1b was designed for the study of the evaporation-guided selfpropulsion, as depicted in Figure 1b. Camphor was placed in the polymer tubing, with a diameter of 1 mm.
Vessels of various shapes were used for the study of the self-propulsion: Petri dishes (Corning Crystal Polystyrene) with the diameters of 140 mm and 85mm, square polystyrene vessels with dimensions of 210x210 mm and 110x180 mm. The de-ionized water, used as supporting liquid, was purified by a synergy UV water purification system from Millipore SAS (France) and its specific resistivity was ̂= 18.2MΩ × cm at 25ºC. The vessels were filled with de-ionized water, the height of the supporting liquid hl was 7±1 mm. Camphor grains with dimensions of (4±1)x(4±1)x(6±2) mm were prepared from Camphor (96%), supplied by Sigma-Aldrich. Temperature of water varied within the range 25-35°C. All the experiments were performed under atmospheric pressure. The self-propelled motion of camphor grains was visualized with Therm-App TAS19AQ-1000-HZ thermal camera.
Thermal imaging of the water/vapor interface registered spiral thermal waves such as those depicted in Figure 2a-c. Spiral waves were observed in the circular and rectangular vessels. Clockwise and counter-clockwise rotation of water was observed within the spiral thermal waves generated by camphor grains and rotors driven by evaporation of camphor. Evaporation-induced rotation may be controlled by the shape of polymer tubing. It should be emphasized that the spiral thermal waves emerged from the both dissolution-and evaporation guided self-propulsion (see supplementary movies S1 and S2). The maximal thermal contrast observed in a course of the motion of grain and rotation of the rotor was Δ ≅ 0.2 K. Thus, the soluto-capillary Marangoni flows are accompanied in the reported experimental situation with the thermo-capillary ones. Recall that the co-occurrence the soluto-and thermo-capillary flows takes place even for the famous phenomenon of "wine tears". 26 Let us estimate the contributions of thermo-and soluto-capillarity to the effect of self-propulsion. The total change in the surface tension Δ ( , ) is expressed as follows: where Δ 1 = ( ) Δ represents the contribution of soluto-capillarity, whereas Δ 2 = ( ) Δ is the term due to the thermo-capillarity. we estimate |Δ 2 | ≅ 3.5 × 10 −5 J m 2 . Thus, we conclude that the interrelation |Δ 1 | ≫ |Δ 2 | takes place and the motion of camphor boats is mainly due to the solutocapillarity. However, the thermal effect may be of the primary importance for the understanding of the self-propulsion, when the strong exponential dependency of water viscosity is considered. 28 Thus, thermal waves play an essential role in breaking of the symmetry, resulting in the motion of the camphor boat. 23 The thermal spirals evolved towards the walls of vessels during ca 0.5-1 s and afterwards remained stable (in other words stationary, see for example Figure 2b,c) during ca 10 s. The radial temporal displacement of the labeled water particle, located at the water/vapor surface, is shown in Figure 3. It is recognized from It was demonstrated that the eventual Archimedean geometry of the spiral appearing under the Belousov-Zhabotinsky reactions may be independent of their chemical kinetic basis and arises from the symmetry considerations. 29 We are far from the exhaustive, quantitative explanation of the observed spiral, thermal waves.
However, qualitative arguments will be useful for understanding of the phenomenon.
What is the physico-chemical source of the observed thermal waves? One of these sources is enthalpy of the chemical reaction of dissolution of camphor by water.
However, thermal waves were observed in the situation when the disc-like rotator, Let us estimate dimensionless numbers, governing the evolving of spiral thermal waves, which are the Reynolds (Re) and Prandtl (Pr) numbers: where , and are viscosity, specific heat and thermal conductivity of water at the conditions of the experiment respectively, v and L are the characteristic velocity and dimension correspondingly. 12,13 Assuming, = 10 3 kg m 3 ; ≅ 9 × 10 −4 Pa × s; To conclude we report the fascinating phenomenon of propagation of spiral thermal waves emerging from the motion of camphor-driven floating self-propelled objects. The soluto-capillarity mainly guides the self-propulsion. Thermo-capillarity in turn, gives rise to propagation of spiral Archimedean thermal waves, resembling those observed under Belousov-Zhabotinsky reaction. [6][7][8][9] We relate the observed thermal effect to the adsorption of camphor molecules at the water/vapor interface. 30,31 It seems reasonable to assume, that spiral thermal surface waves reflect the quasi-periodic distribution of camphor at the water/vapor interface. 30 The reported effect is important for understanding of the self-propulsion of the floating bodies, exploited recently for micro-robotics applications and ecologically friendly generation of electrical energy. [16][17][18]37 Figure 1a. Sketch of the experimental unit used for the study of spiral thermal waves arising from the self-propulsion of camphor grains. The self-propulsion is guided by the dissolution of camphor.