Camphor-Engine-Driven Micro-Boat Guides Evolution of Chemical Gardens

A micro-boat self-propelled by a camphor engine, carrying seed crystals of FeCl3, promoted the evolution of chemical gardens when placed on the surface of aqueous solutions of potassium hexacyanoferrate. Inverse chemical gardens (growing from the top downward) were observed. The growth of the “inverse” chemical gardens was slowed down with an increase in the concentration of the potassium hexacyanoferrate. Heliciform precipitates were formed under the self-propulsion of the micro-boat. A phenomenological model, satisfactorily describing the self-locomotion of the camphor-driven micro-boat, is introduced and checked.

Experimental Methods. The process of self-propelling and the growth of the chemical gardens were registered with the rapid cameras Casio EX-FH20 and the digital microscope BW1008-500X. After capturing the video, the movie was split into separate frames by the VirtualDub software. The frames were treated by a specially developed software, enabling the calculation of the speed of the center mass of the micro-boat.
Surface tensions of potassium hexacyanoferrate solutions with the concentrations varied from 0.125 to 3 wt.% were established using the Ramé-Hart Advanced Goniometer (Model 500-F1) by the pendant droplet method. The dynamic viscosity was measured with an Ostwald-type capillary viscometer consisting of a U-shaped glass tube in a controlled temperature bath (25 ± 0.2 °C). The density was established by a Gay-Lussac type Isolab (Germany) pycnometer with the capacity of 10 ml. Results of the measurements are summarized in Table 1.
The topography of the precipitate was studied with the Carl Zeiss Axiolab A 45 09 09 optical microscope (Germany), and the IDS UI-1490LE-C-HQ digital camera (Germany). Post processing of the stack of images was done with the Zerene Stacker "focus stacking" software. Thermal imaging of the process was carried out with the Therm-App TAS19AQ-1000-HZ thermal camera equipped with a LWIR 6.8 mm f/1.4 lens. Contact angles for the potassium hexacyanoferrate/Petri dish system were established with the Ramé-Hart goniometer (Model 500, USA).
Four series of experiments were carried out, namely: 1) Study of the self-propulsion of the PVC tubing (depicted in Fig. 1a) driven by camphor on distilled water. 2) Study of the self-propulsion of the PVC tubing driven by camphor when placed on potassium hexacyanoferrate aqueous solutions, c = 0.125-3 wt.% (without FeCl 3 seed crystals).
3) Study of the self-propulsion of the PVC tubing containing FeCl 3 seed crystals, driven by camphor when the tubing was placed on potassium hexacyanoferrate aqueous solutions, c = 0.125-3 wt.%. In this case the chemical gardens reaction was observed during the motion of the PVC tubing.

Results and Discussion
Static growing of chemical gardens. At first we studied a static (the micro-boat was at rest) growing of chemical gardens with the PVC tube filled at one end with FeCl 3 seed crystals, as depicted with Fig. 2. The growth of chemical gardens was observed under various concentrations (c = 0.125-3 wt.%) of K 4 Fe(CN) 6 aqueous solutions. The PVC tube containing seed crystals was at rest and the inverse (top-down) growth of chemical gardens was observed for all studied concentrations. Similar downward-growing chemical gardens were already reported in ref. 44, where the gardens grew in aqueous solutions of polymers.
The optical microscopy images of typical cylindrical filaments constituting the "chemical gardens" are supplied in Supplementary Fig. S1. It is noteworthy that the evolution of the gardens was slowed with the increase in the concentration of potassium hexacyanoferrate. The characteristic times of the downward growth of filaments τ 1 , τ 2 were defined as the time span from placing the boat with the seed crystal on the surface of the potassium hexacyanoferrate aqueous solution until the appearance of the filament (as registered with rapid camera and software VirtualDub-1.10.4, used for sequencing of frames), and correspondingly the time measured between its appearance at the end of the tube and time when the filament touched the bottom of the Petri dish. The dependences of τ 1 , τ 2 vs. the concentrations of the solutions are presented in Fig. 3. The data supplied in Table 1, demonstrate that the physical parameters of the aqueous solutions of potassium hexacyanoferrate vary very slightly with the concentration of the solution. Thus, it is reasonable to relate the strong dependences τ 1 (c), τ 2 (c), illustrated in Fig. 3, to the chemical aspects of the evolution of chemical gardens inherent for the studied system, and not to the physical factors.
It is noteworthy that starting from c = 3 wt.% of the solutions, the filaments growing downward did not touch the bottom of the Petri dish and remained "hanging". A profound understanding of the chemistry of growing "inverse" gardens requires future investigations.  The dynamics of growth of chemical gardens inspired by the self-propelled motion of the micro-boat. We studied the self-propulsion of the PVC tubing driven by camphor when placed on distilled water and aqueous solutions of potassium hexacyanoferrate; we also investigated the motion of the tubing with and without FeCl 3 seed crystals. In all the cases the same temporal pattern of the motion was observed, namely: the short interval of the accelerated self-propulsion was followed by relatively long-term decelerated motion. The dynamics of self-propulsion will be discussed below in detail.
When the micro-boat depicted in Fig. 1a, containing both camphor and seed crystals, was placed on the surface of aqueous solutions of K 4 Fe(CN) 6 , it started a self-propelled motion driven by the soluto-capillary Marangoni flow, owing to the dissolution of the camphor 21-26 . At first the boat moved towards skirting (rim) of the Petri dish and afterwards traveled along the skirting at the distance of ca. 1 cm from the rim (see the sequence of images, presented in Fig. 4).
In parallel, the chemical garden reaction resulted in the formation of heliciform precipitate, shown with blue in Fig. 5 as taken from a video (see Supplementary Information).
The total length and the maximal width of the precipitate (assumed as its featuring geometric characteristics) grew with time. The kinetics of their change is illustrated in Supplementary Fig. S2. Now consider in more detail the dynamics of the self-propulsion, depicted schematically in Fig. 6. The camphor-engine-inspired self-propelling of the micro-boat, represented with Fig. 7, accompanied by the growth of chemical gardens, occurs in two distinct stages: accelerated motion which lasts ca. 2-10 s, followed by decelerated motion which continues ca. 40-250 s. The same scales were observed when PVC tubing without seed crystals driven by camphor was placed on aqueous solutions of potassium hexacyanoferrate. However, the time scale of the decelerated motion observed for the self-propulsion of the tubing on the distilled water was ca. 1000 s.  The change in viscosity of water due to the presence of K 4 Fe(CN) 6 is negligible (see Table 1). Thus, it is reasonable to suggest that the presence of K 4 Fe(CN) 6 slows dissolution of camphor, and decreases, in turn, the change of the surface tension, giving rise to the self-propulsion.
The temporal pattern of the motion was the same for micro-boats of various lengths, used in our study, and for various concentrations of aqueous K 4 Fe(CN) 6 solutions, as shown in Fig. 7. A rigorous analysis of the self-propulsion, accompanied with the chemical gardens reaction is an extremely complicated mathematical task, so we restricted ourselves to a very approximate qualitative treatment of the problem. It is reasonable to relate the twin-stage (accelerated/decelerated) nature of the self-propulsion, illustrated with where m, L, D and → v cm are the mass, length, diameter and velocity of the center mass of the boat correspondingly, γ and η are the surface tension and the viscosity of the supporting liquid correspondingly, ∇γ is the gradient of the surface tension due to the dissolution of camphor; α and χ are the dimensionless, phenomenological coefficients, depending on the shape of self-propelled object (PVC tubing carrying the seed crystal in our case). It should be stressed that the self-propelled micro-boat does not touch the skirting (rim) of the Petri dish; thus, the friction force is estimated as: The accurate solution of Eq. (1) is a challenging task; we assume tentatively that: where τ d is the characteristic time of the change in the surface tension due to the dissolution of camphor, followed by its diffusion. When the camphor is placed on the water, the surface tension is decreased rapidly, and then it is slowly decreased with time 51 . |Δγ| 0 ≅ 5 mJ/m 2 is the initial jump in the surface tension due to the dissolution of the camphor 52 . We do not set into the details of the process of dissolution and diffusion of the camphor, but rather describe the process in a purely phenomenological way with Eq. (2). Considering Eq. (2) enables re-shaping of Eq.
(1) for the modulus of the velocity of the center of mass of PVC tubing, in the following way: It is convenient to re-shape Eq. (3) as given below: ; hence, for the mass of the self-propelling system we may assume m ≅ ρ PVC L, where ρ PVC is the length (linear) density of the PVC tubing with the dimensions: [ρ PVC ] = kg/m (for the tubes used in our study, ρ PVC = 3.25 × 10 −3 kg/m). This estimation yields for the characteristic time of friction: τ fr ≅ ρ PVC L/χDη, and it is linearly dependent on the length of the PVC tubing L.
The true values of the parameters α,  a, τ fr and τ d remain unknown, and we consider them as "free" fitting parameters. The solution of the differential equation Eq. (4) and considering the initial condition v cm (t = 0) = 0 yield: Considering τ  a, d and τ fr as fitting parameters we fitted the experimental data by the dependence supplied by Eq. (5). The resulting fitting curves is shown with a solid, blue lines in Fig. 7. The values of fitting parameters calculated for various experimental conditions are summarized in Supplementary Table S1.
It is recognized from the data supplied in Supplementary Table S1, that the values of the characteristic time scale  Supplementary  Table S1 are close, i.e.τ fr ≈ 1 − 4 s for various solution concentrations and lengths of the micro-boat. This result is highly expectable due to the fact that the viscosity of K 4 Fe(CN) 6 aqueous solutions is only slightly dependent on their concentrations, as is seen from the data, summarized in Table 1. It is also reasonable that the time scale τ fr grew with the length of the micro-boat as discussed above. The aforementioned arguments justify the phenomenological twin-time model, proposed for the explanation of self-locomotion of the micro-boat.
Scientific REPORtS | 7: 3930 | DOI:10.1038/s41598-017-04337-w The parameter α γ ≅ ∆  a D m / 0 appearing in Eq. (4) also is confined within the same order of magnitude for various solution concentrations (see Supplementary Table S1), indicating that the initial jump in the surface tension propelling the boat |Δγ| 0 does not change dramatically with the concentration of K 4 Fe(CN) 6 .
The rotational motion of the micro-boat along the rim of the Petri dish should be addressed within the model developed in ref. 53. (see Supplementary Text and Fig. S4). It is also noteworthy that when the boat has been initially placed in the vicinity (ca 1-2 mm) of the rim of the Petri dish, it started rotational motion along the rim, accompanied with the inverse growth of chemical gardens. Thus, the motion of the boat and consequently growth of chemical gardens may be guided by the shape of the vessel.
One more experimental observation should be discussed. To our best knowledge, the thermal effect of the chemical gardens reactions was not explored. Imaging of the self-propulsion of micro-boats with a thermal camera demonstrated that the reaction is exothermic. When PVC tubing containing both FeCl 3 seed crystals and camphor was placed on the surface of water, a marked increase in temperature at the end of the tubing containing the seed crystals was registered, as high as 2 °C, which may also promote Marangoni thermo-capillary flows 54 .
However, the effect of heating relatively quick decayed with time, as shown in Supplementary Fig. S3a. Spatial and temporal distributions of temperature are shown in Supplementary Fig. S3b. It is noteworthy that this effect of heating does not give rise to the observable thermo-capillary Marangoni flow preventing self-propulsion.

Conclusions
Surface-tension driven of micro-swimmers is important in view of numerous medical and engineering (microfluidics and sensing) applications 3-9, 55-57 . We report the use of a self-propelled camphor micro-boat for carrying out a chemical garden reaction. Polymer tubing was filled with camphor at one end and with FeCl 3 seed crystals at the other end. The system was placed carefully on the surface of the aqueous solution of potassium hexacyanoferrate (K 4 Fe(CN) 6 ). The tubing was propelled by the "camphor engine", and concurrently the chemical garden reaction took place. The reaction gave rise to the "inverse chemical gardens" growing from the top downward, similar to those reported in ref. 44., and resulted in the formation of heliciform precipitates. The evolution of the gardens was slowed with an increase in the concentration of potassium hexacyanoferrate. A phenomenological model describing the self-locomotion of the micro-boat is proposed. The model involves two characteristic times, namely the characteristic time scale of the change in the surface tension due to the dissolution of camphor, followed by its diffusion, denoted as τ d , and the characteristic time of the viscous dissipation τ fr , treated as fitting parameters.