Sustained interfacial powering through self-generated mantle and siphon of a gelling droplet

Domain: neuroscience
Published: 2026-02-10
Editorial outcome: major_revision

Abstract
Autonomous motion in a persistent manner such as spinning of Euler’s disk is long-sought-after by natural or artificial microsystems due to their limited energy loading and is particularly challenging for Marangoni motors as inhomogeneity of active molecules is difficult to sustain. Here we show that by releasing a droplet containing hydrogel precursor and non-small active molecules on a diluted crosslinking-agent solution, the droplet self-propels with a lifetime 300-to-1000-fold longer. It is found that continuously crosslinking hydrogel shell cuts rapid surfactant diffusion and accompanying volumetric contraction perforates the shell and generates a vent through which active molecules are unidirectionally released. The mechanism echoes squid’s jet propulsion wherein water is expelled out of a siphon by contracting mantle. Such self-generated contracting mantle-siphon configuration of a gelling droplet maximizes the localized concentration inhomogeneity and protracts adsorption saturation on water surface, improving the efficiency and lifetime of Marangoni motors for sustained powering of interfacial machines. The unfolded strategy potentially provides solutions for microscale release control which will be of interest to microrobots, materials assembly, and biomolecules transport.

Introduction
Persistent motion in an autonomous manner, such as spinning of Euler’s disk, is long-sought-after in small-scale robots because of their limited energy loading. For the terrain of physiological or engineered air-liquid interface, the Marangoni motor is intensively studied due to its simplicity and inherent compatibility with biphasic interface1–4. Such locomotion is fueled by short-lived surfactant non-uniformity, a nonequilibrium state which will be rapidly homogenized by advection and diffusion. Without assistance from specially designed chemistry, the Marangoni motor is plagued by a short lifetime of ~10 s, limiting its practical application as a modular power source1,5. It is found that squid harnesses delicate jet propulsion for locomotive agility and endurance (Fig. 1a). To propel, water is first sucked into its muscular mantle cavity. Then the squid contracts its mantle and expels water out of the narrow siphon6. Utilizing such a contracting-mantle-siphon configuration, the squid, Todarodes pacificus, can continuously swim for months at an average speed of ~1 body length (BL) per second7,8.

Inspired by squid’s propelling skill, we unfold a general strategy to prolong the Marangoni motor’s lifetime by 300-to-1000-fold using an artificial contracting-mantle-siphon system that is self-generated by a gelling droplet. By releasing a 10-μl droplet containing hydrogel precursor and non-small active molecules (low-molecular-weight amphiphilic polymer) on a diluted crosslinking-agent solution, we observe that the denser droplet floats and propels at an average velocity of ~10 mm s-1 for ~100 min, a lifetime ~600 fold longer than that of conventional Marangoni motors such as camphor boats (Fig. 1b, c, Supplementary Fig 1 and Supplementary Movie 1). Note that the highest lifetime we measured is 194 min for a 35-μl droplet.

We find that such a simple gelling system autonomously recapitulates the squid’s contracting-mantle-siphon configuration, producing a buffered surfactant jet for sustained propulsion. As shown in Fig. 1c, e, upon touching the solution bath, the surfactant-loading droplet spreads into a liquid lens, increasing capillary forces for its flotation9. Otherwise, in the absence of surfactant, the alginate-solution droplet sinks in the bath because of its slightly higher density (1.001 g ml-1) and then crosslinks into a gel sphere (Supplementary Movie 3). The persistent gelation forms a contracting hydrogel mantle on the droplet, which cuts surfactant diffusion and squeezes the liquid interior, swiftly forming a siphon by perforating gel (Fig. 1d, f, g)10. Pumping by Laplace pressure, active molecules are unidirectionally released through the siphon whose rate is well-buffered by a prominent viscous force (Fig. 1h, i). In this way, surfactants are released in an anisotropic and controlled manner, a state that maximizes the localized concentration inhomogeneity and prolongs adsorption saturation on the water surface, two effects critical to the efficiency and lifetime of Marangoni motors. Such a sustained artificial “squid” is self-generated and will be of interest and relevant to fields such as cargo delivery, active matter assembly, and microscale robotic powering.

Results
Short-timescale mantle-siphon generation
We start by using a commonly seen gelling pair, that is, sodium alginate and calcium chloride (Supplementary Table 2), which was first used by Ender et al. for micro-swimmers11–14. When a sodium alginate droplet is placed in a calcium chloride solution bath, it sinks and gels into a calcium alginate sphere. By contrast, when amphiphilic molecules are added to the droplet, it spontaneously spreads and floats on the bath surface in ~10 ms, followed by a rapid propulsion in ~1 s which continues for ~100 min (Figs. 1c and 2a, b). Note that the droplet is dyed red using direct red 23 for visualization. Red dyes are trapped inside the droplet as the sodium alginate chain strongly interacts with the dye molecules through hydrogen bonding15. For a 35 μl droplet containing 1-wt% sodium alginate and 25-wt% polyethylene glycol diacrylate (PEGDA) of an average molecular weight of 400, the droplet propels for 194 min at an average velocity of ~10 mm s-1, an unexpectedly long lifetime affected by the short-timescale dynamics which we now investigate (Supplementary Movie 2).

As shown in Fig. 1c, d and Supplementary Movie 3, the lens radius captured through high-speed photography varies in a non-monotonic manner. When the droplet of a surface tension σd = 42 mN m-1 touches the bath of a surface tension σb = 70 mN m-1, where σ is surface tension, and subscripts d, b, a, respectively, denote droplet, bath, and air unless otherwise specified, it instantaneously spreads into a lens of a finite maximum radius Rl in ~10 ms. The surface-active molecules isotropically diffuse across the liquid interface without any barrier (Fig. 1e), a symmetric transport evidenced by the circular region of zero velocity mapped by the particle image velocimetry (PIV) on the surface (Supplementary Fig 2a). Note that the region of zero velocity forms as the Marangoni stress sweeps the tracer particles away, signifying the release of surfactant.

The Marangoni advection near the lens boundary lowers the local bath-air surface tension, causing the spreading coefficient S = σba - (σda + σdb) to be roughly zero whereupon the spreading ends (Supplementary Note 1). Such process is similar to that of alcohol droplet spreading on water surface whose scaling analysis can be used to predict the Rl as follows16:

Rl ~ (ΔσV3 / π3ρ D2s)1/8 (1)

where V is the droplet volume, ρ is the mass density, Ds is the surfactant diffusion coefficient. As shown in Fig. 2e, results largely fit well with the prediction but deviate when droplet volume is less than 6.94 μl.

Upon the charge-compensation crosslinking between carboxyl groups of alginate molecule chains and calcium ions, previously free and dissociated alginate chains aggregate and interconnect, forming a gel of reduced volume17,18. In this way, the lens contracts during the crosslinking of calcium alginate (Fig. 2d). The shrinking radius of the hydrogel mantle increases the curvature ∇·n of the atop droplet, where n is the surface unit normal vector, building the Laplace pressure σd ∇·n up. Note that throughout the lifetime, the motor’s top remains in a liquid state as the upward diffusion of calcium ions is too slow to crosslink the entire droplet. In this way, the pressure inside the droplet can be well described using the interface curvature (if the top was crosslinked, stressing el film would impact the droplet pressure). In Fig. 1g, as the length scale is much smaller than the capillary length, the hydrostatic pressure can be neglected. Beneath the bath-air interface, the pressure in liquid bath pb equals to the ambient pressure pa. By contrast, pressure inside droplet pd is pa + σd ∇·n. Once the siphon forms, surfactant is pumped out because of higher pd (Supplementary Note 1). Because there is no strong pressure gradient inside the droplet, the curvature is largely uniform along the liquid-air interface.

Along the three-phase contact line, Laplace pressure and surface tension force (surface tension of bath-air interface perpendicularly acting along droplet perimeter) radially stretch the newly-crosslinked gel film, making a stress peak at mantle’s perimeter (Supplementary Fig 3). When local circumferential tensile stress exceeds the gel strength, crack starts to form (Supplementary Fig 4). The pressure swiftly perforates the hydrogel mantle in ~1 s, forming a siphon for surfactant release whereupon the motor of a radius Rm initiates its rapid translation (Figs. 1c and 2a).

Unlike the isotropic diffusion, such advected discharge is anisotropic (Supplementary Movie 4). During propulsion, the region of zero velocity becomes asymmetric (Supplementary Fig 2b). As shown by the releasing jet in the top-view Schlieren image in Fig. 1i, the active molecules are ejected through the siphon of ~0.1 Rm in size at the rear of the advancing motor, whereas circumferential rapid diffusion across the interface is largely cut by the gelled mantle. Such anisotropic and directional surfactant discharge maximizes the localized concentration inhomogeneity, substantially prolonging the lifetime.

Long-timescale propulsion
Then we investigate the longer-timescale propulsion (~1000 s). As shown in Fig. 2b, when the motor initiates its locomotion, it rapidly reaches the maximum velocity Umax in ~5 s. For subsequent propulsion, it releases active molecules at a rate proportional to the remaining amount (see details in Supplementary Note 1). Approaching the lifetime, the continuous locomotion becomes pulsed. Such pulsed motion is caused by an intermittent jet containing surface-active agent (Supplementary Fig 5 and Supplementary Movie 5). Therefore, even approaching the end of lifetime, that is, the pulsed mode, the jet accompanies the motor motility. As seen in Supplementary Fig 6 and Supplementary Movie 6, after motor forms and propels in 30 s, we terminate its further crosslinking by transferring it into water. Unlike the continuous-crosslinking one, it has a larger radius, which suggests that the crosslinking and thus slow shrinking continue throughout self-propulsion. Moreover, the continuous-crosslinking motor has a lifetime fourfold higher than that of the terminated one. We propose that as crosslinking proceeds, a thicker mantle forms, which prevents surfactant diffusion across the gel film more effectively.

The side-view PIV measurements unfold asymmetric counter-rotating vortices near the boundaries of a propelling motor (Fig. 2c and Supplementary Movie 4). Such a circulating flow is induced by the viscous shear of the Marangoni stress. A stronger rear vortex indicates higher Marangoni stress and thus faster surfactant release. The vortex convects fresh bulk solution to the surface and assists in breaking the surfactant adsorption saturation on the bath surface16.

The surfactants we used are soluble, and some are even volatile. Nevertheless, for simplification, here we assume that the surfactant is insoluble and nonvolatile so that the evaporation and the evolution of bulk surfactant concentration can be neglected19. The surface concentration of surfactant Γ(x,y,t) evolves according to the advection-diffusion equation as follows:

∂Γ/∂t + ∇s·(Γus) = Sboundary + Ds ∇s2Γ (2)

where ∇s is the surface gradient operator, us is the surface velocity, ∇s2 is the Laplacian, the implicit Sboundary is the boundary source, which is set as a boundary condition in the numerical study. Given Ds ~ 10-10 m2s-1, we have a Péclet number Pe = Rm U/Ds ~ 106, suggesting the advection dominates the transport (Supplementary Note 2).

We then simply assume that in a finite time Δt, surfactants are homogeneously deposited on the liquid surface swept by the droplet translating at a velocity U, providing Γ=J/(0.1 Rm U), where J is the surfactant releasing rate (Supplementary Fig 7b). To verify the simplification, we numerically study the motor motion and evolution of surfactant concentration distribution through finite-element analysis using COMSOL-Multiphysics (see details in Supplementary Note 3 and Supplementary Movie 7). As shown in Supplementary Fig 7, when the motor propels, around its perimeter, the released surfactant is concentrated in the vicinity of releasing siphon. The simplification (pulse concentration distribution) is roughly consistent with such a distribution feature. Such simplification gives a Marangoni force of Fm ~ κΓ·0.1 Rm = κJ/U where κ = -dσ/dΓ.

During the propulsion, the Reynolds number is Re = ρb URm/μb ~ 102-103, implying a resistant force associated with the pressure distribution on the motor surface as Fd = ρb U2 Cd πRm hm, where Cd is the drag coefficient and hm is the height of the motor. A balance between the driving Marangoni force and the drag force provides the U as follows:

U ~ (κJ / ρb Cd πRm hm)1/3 (3)

By substituting the first-order release assumption J = c0 Q e-kt into Eq. 3, we have the temporal evolution of propulsion velocity as U(t) ~ (ρb Cd κ c0 Q m hm)-1/3 e-kt/3 where Umax ~ (ρb Cd κ c0 Q m hm)-1/3. As shown in Fig. 2f, experiments are roughly consistent with the derivation. Note that the scaling in Fig. 2f is semi-quantitative as Rm and Umax span for only one order of magnitude, which is the largest range that we can experimentally obtain.

Generality and performance
To coax the simple gelling system into artificial squid propulsion, two constituents, that is, the hydrogel matrix and surfactant, should be well chosen. The hydrogel can work as a mantle if it gels fast and has sufficient mechanical strength to support a droplet. To show that, we utilize two other possible gelling pairs, sodium carboxymethyl cellulose (CMC-Na)/calcium chloride and chitosan/sodium hydroxide, as motor mantle. Similar to sodium alginate/calcium chloride, CMC-Na/calcium chloride crosslinks in an electrostatic manner. But chitosan/sodium hydroxide gels through hydroxide-induced deprotonation of amines. Using PEGDA 400 as active molecules, all the chosen gelling pairs host sustained propulsion (Fig. 3a, see details in Supplementary Figs. 8–10). The CMC calcium motor lasts the longest (3214 s, 20 m), followed by calcium alginate (2971 s, 71 m) and chitosan (2182 s, 24 m) ones.

As shown in Fig. 3b, hydrogel matrices are inherently porous, limiting the surfactant to be non-small molecules; otherwise, small molecules can quickly diffuse through the nanoscopic pores, leading to fast fuel depletion and reduced concentration non-uniformity. In Fig. 3c, we compare the motor lifetime loaded with different surfactants. The lifetime of small molecule surfactants such as ethanol, isopropanol (Supplementary Tables 3, 4) is limited to be ~100 s. By contrast, the lifetime of non-small-molecule polymer surfactant is ~1000 s. Despite such differences, their normalized temporal positions roughly collapse onto a single non-dimensional curve (Fig. 3d), suggesting that the contrastive kinematics have similar dynamics.

Along with high Umax and long lifetime, the translational performance materialized through such a contracting mantle-siphon is high in view of other aspects. We benchmark the motor performance using two typical metrics for chemical motors, that is, output α = Umax/Vmax (maximum speed per unit volume) and efficiency ε = mU2max/2mf (maximum kinetic energy per unit mass of surfactant), where m is the initial mass of motor and mf is the total mass of surfactant loaded in the motor. These two metrics are used by Grzybowski et al. and Sitti et al. (Fig. 3e, Supplementary Table 5)20,21. The output of our motors can be as high as 2.06 × 105 mm-2 s-1 which is on a par with the highest reported value thus far. The efficiency leapfrogs to a high value, 1830 μJ g-1.

In Fig. 3f, we parameterize the locomotion of natural creatures and artificial motors with respect to body length B and relative velocity U/B (Supplementary Table 6). The natural and artificial locomotion, regardless of terrestrial or aquatic type, shows a clear inverse relationship between relative velocity and body length, potentially owing to mechanical constraints. Among these, our motors have a steeper slope, featuring an exceptionally high relative velocity of 2884.7 BL s-1 for the motor of 0.15 mm in radius.

Interfacial powering source
To explore potential applications and inspired by the work of Yu et al., we utilize our gelling-droplet motor to power their wireless and battery-free ion sensing system for real-time water quality monitoring22. Their system consists of sensing, data transmission, and propelling modules22 (Fig. 4a and Supplementary Fig. 11). For battery-free and wireless sensing and data transmission, potentiometric sensors and near-field communication (NFC) are used in the system23 (Fig. 4b). Our chemical motor is then used to actuate the motion of the sensing system without any connected cables.

We integrate 4-electrodes (3 ion-selective electrodes and 1 reference electrode) ionic sensors targeting 3 ions, Na+, K+, and NH4+, into the mobile electronic monitoring system24 (Fig. 4c). The 3 ion sensors show a log-linear voltage-concentration relationship predicted by the Nernst equation and have strong selectivity and anti-interference capability (Fig. 4d–f and Supplementary Fig. 12). A gelling-droplet motor is then attached to the system and brings it into untethered motion in a confined circular water channel (Fig. 4g, h). By dripping a gelling-droplet motor of only 12.7 μl in volume, the sensor system is continuously propelled for nearly 30 min which shows that the gelling-droplet motor can work as simplified power module for interfacial machines (Fig. 4i and Supplementary Movie 8).

To make the motor perform macroscopic tasks apart from simple translation, we construct elementary interfacial machines such as gear, cam, and crank, and construct them into transmission mechanisms (Fig. 5a-e)25,26. The interfacial machines are made by polyvinyl chloride sheet, allowing them to float on bath surface. As shown in Fig. 5a and Supplementary Movie 9, by depositing the motor on a gear tooth in an off-centre manner, the gear is driven into rotation whose direction is determined by the offset from the centre line in a radially outward direction. For example, the motor placed on the left side of a gear tooth will drive the gear into clockwise rotation. The rotation of the active gear can be transmitted to a passive gear (Fig. 5b).

Using such a mechanism (Supplementary Figs. 13–15 and Supplementary Movies 10, 11), we then construct the translational and swinging cam mechanisms whereby the cam rotation driven by the motor can be transformed into reciprocating rod translation or rocker swinging (Fig. 5c, d and Supplementary Movie 12). Note that in the state recovery stroke, the pushed rod or rocker restore their original position through lateral capillarity adhesion, producing intricate interaction between mechanical contact repulsion and short-range noncontact attraction. To enrich the system, a three-component mechanism is constructed in Fig. 5e and Supplementary Movie 13 wherein the crank rotation driven by motors is transformed into the rocker swinging through the intermediate linkage. The reciprocating translation can be materialized by driving a slider inside a rail (Fig. 5f and Supplementary Movie 14).

Methods
The motor precursor solution is made by dissolving sodium alginate in 90-˚C water with 1000-rpm magnetic stirring for 2 h, followed by surfactant addition at ambient temperature. The bath solution is made by dissolving calcium chloride in water. For motion tracking, the precursor solution is dyed red using direct red 23 (typically ~0.5 to 1 wt%). To initiate the self-propulsion, precursor solution droplets are generated and released from a steel nozzle fixed atop the liquid bath surface at ~4 mm. Droplets’ volume is controlled through the diameter of the nozzle.

Upon touching the bath solution, the instantaneous spreading and ensuing self-propulsion are recorded using high-speed photography at up to 5000 frames per second (Photron UX50). A single-mirror Schlieren optics setup is used to visualize the surfactant release.

For side-view PIV analysis, polystyrene microspheres of 50 μm in diameter are doped into the bath solution as tracer particles. For top-view PIV analysis, hydrophobic baby powder is seeded on the water surface as tracer particles. The velocity field is analysed using an open-source MATLAB code, PIVlab.

For interfacial machine powering, elementary machines of different geometries are fabricated by cutting a polyvinyl chloride sheet of 3 mm in thickness. Then the precursor solution is dripped at the edge of the machines for actuation.

The potentiometric ion-selective sensor is fabricated by patterning solid-state reference and working electrodes whose potential difference is measured to calculate ion concentration. The reference electrode is prepared by screen-printing Ag/AgCl ink onto a gold electrode. To minimize potential drift, a 2.5-μl methanol solution containing 79.1 mg ml-1 polyvinyl alcohol butyral (PVB), 50 mg ml-1 NaCl, 2 mg ml-1 triblock copolymer poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO, F127), and 0.2 mg ml-1 carbon nanotubes is deposited onto the Ag/AgCl electrode. For the working electrodes, poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) is electrochemically deposited onto three gold electrodes using an electrochemical workstation (CHI 660E) at a constant current of 141.36 µA for 1200-1800 s using a deposition solution containing 0.01 M 3,4-ethylenedioxythiophene (EDOT) and 0.1 M polystyrene sulfonate (NaPSS). Ion-selective membranes for Na+, K+, and NH4+ are then deposited. The ionophore cocktail is a tetrahydrofuran solution containing 1.51 mg ml−1 ionophore, 0.83 mg ml−1 sodium tetrakis [3,5-bis(trifluoromethyl)phenyl] borate (NaTFPB), 50 mg ml−1 polyvinyl chloride (PVC, K-value 72-1), and 99.17 mg ml−1 bis(2-ethylehexyl) sebacate (DOS). The ionophores used for the Na+, K+, and NH4+ ion sensors, respectively, are Na ionophore X, valinomycin, and NH4+ ionophore (nonactin).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors present Marangoni-driven soft motors with extreme lifetimes using calcium alginate, carboxymethyl cellulose and chitosan polymers. The original idea is not new as soft motors have been published for calcium alginate (references 11-13) and chitosan (not referenced, https://doi.org/10.1063/5.0097035) but the novelty is the addition of another polymer (PEGDA) with which extreme lifetime can be achieved and the use as an interfacial sensor. Furthermore, from the motors machines performing more complex tasks than simple translation and rotation are created.\nThe manuscript is nicely built up using the analogy with the squid as \"contracting-mantle-siphon configuration\".\nThe formation of the soft motors floating on solution is adequately characterized. The generality and the performance of the motors are excellently compared in Fig. 3 e and f with various artificial motors and animals (mammals, insects...).\nThe movies are of excellent quality, up to the point with correct lengths. The figures are of several subfigures but all needed and explained in the text. The SI contains the derivations but some are not sufficiently clear and the quantities yielding the dimensional numbers used should be also given.\nSuggestions in detail:\n-The amount/percentage of the added dye (direct red 23) should be added to the Materials section.\n-Fig. 2: What is used for normalization in U/D in Fig. 2b, please specify.\n2e: x axis should be shortened so the measurements are taking the larger part of the figure.\n2f: y axis should be between 10^2 and 10^3.\n-Typo in Fig. 1 i: Expulsion is the correct word (not Explusion)\n-Typo in Eqn. (3) - same as Eqn. S6: c_d should be C_d as this symbol was used as the drag coefficient above\nComments/suggestions related to SI:\n- mu is dynamic viscosity, it should be changed throughout the text\n- Re number: the relevant data from which Re=100 should be added (rho, mu, R, and U)\n- Derivation of S2 and S3 needs further explanation\n- Ca number: relevant data or reference to the used data (mu_b, gamma, U) from which Ca is between 0.01 and 0.1 should be added\n- Pe number: relevant data or reference to the used data from which Pe = 10^6 should be added\n- Gamma: probably the surfactant surface concentration, should be defined in the SI, the derivation of gamma = J_r/(2 R_m U) not clear, more explanation should be added\n- typo in Eqn S6: c_d should be C_d as this symbol was used as the drag coefficient above\n- Supp. Fig 2: Supp. Movie 3 is mentioned which is about gelation. What is the relevance to the figure. May be a typo?\n- Supp Fig. 4 and 5 a and d: U_max/B based on the unit of BL s^-1 is probably a relative velocity for the body size. Is it correct? Please specify it in the caption.\n- Sup Table 1: Density values should be centered throughout.\n- Overall a list of abbreviation is very helpful for the readers, the addition of the units would be beneficial as well. Moving the list from the end of SI to the beginning would be better for the reader.\nBased on above, I recommend the manuscript for publication after revision.", "reviewer_2": "The present manuscript tries to describe the underlying mechanism behind a self-propelling mantle and siphon swimmer created using a hydrogel-droplet combination. The manuscript also demonstrates a few applications of the aforementioned swimmer.\n1. Mechanism of self-propulsion: My major concern with the present manuscript is that the mechanism of self-propulsion is poorly explained.\n(a) To begin with, where and why does the hydrogel mantle perforate? The authors' explanation is that the shrinking hydrogel mantle results in increasing curvature of the floating lens, and hence increasing Laplace pressure, which eventually ruptures the mantle. What is the physics behind the shrinking hydrogel mantle? How is this related to the performance of the motor? Where is the location of the highest curvature? Is it at the three-phase contact line? What necessitates the rupture at that precise location? Does the hydrogel continue to shrink as the swimmer self-propels.\nMoreover, I failed to understand the shape of the swimmer from Fig. 1(i).\n(b) I do not agree with the authors' conjecture that the surface tension gradient near the boundary of the swimmer is a constant (top of p. 6). The surfactant volumetric release rate is strictly not a constant over time since the liquid inside the hydrogel shell gets depleted over time. Moreover, if I understand correctly, equation S3 (in the supplementary material) is the reason for a source term in Eq. 2 (Eq. S4 in the supplementary material). If that is indeed the case, then the expression in equation S3 should be multiplied with some reference volumetric concentration of surfactant. Moreover, the relationship between $\\Gamma$ and $J_r$ looks dimensionally inconsistent to me. I would request the authors to check this.\n(c) The assumption of homogeneous surfactant deposition on the liquid surface swept by the swimmer is too simplistic, and almost borders on incorrect. This assumption overlooks the important fact that over the length scale of the swimmer $(R_m)$ there has to be a finite gradient in the surfactant concentration in order to have self-propulsion. Ideally, Eq. 2 (or Eq. S4) needs to be solved along with the Euler's equations to obtain the distribution of the surfactant surface concentration since it is coupled to the high Reynolds number hydrodynamics.\n(d) Unfortunately, I am not convinced with the data presented in Figs. 2(e) and (f). In 2(e), there are only 3 to 4 data points for each weight percentage, that too without any errorbars. Similarly, in 2(f), I am not convinced that the fitting line (I am guessing which represents Eq. 3) truly represents the experimental trend.\n2. The definition of motor efficiency, and its subsequent calculation, are unclear.\n3. In the conclusion, the authors' mention- ``Our design works for different gelation and surfactant chemical pairs and performs exceptionally well in terms of metrics such as output and efficiency.\" It is unclear to me what are the `design' parameters that are controllable apart from the choice of the chemicals.\n4. The quality of the figures, specifically some of the graphs, leaves much to be desired.\nTo summarize, the manuscript fails to clearly explain and characterize the self-propulsion mechanism of the mantle and siphon droplet swimmer. In my opinion, the underlying physical mechanism is not rigorously explained in a quantitative manner to merit publication in Nature Communications. The applications demonstrated in the manuscript can only be useful to the broader scientific community once the underlying physical mechanism of the swimmer is fully grasped. Moreover, is it not possible for a simple camphor boat to perform these functions? Unfortunately, I cannot recommend the present manuscript for publication.", "reviewer_4": "The authors present a novel form of active soft matter which uses a combination of effects to produce truly fast (10mm/s), and long lived (~100minute) activity. This is enabled the the anisotropic crosslinking of a droplet which contains a surface active agent, and a cross linking polymer. As the polymer crosslinks, the surface active agent can only be released into the liquid as a perforation is formed as a result of anisotropic crosslinking. This technique is novel, and the effect it has as a combinatorial piece of active matter is phenomenologically rich. In this manuscript, the authors explore the mechanism with PIV, characterize other material systems which perform the same effect, and characterize the energetic limits with comparisons to literature. The authors also implement this system to push a water sensor, and to operate various examples of machines. This work is significant to the field, and the implementation of an actuation-marangoni soft matter robot is novel. The work largely supports its claims, while I have some concerns about a few details about the manuscript, listed below. The work is robust, and impressive, and after adressing the following concerns, including clarifying the mechanism and language, is suitable for publication.\nMajor:\n- A central point of the manuscript is the relationship between the effect of the siphon, and the effect on the movement of the droplet, but this interaction is not well characterized when compared to the rest of the manuscript (which is robust). What does the perforation look like? Does the capsule perforate, or does the droplet simply not crosslink at one zone? Does the \"jet\" of surface-active agent proceed throughout the experiment?\n- Continuing in this direction, references to the importance of \"laplace\" pressure occur frequently in the manuscript. The curvature does increase, but at the lengthscale of the droplet, the authors should demonstrate that it is the Laplace pressure that is moving surfactant out of the droplet.\nMinor:\n- The references and comparisons to the literature is somewhat incomplete, especially considering water-air interface swimmers and their introduction of anisotropy, and with reference to pulsing microrobots e.g., symmetry breaking.\n- The authors refer to the system as a \"host-guest\" system, could they elaborate on why this system qualifies as a host-guest system?\n- The authors claim that \"Marangoni motor is plagued by short lifetime of ~10 s, limiting its practical application for modular powering source\". It would be helpful to understand the intended object the proposed method would be used to power, and specifically what the physical limitations of traditional Marangoni-powered devices are.\n- In paragraph 3 the authors state: \"As shown in Figure 1c,e, upon touching solution bath, the surfactant-loading droplet spreads into a liquid lens, increasing capillary forces for its flotation9\". What are the components of the droplet, is it more dense than water, and should I expect it to sink if not placed above the solution?\n- The order, and depiction of figure 1 should be reconsidered. The connection to the various timescales of the experiment is an interesting way to depict the various behaviors of the droplet, but is confusing. To this end, the idea that the droplet is contracting when in contact with the solution (f) is very far away from 1h, where the importance of mantle contraction becomes apparent. Furthermore, indication of the crosslinking of the droplet-water interface would be helpful.\n- The authors should consider using a phrase such as self-generated, self-directed as opposed to \"malice of forethought\" at the end of page 3, and should take a general look at the manuscript to clarify language in and around experiment, such as the word \"liberating\", or \"lowers\" rather than \"weakens\" surface tension.\n- Figure 2a, the authors dyed the droplet red (alginate containing PEGDA), why is the droplet trapped in the PEGDA and not released?\n- Supplementary movie 1: the authors compare a camphor boat to their own method to demonstrate the \"long-lived\" nature, can the authors provide a comparison of the \"energy input\" into either motor? What is the relative mass of the camphor, to the propellant in the viscous example? Why does the viscous example have a stated speed of ~100s mm/s, when the authors mention ~10s of mm/s in the introduction.\n- Figure 2d/e/f: what is the wt% noted in the figure?\n- Can the authors clarify what surface tensions they refer to, as in to which interface is this surface tension applied?\n- The authors refer to a period of \"pulsed motion\", but the effect of the pulsed motion is not visible in the figure, or in any of supplementary videos. Can the authors include a note on the pulsed motion, the scale or reliability of pulsing, and a video?\n- The perforated syphon should be shown in some capacity, either by microscopy, or post-experiment to demonstrate, or measure the size of the syphon.\n- Does the top of the droplet gel? Does this gelling of the top of the droplet (if it does not occur) affect the performance of the droplet?"}, "author_response": "Response to Reviewers\nReviewer: 1\nComment 1:\nThe authors present Marangoni-driven soft motors with extreme lifetimes using calcium\nalginate, carboxymethyl cellulose and chitosan polymers. The original idea is not new as soft\nmotors have been published for calcium alginate (references 11-13) and chitosan (not\nreferenced, https://doi.org/10.1063/5.0097035) but the novelty is the addition of another\npolymer (PEGDA) with which extreme lifetime can be achieved and the use as an interfacial\nsensor. Furthermore, from the motors machines performing more complex tasks than simple\ntranslation and rotation are created. The manuscript is nicely built up using the analogy with\nthe squid as \"contracting-mantle-siphon configuration\". The formation of the soft motors\nfloating on solution is adequately characterized. The generality and the performance of the\nmotors are excellently compared in Fig. 3 e and f with various artificial motors and animals\n(mammals, insects...). The movies are of excellent quality, up to the point with correct lengths.\nThe figures are of several subfigures but all needed and explained in the text. The SI contains\nthe derivations but some are not sufficiently clear and the quantities yielding the dimensional\nnumbers used should be also given.\nOur response: We sincerely thank the reviewer for his/her valuable and constructive comments,\nwhich have greatly contributed to improving the quality of our manuscript. We have revised\nthe manuscript accordingly and provided the following point-by-point responses to each\ncomment.\nOur modification to the manuscript: In the Manuscript, we cited the paper of self-propelled\nchitosan hydrogel as Reference 14 (Page 14).\n14. Kumar, P., Horváth, D. & Tóth, Á. Sol-gel transition programmed self-propulsion of\nchitosan hydrogel. Chaos: An Interdisciplinary Journal of Nonlinear Science 32 (2022).\nComment 2:\nSuggestions in detail: -The amount/percentage of the added dye (direct red 23) should be added\nto the Materials section.\nOur response: We thank the reviewer for this valuable suggestion. The amount of the dye is\ntypically ~0.5 to 1 wt% which is added in the Materials and Methods section.\nOur modification to the manuscript: In the Manuscript, we added the percentage of added\ndye in the Materials and Methods section (Page 16, Line 5).\nComment 3:\n-Fig. 2: What is used for normalization in U/D in Fig. 2b, please specify.\n2e: x axis should be shortened so the measurements are taking the larger part of the figure.\n2f: y axis should be between 10^2 and 10^3.\nOur response: We thank the reviewer for these valuable suggestions to enhance the readability\nof the manuscript. In Figure 2b, velocity U was normalized by the motor diameter D. In Figure\n2e, x-axis was shortened so the measurements take a larger part of the figure. In Figure 2f, y-\naxis was set between 102 and 103.\nOur modification to the manuscript: In the Manuscript, we added sentences in the caption\nof Figure 2b to specify that the propelling velocity U is normalized by motor diameter D (Page\n21, Lines 6,7); we replotted Figure 2e so that data takes a larger part of the figure (Page 21);\nwe shortened the y-axis of Figure 2f so that its range is from 102 to 103 (Page 21).\nComment 4:\n-Typo in Fig. 1 i: Expulsion is the correct word (not Explusion)\n-Typo in Eqn. (3) - same as Eqn. S6: c_d should be C_d as this symbol was used as the drag coefficient above\nOur response: We sincerely thank the reviewer for giving us the opportunity to correct the\ntypos. In Figure 1i, original word “Explusion” is corrected to be “Expulsion”. The symbol\ndenotes for drag coefficient is revised to be C .\nd\nOur modification to the manuscript: In the Manuscript, we corrected the word from\n“Explusion” to “Expulsion” in Figure 1i (Page 19); we corrected the symbol for drag\ncoefficient from “c ” to “C ” in Equation 3 (Page 8). In the Supplementary Materials, we\nd d\ncorrected the symbol for drag coefficient from “c ” to “C ” in Equation S9 which is the original\nd d\nEquation S6 (Page 5).\nComment 5:\nComments/suggestions related to SI:\n- mu is dynamic viscosity, it should be changed throughout the text\n- Re number: the relevant data from which Re=100 should be added (rho, mu, R, and U)\n- Derivation of S2 and S3 needs further explanation\n- Ca number: relevant data or reference to the used data (mu_b, gamma, U) from which Ca is\nbetween 0.01 and 0.1 should be added\n- Pe number: relevant data or reference to the used data from which Pe = 10^6 should be added\nOur response: We thank the reviewer for giving us the opportunity to clarify the key details.\nThroughout the text, we clarified that μ is dynamic viscosity. In the Supplementary Materials,\nRe = 100 is calculated using ρ ≈ 103 kg m-3, u ≈ 0.1 m s-1, R ≈ 10-3 m, μ ≈ 10-3 Pa s; Re = 102-\nd l d\n103 is calculated using ρ ≈ 103 kg m-3, U ≈ 0.1 to 1 m s-1, R ≈ 10-3 m, μ ≈ 10-3 Pa s; Ca = 10-\nb m b\n2-10-1 is calculated using μ ≈ 10-3 Pa s, U ≈ 0.1 to 1 m s-1, σ ≈ 0.01 N m-1; Pe = 106 is calculated\nb\nusing D ~ 10-10 m2 s-1, U ≈ 0.1 m s-1, R ≈ 10-3 m. All the data used was added in the\ns m\nSupplementary Materials. We added further explanation of Equation S2 and S3 in\nSupplementary Materials.\nOur modification to the manuscript: Throughout the text, we clarified that μ is dynamic\nviscosity. In the Supplementary Materials, we added relevant data to calculate Re (Page 1,\nLines 16, 17 and Page 5, Lines 11, 12), Ca (Page 4, Line 5), and Pe (Page 4, Line 10); we added\nexplanation (Page 2, Lines 1-6 and 10 for Equation S2 and Page 3, Lines 1-6 for Equation S3)\nto detail the derivation of Equation S2 and S3.\nComment 6:\n- Gamma: probably the surfactant surface concentration, should be defined in the SI,\nthe\nderivation of gamma = J_r/(2 R_m U) not clear, more explanation should be added\nOur response: We thank the reviewer for these valuable suggestions to enhance the readability\nof the manuscript. We defined Г as surfactant surface concentration and added explanation to\ndetail the derivation of Equation S7 in the Supplementary Materials.\nOur modification to the manuscript: In the Supplementary Materials, we defined Г as\nsurfactant surface concentration (Page 4, Line 2); we added explanation to detail the derivation\nof Equation S7 (Page 4, Lines 12-16).\nComment 7:\n- typo in Eqn S6: c_d should be C_d as this symbol was used as the drag coefficient above\nOur response: We sincerely thank the reviewer for giving us the opportunity to correct the\ntypos. Throughout the manuscript, the symbol for drag coefficient is revised to be C .\nd\nOur modification to the manuscript: In the Supplementary Materials, we corrected the\nsymbol for drag coefficient from “c ” to “C ” in Equation S9 which is the original Equation S6\nd d\n(Page 5).\nComment 8:\n- Supp. Fig 2: Supp. Movie 3 is mentioned which is about gelation. What is the relevance to\nthe figure. May be a typo?\n- Supp Fig. 4 and 5 a and d: U_max/B based on the unit of BL s^-1 is probably a relative\nvelocity for the body size. Is it correct? Please specify it in the caption.\nOur response: We sincerely thank the reviewer for giving us the opportunity to correct the\ntypos as well as provide essential details. We revised original “Supplementary Movie 3” to\n“Supplementary Movie 4” in the caption of Supplementary Figure 2 so that correct video is\nreferred to. We added description in the caption of Supplementary Figure 8, 9 (original\nSupplementary Figure 4, 5) to specify that it is the relative velocity calculated by normalizing\npropelling velocity U by motor diameter D.\nOur modification to the manuscript: In the Supplementary Materials, we revised original\n“Supplementary Movie 3” to “Supplementary Movie 4” in the caption of Supplementary\nFigure 2 (Page 10, Line 7); We added sentences in the caption of Supplementary Figure 8, 9,\nwhich are original Supplementary Figure 4, 5 (Page 16, Lines 3, 8, 9 and Page 17, Lines 3, 8)\nto specify that it is the relative velocity calculated by normalizing propelling velocity U by\nmotor diameter D.\nComment 9:\n- Sup Table 1: Density values should be centered throughout.\n- Overall a list of abbreviation is very helpful for the readers, the addition of the units would\nbe beneficial as well. Moving the list from the end of SI to the beginning would be better for\nthe reader.\nBased on above, I recommend the manuscript for publication after revision.\nOur response: We sincerely thank the reviewer for pointing these out. We centred the density\nvalues in Supplementary Table 2 (original Supplementary Table 1). We added units in the list\nof symbols and moved the list to the beginning of Supplementary Tables so that it becomes\nSupplementary Table 1.\nOur modification to the manuscript: In the Supplementary Materials, we centred the density\nvalues throughout in Supplementary Table 2, which is original Supplementary Table 1 (Page\n25); we added units in the list of symbols and moved the list to the beginning of supplementary\ntables (Page 23, 24).\nWe would like to thank the reviewer once again for expending so much time and effort in\nproviding a review which has helped us to improve the clarity and specificity of our manuscript.\nReviewer: 2\nComment 1:\nThe present manuscript tries to describe the underlying mechanism behind a self-propelling\nmantle and siphon swimmer created using a hydrogel-droplet combination. The manuscript\nalso demonstrates a few applications of the aforementioned swimmer.\nOur response: We sincerely thank the reviewer for his/her valuable and constructive comments,\nwhich have greatly contributed to improving the quality of our manuscript, particularly in the\nmechanism section. We have revised the manuscript accordingly and provided the following\npoint-by-point responses to each comment.\nComment 2:\n1. Mechanism of self-propulsion: My major concern with the present manuscript is that the\nmechanism of self-propulsion is poorly explained.\n(a) To begin with, where and why does the hydrogel mantle perforate? The authors' explanation\nis that the shrinking hydrogel mantle results in increasing curvature of the floating lens, and\nhence increasing Laplace pressure, which eventually ruptures the mantle.\nOur response: We thank the reviewer for these insightful comments. Expansion pressure is\napplied across the mantle surface because of pressure difference between droplet and liquid\nbath. Apart from that, extra surface tension force acts along three-phase contact line and\nradially stretch the gel mantle. In this way, the stress tends to localize at motor’s perimeter.\nWhen circumferential tensile stress in the perimeter exceeds the gel strength, the gel fractures.\nBecause of inhomogeneity in gel strength or localized stress concentration, the exact\nperforation position along the perimeter cannot be precisely controlled. However, because of\nhigh tensile stress, the perforation preferentially occurs at the contact line.\nOur modification to the manuscript: In the Manuscript, we added sentences (Page 6, Lines\n2-5) to explain that the hydrogel mantle is perforated at the three-phase contact line when local\ncircumferential tensile stress exceeds the gel strength. We added sentences (Page 12, Lines 18,\n19) to acknowledge that the exact fracture position on the three-phase contact line cannot be\ncontrolled yet.\nComment 3:\n(A) What is the physics behind the shrinking hydrogel mantle? (B) How is this related to the\nperformance of the motor?\nOur response: We sincerely appreciate the reviewer’s insightful comments. To provide clearer\nresponses, we have divided them into two sections.\n(A) What is the physics behind the shrinking hydrogel mantle?\nOur response: We thank the reviewer for the insightful comment. As alginate molecular chain\ncrosslinks with calcium ions, those previously free chains aggregate and connect with each\nother, forming a tight network of reduced volume. Such volume-shrinking effect associated\nwith the alginate gel is reported in Reference 17 & 18.\nOur modification to the manuscript: To explain the physics behind the shrinking hydrogel\nmantle, in the Manuscript, we added sentences (Page 5, Lines 8-11) and Reference 17,18; in\nthe Supplementary Materials, we added sentences (Page 2, Line 15).\n17. Gong, J., Schuurmans, C. C., Genderen, A. M. v., Cao, X., Li, W., Cheng, F., He, J. J.,\nLópez, A., Huerta, V. & Manríquez, J. Complexation-induced resolution enhancement of 3D-\nprinted hydrogel constructs. Nature communications 11, 1267 (2020).\n18. Cao, P., Tao, L., Gong, J., Wang, T., Wang, Q., Ju, J. & Zhang, Y. 4D printing of a sodium\nalginate hydrogel with step-wise shape deformation based on variation of crosslinking density.\nACS Applied Polymer Materials 3, 6167-6175 (2021).\n(B) How is this related to the performance of the motor?\nOur response: We sincerely thank the reviewer for the constructive comment. As shown in\nFigure R1 and Supplementary Movie 6, we added experiments to examine the impact of\nshrinking hydrogel mantle on the performance of the motor. Micromotors are firstly formed in\nCaCl liquid bath for ~30 s and then transferred into water whereupon crosslinking is\n2\nterminated. Their radius R , lifetime t , and maximum velocity U are compared with those\nm max max\nof ones maintained in CaCl (crosslinking persists for the entire lifetime). The transferred ones\n2\nhave slightly larger radius, suggesting that the crosslinking and thus very slow shrinking\ncontinues throughout self-propulsion. Because the two groups have the same conditions in the\nvery first 30 s, so they have basically the same maximum velocity. By contrast, the continuous-\ncrosslinking motor has a lifetime fourfold higher than that of the terminated one. We propose\nthat as crosslinking proceeds, thicker mantle forms which prevents surfactant diffusion across\ngel film more effectively. Therefore, continuous crosslinking has impact on motor’s\nperformance. However, the size shrinking associated with the continuous crosslinking is very\nsmall. Therefore, in such long timescale, the size shrinking has limited impact on the motor\nperformance.\nFigure R1 (Supplementary Figure 5 in the Supplementary Materials). Continuous\ncrosslinking during self-propulsion. (a) Micromotors are formed in CaCl liquid bath for ~30\n2\ns and then transferred into water whereupon crosslinking is largely terminated (see\nSupplementary Movie 6). Comparison of micromotor’s radius R (b), lifetime t (c), and\nm max\nmaximum velocity U (d) for ones maintained in CaCl (crosslinking persists for the entire\nmax 2\nlifetime) and ones transferred into water after ~30 s (crosslinking only persists for the first 30\ns). Error bars denote standard deviation of 3 experiments.\nOur modification to the manuscript: To explain how the continuous crosslinking relates to\nthe performance of the motor, in the Manuscript, we added sentences (Page 7, Lines 2-8); in\nthe Supplementary Materials, we added Supplementary Figure 5 and Supplementary Movie 6.\nComment 4:\nWhere is the location of the highest curvature? Is it at the three-phase contact line?\nOur response: We sincerely thank the reviewer for the insightful comment. The curvature of\nliquid-air interface signifies the pressure inside the droplet. Because there is no strong pressure\ngradient inside the droplet, the curvature is uniform along the liquid-air interface at droplet’s\ntop.\nOur modification to the manuscript: In the Manuscript, we added sentences (Page 5, Lines\n20 and 21; Page 6, Line 1) to explain that as no strong pressure gradient is present in droplet,\ntherefore, the curvature is largely uniform.\nComment 5:\nWhat necessitates the rupture at that precise location?\nOur response: We sincerely thank the reviewer for this constructive comment. Along three-\nphase contact line (note that thin gel film forms at the droplet-bath interface), Laplace pressure\nand surface tension force (surface tension of bath-air interface perpendicularly acting along\ndroplet perimeter) radially stretch the newly-crosslinked gel film. When local circumferential\ntensile stress exceeds the gel strength, crack starts to form. In this way, the rupture preferentially\noccurs at the contact line. The exact rupture location may be associated with sites of stress\nconcentration or gel defect. In our incipient approach, we cannot control the exact rupture point\nalong the contact line.\nOur modification to the manuscript: In the Manuscript, we added sentences (Page 6, Lines\n2-5) to explain that the rupture occurs at the three-phase contact line; we added sentences (Page\n12, Lines 18 and 19) to acknowledge that we cannot control the precise rupture location along\nthe three-phase contact line.\nComment 6:\nDoes the hydrogel continue to shrink as the swimmer self-propels.\nOur response: We appreciate the reviewer’s insightful comment. As shown in Figure R1 and\nSupplementary Movie 6, we added experiments to examine the continuous shrink throughout\nself-propulsion. After motor forms and propels in 30 s, we terminate its further crosslinking by\ntransferring it into water. Unlike the continuous-crosslinking one, it has larger radius which\nsuggests that the crosslinking and thus slow shrinking continues throughout self-propulsion.\nFigure R1 (Supplementary Figure 5 in the Supplementary Materials). Continuous\ncrosslinking during self-propulsion. (a) Micromotors are formed in CaCl liquid bath for ~30\n2\ns and then transferred into water whereupon crosslinking is largely terminated (see\nSupplementary Movie 6). Comparison of micromotor’s radius R (b), lifetime t (c), and\nm max\nmaximum velocity U (d) for ones maintained in CaCl (crosslinking persists for the entire\nmax 2\nlifetime) and ones transferred into water after ~30 s (crosslinking only persists for the first 30\ns). Error bars denote standard deviation of 3 experiments.\nOur modification to the manuscript: To verify that the droplet continues to shrink as the\ndroplet self-propels, in the Manuscript, we added sentences (Page 7, Lines 2-5); in the\nSupplementary Materials, we added Supplementary Figure 5 and Supplementary Movie 6.\nComment 7:\nMoreover, I failed to understand the shape of the swimmer from Fig. 1(i).\nOur response: Thanks for bringing this to our attention. As motor propels, it creates water\nwave around it. Such uneven water surface distorts its image in the Schlieren visualization.\nAs\nshown in Supplementary Movie 5, when the motor is static, it appears circular. Once it moves,\nits profile in Schlieren image is distorted.\nOur modification to the manuscript: In the Manuscript, we added sentences in caption of\nFigure 1i (Page 20, Lines 6-8) to explain that the water wave caused by motion distorts the\ndroplet’s profile in the Schlieren image. In the Supplementary Materials, we added\nSupplementary Movie 5 to confirm such image distortion.\nComment 8:\n(b) I do not agree with the authors' conjecture that the surface tension gradient near the\nboundary of the swimmer is a constant (top of p. 6).\nOur response: We thank the reviewer for giving us the opportunity to clarify our misleading\ndescription. We want to express that the vortex convects fresh bulk solution to the surface and\nassists to break the surfactant adsorption saturation on bath surface. The original misleading\ndescription has been revised accordingly.\nOur modification to the manuscript: In the Manuscript, we rewrote the original misleading\nsentence “The vortex assists to sustain a constant surface tension gradient near the boundary\nby convecting fresh bulk solution to the surface, a flow breaking the surfactant adsorption\nsaturation on bath surface.” into “The vortex convects fresh bulk solution to the surface and\nassists to break the surfactant adsorption saturation on bath surface” (Page 7, Lines 12 and\n13).\nComment 9:\nThe surfactant volumetric release rate is strictly not a constant over time since the liquid inside\nthe hydrogel shell gets depleted over time. Moreover, if I understand correctly, equation S3 (in\nthe Supplementary Materials) is the reason for a source term in Eq. 2 (Eq. S4 in the\nSupplementary Materials). If that is indeed the case, then the expression in equation S3 should\nbe multiplied with some reference volumetric concentration of surfactant.\nOur response: We sincerely thank the reviewer for this valuable comment. For source term,\nR (t)3n\nwe derived that the liquid volumetric releasing rate out of the droplet is Q~103 m d\n\nd\n(Equation S3). For long-timescale propulsion (~1000 s), motor size R slightly shrinks, σ and\nm d\nμ\nd\ncan be considered constant, so variation of Q is controlled by n. However, the temporal\nevolution of n is exceptionally challenging to experimentally capture for the rapidly\nmoving millimetre motor. In accordance with the reviewer’s suggestion, as shown in Figure\nR2, for long-timescale propulsion (~1000 s), droplet’s velocity decreases in an exponential\nmanner, suggesting surfactant release is the first-order type wherein the releasing rate is\nproportional to the remaining amount. On the basis of such velocity evolution feature, releasing\nrate can be phenomenologically considered as the first-order release. Thus, we can simplify the\nliquid volumetric releasing rate as Q~Qekt (Equation S4 in the Supplementary Materials),\nwhere Q 0 is the initial volumetric releasing rate Q 103 m d i with n being\n0  i\nd\ndroplet-air curvature upon motion initiation, k is the first-order releasing rate constant. In this\nway, surfactant releasing rate in the unit of mol s-1 is J ~c Qekt (Equation S5 in the\nm 0\nSupplementary Materials), where c is the surfactant concentration in the droplet.\nm\nFigure R2 (revised Figure 2b in the Manuscript). The distance and propelling velocity\nnormalized by motor diameter D as a function of time. Purple and magenta shadings,\nrespectively, denote continuous and pulsed motion mode. Purple dashed line denotes the\nexponential fitting line, y53e0.0016x, for the propelling velocity after initial 5 s.\nOur modification to the manuscript: In the Manuscript, we added an exponential fitting line\nfor motor’s velocity evolution in Figure 2b (Page 21) and sentences (Page 6, Lines 18-20) to\nhighlight the potential first-order releasing feature associated with the velocity exponential\ndecrease. We added sentences in the Supplementary Materials (Page 3, Lines 7-15) to detail\nthe derivation of such first-order surfactant release.\nComment 10:\nMoreover, the relationship between $\\Gamma$ and $J_r$ looks dimensionally inconsistent to\nme. I would request the authors to check this.\nOur response: We thank the reviewer for giving us an opportunity to check and correct the\nterms in Equation 2. In the corrected Equation 2, the implicit source term S , which is set\nboundary\nas a boundary source in numerical study, has a unit of mol m-2 s-1. In this way, it has a physical\ndimension of [mol L-2 T-1], which is the same as that of the other terms in Equation 2 such as\nthe change rate of surface concentration dГ/dt.\nOur modification to the manuscript: In the Supplementary Materials, we added units in the\nTable 1. List of Symbols (Page 23 and 24) to show that the source term S has a unit of\nboundary\nmol m-2 s-1 which is consistent with that of change rate of surface concentration dГ/dt in the\nEquation 2 (Page 7).\nComment 11:\n(c) The assumption of homogeneous surfactant deposition on the liquid surface swept by the\nswimmer is too simplistic, and almost borders on incorrect. This assumption overlooks the\nimportant fact that over the length scale of the swimmer $(R_m)$ there has to be a finite\ngradient in the surfactant concentration in order to have self-propulsion. Ideally, Eq. 2 (or Eq.\nS4) needs to be solved along with the Euler's equations to obtain the distribution of the\nsurfactant surface concentration since it is coupled to the high Reynolds number\nhydrodynamics.\nOur response: We thank the reviewer for this insightful comment. We numerically solved\nEquation 2 coupled with fluid dynamics and motor motions. As shown in Figure R3, we\nnumerically study the motor motion and evolution of surfactant concentration distribution\nthrough finite-element analysis using COMSOL-Multiphysics. When the motor propels,\naround its perimeter, the released surfactant is concentrated in the vicinity of releasing siphon.\nFar behind motor, the released surfactant is diffused and spread out. In terms of Marangoni\npropulsion, the surface concentration in the vicinity of contact line matters as Marangoni force\nis the line integral of surface tension acting on motor’s perimeter. Near the contact line, the\nsimplified assumption (Equation S7, pulse concentration distribution) is roughly in consistent\nwith such concentrated distribution feature. Therefore, the simplification is used to\napproximate the magnitude of Marangoni force.\nFigure R3 (Supplementary Figure 6 in the Supplementary Materials). Evolution of\nsurfactant distribution. Schematics of concentration distribution with (a) and without (b)\nsurfactant transport through diffusion and advection. (c) Numerically-calculated distribution of\nsurfactant at t = 0.8 s (Supplementary Movie 7). (d) Numerically-calculated surfactant\nconcentration along the perimeter of motor. The surfactant is concentrated around the releasing\nsiphon. In derivation of Equation S7, we simplify the concentration around the perimeter as a\npulse function denoted by the red line.\nOur modification to the manuscript: In the Manuscript, we added sentences (Page 8, Lines\n4-10) to explain the simplification and numerical study of surfactant concentration distribution.\nIn the Supplementary Materials, we added Supplementary Note 3 (Page 5, Lines 17-19 and\nPages 6-8) to explain details of our numerical model and Supplementary Figure 6,\nSupplementary Movie 7 to show results of our numerical study and verify our simplified\nassumption on the basis of numerical surfactant concentration distribution.\nComment 12:\n(d) Unfortunately, I am not convinced with the data presented in Figs. 2(e) and (f). In 2(e),\nthere are only 3 to 4 data points for each weight percentage, that too without any error bars.\nOur response: We thank the reviewer for this insightful suggestion. By experimentally varying\ndroplet volume V, we added more data in Figure R4 (revised Figure 2e). For each data point,\nexperiments are repeated for 5 times so that error bar denoting the standard deviation is added.\nFigure R4 (revised Figure 2e in the Manuscript). Logarithmic representation of the\nmeasured finite spreading radius R and its scaling prediction. Error bars denote standard\nl\ndeviation of 5 experiments. Colour denotes mass percentage of calcium chloride in the liquid\nbath. The droplet is aqueous solution of 1 wt% sodium alginate and 25 wt% PEGDA400.\nOur modification to the manuscript: In the Manuscript, we added more data in Figure 2e\n(Page 21) and added error bar by repeating each experiment for 5 times.\nComment 13:\nSimilarly, in 2(f), I am not convinced that the fitting line (I am guessing which represents Eq.\n3) truly represents the experimental trend.\nOur response: We thank the reviewer for pointing this out. Because it is experimentally\nchallenging to increase the order of magnitude of R and U in Figure 2f, therefore, the\nm max\nrelationship indicated by the fitting line is not exceptionally convincing. We highlight the\nlimitation of Figure 2f by stating “Note that the scaling in Figure 2f is semi-quantitative as R\nm\nand U span for only one order of magnitude which is the largest range that we can\nmax\nexperimentally obtain.” in the Manuscript.\nOur modification to the manuscript: In the Manuscript, we added sentences (Page 8, Lines\n16-18) to explain limitation of Figure 2f, that is, it spans for only one order of magnitude and\nhighlight that it is only semi-quantitative because of such limitation.\nComment 14:\n2. The definition of motor efficiency, and its subsequent calculation, are unclear.\nOur response: We apologize for the unclear definition of motor efficiency. We added the\ndefinition of motor output  U V as maximum speed per unit volume and the\nmax max\ndefinition of efficiency  mU2 2m as maximum kinetic energy per unit mass of\nmax max f\nsurfactant. These two metrics are used for chemical motors and their sources are cited as\nReference 20, 21.\n20. Pena-Francesch, A., Giltinan, J. & Sitti, M. Multifunctional and biodegradable self-\npropelled protein motors. Nature communications 10, 3188 (2019).\n21. Park, J. H., Lach, S., Polev, K., Granick, S. & Grzybowski, B. A. Metal–organic framework\n“swimmers” with energy-efficient autonomous motility. ACS nano 11, 10914-10923 (2017).\nOur modification to the manuscript: In the Manuscript, we added sentences (Page 9, Lines\n21 and 22) to detail the definition of motor efficiency and output and cited References 20 and\n21 to provide source of such definition.\nComment 15:\n3. In the conclusion, the authors' mention- ``Our design works for different gelation and\nsurfactant chemical pairs and performs exceptionally well in terms of metrics such as output\nand efficiency.\" It is unclear to me what are the `design' parameters that are controllable apart\nfrom the choice of the chemicals.\nOur response: We thank the reviewer for pointing this out. We revised the inaccurate word\n“design” to be “approach” and highlight that the approach is based on “combination of\nchemicals”. In this way, the original sentence “Our design works for different gelation and\nsurfactant chemical pairs and performs exceptionally well in terms of metrics such as output\nand efficiency.” is rewrote into “Our approach, the crosslinking-mediated surfactant release\nachieved through combination of chemicals, works for different gelation and surfactant\nchemical pairs and performs exceptionally well in terms of metrics such as output and\nefficiency.”\nOur modification to the manuscript: In the Manuscript, we rewrote the original sentence\n“Our design works for different gelation and surfactant chemical pairs and performs\nexceptionally well in terms of metrics such as output and efficiency.” into “Our approach, the\ncrosslinking-mediated surfactant release achieved through combination of chemicals, works\nfor different gelation and surfactant chemical pairs and performs exceptionally well in terms\nof metrics such as output and efficiency.” (Page 12, Lines 9-12) to clarify that the main\ncontrollable parameters for the incipient approach are combination of chemicals.\nComment 16:\n4. The quality of the figures, specifically some of the graphs, leaves much to be desired. To\nsummarize, the manuscript fails to clearly explain and characterize the self-propulsion\nmechanism of the mantle and siphon droplet swimmer. In my opinion, the underlying physical\nmechanism is not rigorously explained in a quantitative manner to merit publication in Nature\nCommunications. The applications demonstrated in the manuscript can only be useful to the\nbroader scientific community once the underlying physical mechanism of the swimmer is fully\ngrasped. Moreover, is it not possible for a simple camphor boat to perform these functions?\nUnfortunately, I cannot recommend the present manuscript for publication.\nOur response: In accordance with the review’s insightful comments, we upgraded the quality\nof graphs, performed experiments and numerical studies so that the explanation of the physical\nmechanism is more rigorous. Our approach provides a strategy to extend the lifetime of\nMarangoni motor. Although a simple camphor boat can also, for example, actuate an interfacial\nsensor, it cannot achieve long timescale propulsion. It is hoped that the revised version will\nmeet the requirements for publication.\nWe would like to thank the reviewer once again for expending so much time and effort in\nproviding a review which has helped us to improve the clarity and specificity of our manuscript.\nReviewer: 3\nComment 1:\nThe authors present a novel form of active soft matter which uses a combination of effects to\nproduce truly fast (10mm/s), and long lived (~100minute) activity. This is enabled the the\nanisotropic crosslinking of a droplet which contains a surface active agent, and a cross linking\npolymer. As the polymer crosslinks, the surface active agent can only be released into the liquid\nas a perforation is formed as a result of anisotropic crosslinking. This technique is novel, and\nthe effect it has as a combinatorial piece of active matter is phenomenologically rich. In this\nmanuscript, the authors explore the mechanism with PIV, characterize other material systems\nwhich perform the same effect, and characterize the energetic limits with comparisons to\nliterature. The authors also implement this system to push a water sensor, and to operate various\nexamples of machines. This work is significant to the field, and the implementation of an\nactuation-marangoni soft matter robot is novel. The work largely supports its claims, while I\nhave some concerns about a few details about the manuscript, listed below. The work is robust,\nand impressive, and after adressing the following concerns, including clarifying the mechanism\nand language, is suitable for publication.\nOur response: We sincerely thank the reviewer for the positive feedback and insightful\nsuggestions, which have been invaluable in enhancing the manuscript. We have revised the\nmanuscript accordingly and provided detailed point-by-point responses to each comment.\nComment 2:\nMajor:\n- A central point of the manuscript is the relationship between the effect of the siphon, and the\neffect on the movement of the droplet, but this interaction is not well characterized when\ncompared to the rest of the manuscript (which is robust). What does the perforation look like?\nDoes the capsule perforate, or does the droplet simply not crosslink at one zone?\nOur response: We appreciate the reviewer’s insightful comment and apologize for the\ninsufficient description of siphon in the original manuscript. Along three-phase contact line,\nthe newly-crosslinked gel film is radially stretched by the Laplace pressure and surface tension\nforce (surface tension of bath-air interface perpendicularly acting along droplet perimeter).\nWhen local circumferential tensile stress exceeds the gel strength, crack starts to form. As\nshown in Figure R5, when the gel film fractures, the siphon is formed. Therefore, the\nperforation appears as a crack on the gel film.\nFigure R5 (Supplementary Figure 3 in the Supplementary Materials). Siphon formed by\ngel fracture. Fluorescence image of motor (a) and magnified siphon (b) showing that the\nreleasing hole appears as a fracture on the gel mantle. The opening has a maximum width of\nroughly 6% of motor’s radius.\nOur modification to the manuscript: In the Manuscript, we added sentences (Page 6, Lines\n4 and 5) to explain that the siphon forms because of gel mantle fracture. In the Supplementary\nMaterials, we added Supplementary Figure 3 (Page 11) to show image of the perforation.\nComment 3:\nDoes the \"jet\" of surface-active agent proceed throughout the experiment?\nOur response: We thank the reviewer for pointing this out. The jet accompanies the motor\nmotility throughout the experiment. Because approaching the end of motor’s lifetime, that is,\nthe pulsed mode, the motor only moves when jet forms (Figure R6 and Supplementary Movie\n5). Without jet, the motor cannot move.\nFigure R6 (Supplementary Figure 4 in the Supplementary Materials). Pulsed motion. (a)\nImage of a motor after 7 pulsed motions (Supplementary Movie 5). (b) Displacement,\nvelocity,\nand acceleration of the 7 pulsed motions.\nOur modification to the manuscript: In the Manuscript, we added sentences (Page 6, Lines\n21 and 22; Page 7, Lines 1 and 2) to explain that the jet proceeds as motor propels. In the\nSupplementary Materials, we added Supplementary Figure 4 and Supplementary Movie 5 to\nshow that even approaching the end of motor lifetime, that is, in the pulsed motion mode, the\njet accompanies the propulsion.\nComment 4:\n- Continuing in this direction, references to the importance of \"laplace\" pressure occur\nfrequently in the manuscript. The curvature does increase, but at the length scale of the droplet,\nthe authors should demonstrate that it is the Laplace pressure that is moving surfactant out of\nthe droplet.\nOur response: We apologize for insufficient discussion of Laplace-pressure-driven release in\nthe original manuscript. As shown in Figure R7 (revised Figure 1g), the pressure inside the\ndroplet can be well described using the interface curvature as the top of droplet is not\ncrosslinked. Because the height of droplet is much smaller than the capillary length, thus\nhydrostatic pressure can be neglected. Beneath the bath-air interface, the pressure in liquid bath\np b equals to the ambient pressure p a . By contrast, pressure inside droplet p d is p n .\na d\nOnce the siphon forms, surfactant is pumped out because of higher p . The detailed discussion\nd\nis added in the Manuscript.\nFigure R7 (revised Figure 1g in the Manuscript). The gradual crosslinking lowers droplet\nradius R (t), increasing the Laplace pressure of liquid interior. Pressure buildup swiftly\nm\nperforates the gel mantle, forming a siphon through which surfactant is released.\nOur modification to the manuscript: In the Manuscript, we added sentences (Page 5, Lines\n15-20) to analyse that pressure inside the droplet is higher than that outside of the droplet by\nan amount of n . Therefore, it is the Laplace pressure which pumps surfactant out of\nd\ndroplet.\nComment 5:\nMinor:\n- The references and comparisons to the literature is somewhat incomplete, especially\nconsidering water-air interface swimmers and their introduction of anisotropy, and with\nreference to pulsing microrobots e.g., symmetry breaking.\nOur response: We sincerely thank the reviewer for this valuable suggestion. As shown in\nFigure R8 (revised Figure 3f), we have classified and added water-air interface swimmer in the\nliterature to compare with our approach. Full references of those water-air interface swimmers\nare listed in Supplementary Table 6.\nFigure R8 (revised Figure 3f in the Manuscript). Logarithmic representation of the\nmaximum relative velocities U/B and size B for insects, terrestrial and aquatic animals,\nartificial\nrobots, and water-air interface swimmers. The light violet, blue violet, green, orange, and red\nshadings, respectively, denotes rigid robot, terrestrial soft robot, aquatic soft robot, water-air\ninterface swimmer, and our gelling-droplet motor. Full references are given in Supplementary\nTable 6.\nOur modification to the manuscript: In the Manuscript, we added data of water-air interface\nswimmer in Figure 3f (Page 23). In the Supplementary Materials, we updated relevant\nreferences in Supplementary Table 6 (Pages 34 and 35) to complete the comparison between\nour work and reported water-air interface swimmer.\nComment 6:\n- The authors refer to the system as a \"host-guest\" system, could they elaborate on why this\nsystem qualifies as a host-guest system?\nOur response: We apologize for our misuse of “host-guest system” in the original manuscript.\nWe replaced the original “host-guest system” with “gelling system” to make the use of\ntechnical term more accurate.\nOur modification to the manuscript: In the Manuscript, we revised the original “host-guest\nsystem” into “gelling system” (Page 3, Line 7; Page 8, Line 20; Page 12, Line 17) to improve\ndescription accuracy.\nComment 7:\n- The authors claim that \"Marangoni motor is plagued by short lifetime of ~10 s, limiting its\npractical application for modular powering source\". It would be helpful to understand the\nintended object the proposed method would be used to power, and specifically what the\nphysical limitations of traditional Marangoni-powered devices are.\nOur response: We thank the reviewer for this valuable suggestion. We added that the intended\nobject that the proposed method would be used to power, which includes devices such as sensor,\ndrug capsule, and even mini-generator. These Marangoni-powered devices have been reported\nin other literature. The physical limitations of the powered devices are that they must be light-\nweight and floatable.\nOur modification to the manuscript: In the Manuscript, we added sentences (Page 12, Lines\n19 and 20) to mention the intended object to be powered and the physical limitations (floatable\nand light-weight) of Marangoni-powered device.\nComment 8:\n- In paragraph 3 the authors state: \"As shown in Figure 1c,e, upon touching solution bath, the\nsurfactant-loading droplet spreads into a liquid lens, increasing capillary forces for its\nflotation9\". What are the components of the droplet, is it more dense than water, and should I\nexpect it to sink if not placed above the solution?\nOur response: We thank the reviewer for pointing this out. The droplet is aqueous solution of\nsodium alginate and has a slightly higher density (1.001 g ml-1) than that of water. As shown\nin Figure R9 and Supplementary Movie 3, in the absence of surfactant, the droplet sinks in the\nbath and then crosslinks into a gel sphere.\nFigure R9 (images in Supplementary Movie 3). Sinking of alginate-solution droplet without\nsurfactant.\nOur modification to the manuscript: In the Manuscript, we added sentences (Page 3, Lines\n10-12) to explain that without surfactant, the alginate solution droplet sinks in bath because of\nhigher mass density. In the Supplementary Materials, we added video into Supplementary\nMovie 3 to show that the droplet indeed sinks without surfactant.\nComment 9:\n- The order, and depiction of figure 1 should be reconsidered. The connection to the various\ntimescales of the experiment is an interesting way to depict the various behaviors of the droplet,\nbut is confusing. To this end, the idea that the droplet is contracting when in contact with the\nsolution (f) is very far away from 1h, where the importance of mantle contraction becomes\napparent. Furthermore, indication of the crosslinking of the droplet-water interface would be\nhelpful.\nOur response: We thank the reviewer for this valuable suggestion. In accordance with the\nreviewer’ comment, we replotted original Figure 1f, g. As shown in Figure R10 (revised Figure\n1f, g), mantle contraction is drawn in Figure 1g so that droplet contracting is close to Figure 1f.\nWe indicated the crosslinking of the droplet-bath interface in Figure 1f. In this way, the\ndescription of Figure 1 becomes clearer.\nFigure R10 (revised Figure 1f,g in the Manuscript). (f) Diffusion of calcium ions from bath\nto droplet triggers the chelation, forming the gel mantle which significantly cuts rapid\nsurfactant diffusion. The crosslinking starts at droplet-bath interface and advances toward\ndroplet bulk solution. (g) The gradual crosslinking lowers droplet radius R (t), increasing the\nm\nLaplace pressure of liquid interior. Pressure buildup swiftly perforates the gel mantle, forming\na siphon through which surfactant is released.\nOur modification to the manuscript: In the Manuscript, we redraw Figure 1f, g (Page 19). In\nthe revised Figure 1f, indication of the crosslinking of the droplet-water interface is added. In\nthe revised Figure 1g, mantle contraction is added so that the indication of such important factor\nis next to Figure 1f.\nComment 10:\n- The authors should consider using a phrase such as self-generated, self-directed as opposed\nto \"malice of forethought\" at the end of page 3, and should take a general look at the manuscript\nto clarify language in and around experiment, such as the word \"liberating\", or \"lowers\"\nrather\nthan \"weakens\" surface tension.\nOur response: We thank the reviewer for this valuable suggestion. We clarified the language\nused in the manuscript. The phrase such as original “malice of forethought” was deleted; the\noriginal word “liberating” was replaced by “placing”; the original word “weakens” was\nreplaced by “lowers”. These changes improve the accuracy of language in the manuscript.\nOur modification to the manuscript: In the manuscript, we deleted the original “malice of\nforethought”; we replaced the original word “liberating” with “placing” (Page 4, Line 3); we\nreplaced the original word “weakens” with “lowers” (Page 5, Line 1). In the Supplementary\nMaterials, we replaced the original word “weakens” with “lowers” (Page 1, Line 11). In this\nway, the language used in the manuscript is clarified.\nComment 11:\n- Figure 2a, the authors dyed the droplet red (alginate containing PEGDA), why is the droplet\ntrapped in the PEGDA and not released?\nOur response: We sincerely thank the reviewer for this insightful comment. We think that the\nreviewer intends to ask that why the red dye is trapped in the droplet and not released. We used\ndirect red 23 to dye the droplet for visualization. Because of many free hydroxyl and carboxyl\ngroups, the sodium alginate linear chain strongly interacts with direct red dye molecules\nthrough hydrogen bonding. In this way, red dyes are trapped inside the droplet and not released.\nSource of this mechanism is cited as Reference 15.\n15. Chen, C., He, E., Jia, W., Xia, S. & Yu, L. Preparation of magnetic sodium alginate/sodium\ncarboxymethylcellulose interpenetrating network gel spheres and use in superefficient\nadsorption of direct dyes in water. International Journal of Biological Macromolecules 253,\n126985 (2023).\nOur modification to the manuscript: In the Manuscript, we added sentences (Page 4, Lines\n6-8; Page 21, Lines 4-6) to explain why the red dye is trapped in droplet and cited Reference\n15 to provide the source of the explanation.\nComment 12:\n- Supplementary movie 1: the authors compare a camphor boat to their own method to\ndemonstrate the \"long-lived\" nature, can the authors provide a comparison of the \"energy input\"\ninto either motor? What is the relative mass of the camphor, to the propellant in the viscous\nexample? Why does the viscous example have a stated speed of ~100s mm/s, when the authors\nmention ~10s of mm/s in the introduction.\nOur response: We thank the reviewer for pointing this out. For both cases in Supplementary\nMovie 1 (left: camphor boat; right: gelling droplet, the original viscous example), same amount\nof surfactant is used (0.004 g PEGDA400). In both cases, boats are fabricated from a polyvinyl\nbutyral sheet and has the same weight of 0.0029 g. The gelling-droplet powered one has extra\ndroplet weight of 0.016 g. For the gelling-droplet powered one, it has the maximum velocity\nof 141.99 mm s-1 (originally stated in the supplementary movie) and an average velocity of\n19.33 mm s-1 (originally stated in the introduction of the Manuscript). These descriptions were\nadded in the caption of Supplementary Figure 1.\nOur modification to the manuscript: In the Supplementary Materials, we added sentences in\nthe caption of Supplementary Figure 1 (Page 9, Lines 3-8) to provide experimental details\n(input surfactant mass, weight of the boat and droplet) and to explain that the gelling-droplet\npowered boat has the maximum velocity of ~100 mm s-1 and an average velocity of ~10 mm s-\n1.\nComment 13:\n- Figure 2d/e/f: what is the wt% noted in the figure?\nOur response: We apologize for insufficient description of figures. In Figure 2d, the wt% in\nthe figure represents mass percentage of calcium chloride in the liquid bath. In Figure 2e, the\nwt% in the figure represents mass percentage of calcium chloride in the liquid bath. In figure\n2f, wt% in the figure represents mass percentage of sodium alginate and surfactant in the\ndroplet solution. These descriptions were added in the caption of Figure 2d, e, f.\nOur modification to the manuscript: In the Manuscript, we added sentences in caption of\nFigure 2d, e, f (Page 21, Lines 12, 13; Page 22, Lines 1, 3, 4, 6-8) to explain the meaning of\nwt% in the Figure.\nComment 14:\n- Can the authors clarify what surface tensions they refer to, as in to which interface is this\nsurface tension applied?\nOur response: We thank the reviewer for this valuable suggestion. Throughout the manuscript,\nwe clarified the interface with which the interfacial tension or surface tension is associated. In\nthis way, the readability is improved.\nOur modification to the manuscript: In the Manuscript, we added words (Page 4, Line 15).\nIn the Supplementary Materials, we added words (Page 1, Line 12; Page 3, Line 19; Page 5,\nLine 5) to clarify the surface tension we refer to.\nComment 15:\n- The authors refer to a period of \"pulsed motion\", but the effect of the pulsed motion is not\nvisible in the figure, or in any of supplementary videos. Can the authors include a note on the\npulsed motion, the scale or reliability of pulsing, and a video?\nOur response: We thank the reviewer for this valuable suggestion. As shown in Figure R6\n(Supplementary Figure 4) and Supplementary Movie 5, we added figures and videos on the\npulsed motion mode. Such pulsed motion is caused by intermittent jet containing surface-active\nagent.\nFigure R6 (Supplementary Figure 4 in the Supplementary Materials). Pulsed motion. (a)\nImage of a motor after 7 pulsed motions (Supplementary Movie 5). (b) Displacement,\nvelocity,\nand acceleration of the 7 pulsed motions.\nOur modification to the manuscript: In the Manuscript, we added sentences (Page 6, Lines\n21 and 22) to explain that the pulsed motion is associated with pulsed jet. In the Supplementary\nMaterials, we added Supplementary Figure 4 and Supplementary Movie 5 to visualize and\ndescribe the feature of pulsed motions.\nComment 16:\n- The perforated syphon should be shown in some capacity, either by microscopy, or post-\nexperiment to demonstrate, or measure the size of the syphon.\nOur response: We sincerely thank the reviewer for the insightful comment. As shown in Figure\nR5 (Supplementary Figure 3), we visualize the siphon using fluorescence microscope and\nmeasure its size to be roughly 6% of motor’s radius.\nFigure R5 (Supplementary Figure 3 in the Supplementary Materials). Siphon formed by\ngel fracture. Fluorescence image of motor (a) and magnified siphon (b) showing that the\nreleasing hole appears as a fracture on the gel mantle. The opening has a maximum width of\nroughly 6% of motor’s radius.\nOur modification to the manuscript: In the Supplementary Materials, we added\nSupplementary Figure 3 (Page 11) to visualize the siphon and measure its size.\nComment 17:\n- Does the top of the droplet gel? Does this gelling of the top of the droplet (if it does not occur)\naffect the performance of the droplet?\nOur response: We sincerely thank the reviewer for the insightful comment. Throughout the\nlifetime, motor’s top remains in liquid state as the upward diffusion of calcium ion is too slow\nto crosslink the entire droplet. Because the droplet top is not crosslinked, it allows us to describe\nthe pressure inside the droplet using the interface curvature. Such description was added in the\nManuscript.\nOur modification to the manuscript: In the Manuscript, we added sentences (Page 5, Lines\n13-16) to explain that throughout the motor lifetime, the droplet top has not crosslinked.\nWe would like to thank the reviewer once again for expending so much time and effort in\nproviding a review which has helped us to improve the clarity and specificity of our manuscript."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors revised their manuscript where they considered my suggestions and comments. The typos were corrected and the physical quantities are added when it was necessary.\nThe list of symbols in the SI is very useful.\nThe newly added movies are of high quality.\nI accept all of the changes and recommend the manuscript for publication in the present form.", "reviewer_2": "I have now carefully gone through the authors' responses to my previous comments. I still have some questions, as mentioned below, which I think are critical to the scientific understanding of the work. I cannot recommend the publication of the present manuscript until these questions are unambiguously clarified.\n1. I found the authors' arguments regarding the perforation of the hydrogel mantle to be hand-waving at best. If I understand the system correctly then there are two types of stresses acting on an elemental area of the hydrogel mantle-- one, a compressive stress due to the local Laplace pressure (this is the stress which is dependent on the curvature), and two, a tensile stress due the inherent tendency of the interfacial tension to minimize the surface area. If the perforation of the hydrogel mantle is dependent on the curvature (i.e. the shell perforates only once a critical shape is reached), then the compressive stress due to the Laplace pressure plays a dominant role in the rupture of the mantle. This is only my conjecture; the authors must explain it better. I think that even if the exact location of the rupture is not deterministic in nature, the mechanism of the rupture should be clearly explained. Otherwise, it will be impossible to engineer the system.\n2. Supplementary Figure 5 (Figure R1): What does the constant value of the radius $R_m$ represent, especially for the micromotors in calcium chloride solution? If gelation continues, then I would expect $R_m$ to be a function of time. In fact, the authors also consider the same during the evaluation of the liquid release rate from the micromotor (Eq. S3). Then what does the constant value of $R_m$ represent in Figure S5/R1 (b) for a given concentration of calcium chloride?\nIf $R_m(t)$ variation is insignificant as the authors claim, then the variation in the average curvature may also be insignificant. If that is the case, then why should the liquid release rate vary over time? More importantly, why should the speed $U$ decay over time? Is $R(t)$ variation really negligible even for t~ O(10^2-10^3) s? Note that Figure 2(d) shows the variation only for the first 3 seconds. How would this variation look for t~ O(10^3) s?\nI would request the authors to show the decay of $U$ over time in water, as well as in calcium chloride solutions of different concentrations.\n3. Figure 2b (Figure R2): At present, the form of the exponential fit to the decay of $U$ holds no physical justification. I would request the authors to investigate whether the co-efficient and the characteristic decay time can be estimated (at least the order of magnitude) from the explanation for the propulsion dynamics presented in section 2 of the supplementary material.\nCurrently, $53$ and $0.0016^{-1}$ have no physical meaning.\nMoreover, the right-hand side Y-axis should be $L/D$.\n4. I am still confused with Fig. 2e. Equation S2 does not have a prefactor; therefore, in the log-log plot there should be no intercept. Right now for the plot to have slope 1, there has to be an intercept. Is there a physical genesis for the intercept?\n5. The major concern with Fig. 2f is that the spread in the data is too great to reach any meaningful conclusion. In fact, on apparent inspection, a line with a higher slope seems to be a better fit than the line with slope $1/3$.\n6. The definition of efficiency is still unclear. I did not understand what the authors mean by `per unit mass of surfactant'. Can the authors please explain how they calculate this quantity?", "reviewer_4": "The authors have succesfully addressed all of my comments, and suggestions. I believe that with the added data, explanations, i.e., with laplace pressure, and relevant literature, this manuscript is now suitable for publishing in Nature communications. The conclusions are now well-supported, and the work is of high quality."}, "author_response": "Response to Reviewer\nReviewer 2:\nComment 1:\nI have now carefully gone through the authors' responses to my previous comments. I still have\nsome questions, as mentioned below, which I think are critical to the scientific understanding\nof the work. I cannot recommend the publication of the present manuscript until these questions\nare unambiguously clarified.\nOur response: We sincerely thank the reviewer for his/her valuable and constructive\ncomments, which have greatly contributed to improving the quality of our manuscript. We have\nrevised the manuscript accordingly and provided the following point-by-point responses to\neach comment.\nComment 2:\n1. I found the authors' arguments regarding the perforation of the hydrogel mantle to be hand-\nwaving at best. If I understand the system correctly then there are two types of stresses acting\non an elemental area of the hydrogel mantle-- one, a compressive stress due to the local Laplace\npressure (this is the stress which is dependent on the curvature), and two, a tensile stress due\nthe inherent tendency of the interfacial tension to minimize the surface area. If the perforation\nof the hydrogel mantle is dependent on the curvature (i.e. the shell perforates only once a\ncritical shape is reached), then the compressive stress due to the Laplace pressure plays a\ndominant role in the rupture of the mantle. This is only my conjecture; the authors must explain\nit better. I think that even if the exact location of the rupture is not deterministic in nature, the\nmechanism of the rupture should be clearly explained. Otherwise, it will be impossible to\nengineer the system.\nOur response: We thank the reviewer for the insightful comment. We numerically mapped the\ndistribution of stress in the mantle before perforation so that the mechanism can be clearly\nexplained. As shown in Figure R1, because of negligible hydrostatic force, the mantle is\nsubjected to surface tension force σ , σ acting on its perimeter and Laplace pressure  n\nda ba\nda\nacting on its interior surface. As the curvature increases, the Laplace pressure and angle θ , that\nd\nis, the direction of surface tension force σ , increase. We calculated the distribution of von\nda\nMises stress (T ) in the mantle subjected to these dominant external forces using finite\nvon\nelement analysis. It is found that the maximum von Mises stress appears at the perimeter of the\nmantle. The position of the maximum von Mises stress corresponds to the region where\nperforation preferentially occurs.\nFigure R1 (Supplementary Figure 3 in the Supplementary Materials). Stress in mantle\nbefore perforation. (a) Because of negligible hydrostatic force, the mantle is subjected to\nsurface tension force σ , σ and Laplace pressure\nda ba\nda\n   n . (b) Schematics of configuration\nfor finite element analysis. Surface tension forces, σ = 42 mN m-1 and σ = 70 mN m-1, act\nda ba\nalong the contact line which is denoted blue. Laplace pressure,  n = 12.24 N m-2, acts on\nda\ninner surface of the mantle. Based on experiment, θ = 30˚ and θ = 2˚. Centre of contact line\nd b\nring is set as origin. B(0, 0, -1 mm) is the bottom point of the mantle. R is set to be 2.8 mm.\nm\nFor boundary conditions, the contact line remains on water surface, thus its displacement in z-\ndirection is 0. Because of axisymmetric configuration, the displacement of point B in x- and y-\ndirection is 0. Properties of the calcium alginate gel are set as follows: Young’s modulus is 30\nkPa, Poisson’s ratio is 0.5, and density is 2200 kg m-3. (c) The numerically-calculated von\nMises stress (T ) in the mantle. The maximum stress appears at the perimeter where\nvon\nperforation preferentially occurs.\nOur modification to the manuscript: In the Manuscript, we added sentences (Page 6, Line4)\nto explain that stress peaks at mantle’s perimeter where perforation preferentially occurs. In the\nSupplementary Materials, we added Supplementary Figure 3 to show the numerical stress\ndistribution in the mantle.\nComment 3:\n2. Supplementary Figure 5 (Figure R1): What does the constant value of the radius\n$R_m$ represent, especially for the micromotors in calcium chloride solution? If gelation continues,\nthen I would expect $R_m$ to be a function of time. In fact, the authors also consider the same\nduring the evaluation of the liquid release rate from the micromotor (Eq. S3). Then what does\nthe constant value of $R_m$ represent in Figure S5/R1 (b) for a given concentration of calcium\nchloride?\nIf $R_m(t)$ variation is insignificant as the authors claim, then the variation in the average\ncurvature may also be insignificant. If that is the case, then why should the liquid release rate\nvary over time? More importantly, why should the speed $U$ decay over time? Is\n$R(t)$ variation really negligible even for t~ O(10^2-10^3) s? Note that Figure 2(d) shows the\nvariation only for the first 3 seconds. How would this variation look for t~ O(10^3) s?\nI would request the authors to show the decay of $U$ over time in water, as well as in calcium\nchloride solutions of different concentrations.\nOur response: We sincerely thank the reviewer for the constructive comment. We apologize\nfor the insufficient description of R in Supplementary Figure 6b (original Supplementary\nm\nFigure 5b), the R here is the micromotor’s radius measured at the end of its lifetime.\nm\nWe update original Figure 2d by providing a longer-timescale (~1000 s) evolution of\nmicromotor’s radius (Figure R2), the motor’s radius R is indeed a function of time as the\ncrosslinking continues throughout its propulsion. The motor’s radius rapidly decreases in the\nvery first ~50 s and then gradually decreases at a much lower rate in the rest ~1000 s.\nAs shown in Figure R3, we provide the decay of U over time in water (30 s in CaCl\n2\nsolution and then in water) as well as in calcium chloride solutions (maintained in CaCl\n2\nsolution) of different concentrations (0.5 and 2 wt%). Velocities decay in an exponential\nmanner.\nThe propelling velocity U relates to the surfactant releasing rate J through\nU ~\nd\nJ\nR\nm\nh\nm\n\n(Equation S9). In physical rather than phenomenological perspective, flow\n \nof surfactant solution through the siphon is approximated as the Poiseuille flow driven by the\nLaplace pressure and has an expression J ~ c\nm\nQ ~ 1 0 3 c\nm\nR\nm\n( t ) 3\nd\nd\n( t ) \n\n−\n  n\n(see Equation S3).\nThe motor radius R as well as the droplet-air curvature\nm\n  n are both time-dependent. The\ndroplet curvature is impacted by two factors, that is, the volume of droplet (Figure R4) and the\nmotor radius R which sets the boundary of droplet. Although R largely plateaus after the very\nm m\nfirst ~50s, the continuous decrease in droplet volume decreases the curvature and thus brings\nabout decay in velocity.\nFigure R2 (Updated Figure 2d in the Manuscript). Temporal evolution of the droplet radius\nR(t)/R for a longer timescale (~1000 s). The moment when droplet touches the bath is defined\n0\nas t = 0. Colour denotes mass percentage of calcium chloride in the liquid bath. The droplet is\naqueous solution of 1 wt% sodium alginate and 25 wt% PEGDA400.\nFigure R3 (Supplementary Figure 6e,f in the Supplementary Materials). The normalized\npropelling velocity as a function of time for 0.5-wt% (a) and 2-wt% (b) CaCl solution.\ndroplet’s volume.\nOur modification to the manuscript: In the Manuscript, we updated Figure 2d so that a\nlonger-timescale (~1000 s) evolution of micromotor’s radius is provided. In the Supplementary\nMaterials, we added sentences (Page 14, Lines 7,8) to explain that the R in Supplementary\nm\nFigure 6b is the micromotor’s radius measured at the end of lifetime and sentences (Page 3,\nLines 2-4) to explain that the droplet curvature is impacted by two factors, that is, the volume\nof droplet and the motor radius; we added Supplementary Figure 6e,f to show the decay of U\nover time in water (30 s in CaCl solution and then in water) as well as in calcium chloride\n2\nsolution (maintained in CaCl solution) of different concentrations (0.5 and 2 wt%)\n3. Figure 2b (Figure R2): At present, the form of the exponential fit to the decay of $U$ holds\nno physical justification. I would request the authors to investigate whether the co-efficient and\nthe characteristic decay time can be estimated (at least the order of magnitude) from the\nexplanation for the propulsion dynamics presented in section 2 of the supplementary material.\nCurrently, $53$ and $0.0016^{-1}$ have no physical meaning.\nMoreover, the right-hand side Y-axis should be $L/D$.\nOur response: We sincerely thank the reviewer for this valuable and constructive comment.\nWe estimate the first-order releasing rate constant and characteristic decay time from the\nexplanation of the propulsion dynamics in Supplementary Note 2. By substituting equation S5\ninto S9, we have the relationship between temporal evolution of propulsion velocity and the\n13\n c Q \nfirst-order release of surfactant as U(t)~ m 0  e−kt3 . By referring to the fitted\nCR h \nb d m m\nexponential decay of velocity U D=53e−0.0016t in Figure 2b (propelling velocity after initial\n5 s is exponentially fitted), we estimate the releasing rate constant by k/3 = 0.0016 s-1, giving k\n= 0.0048 s-1 and a characteristic decay time 1/k~208 s. The coefficient\nCb\nc\nd\nm\nQ\nR\n0\nm\nh\nm\n1 3\n\n \n \nwith a\nunit of m s-1 is the maximum propulsion velocity which is associated with the coefficient 53\nBL s-1 in the exponential fitting of propulsion velocity. We have changed the right-hand side Y-\naxis to be L/D.\nOur modification to the manuscript: In the Manuscript, we added sentences (Page 8, Lines\n17-19) to explain the derivation of temporal propulsion velocity and changed the right-hand\nside Y-axis of Figure 2b to be L/D. In the Supplementary Materials, we added sentences (Page\n5, Lines 17,18 and Page 6, Lines 1-3) to detail the derivation of temporal propulsion velocity\nand estimate the releasing rate constant k and characteristic decay time of the first-order release.\nComment 5:\n4. I am still confused with Fig. 2e. Equation S2 does not have a prefactor; therefore, in the log-\nlog plot there should be no intercept. Right now for the plot to have slope 1, there has to be an\nintercept. Is there a physical genesis for the intercept?\nOur response: We thank the reviewer for giving us the opportunity to clarify the interception\nin Figure 2e. Figure 2e is the logarithmic representation of the measured finite spreading radius\n1/8\n V3 \nR and its scaling prediction . The slope of 1 is captured but the prediction\nl  \n3D2\n\nd s\noverestimates measured R by roughly an order of magnitude so that an intercept appears. The\nl\nintercept is potentially due to simplification in the assumption of spreading cessation and\nestimation of diffusion coefficient.\nFor the assumption of spreading cessation, when diffusion homogenizes the surfactant at\nthe leading edge, the driving force, that is, surface tension difference Δσ vanishes so that the\nspreading stops. Similar to Kim et al. (Nature Physics 13, 1105-1110), it is assumed that such\nscenario happens when the surfactant diffusion boundary layer thickness l equals to the lens\nd\nthickness h. This is a physically-motivated but simplified criterion, particularly for the\nquantitative relationship between l and h. For example, the spreading may stop when h = bl\nd d\ngives R\nl\n~ b 1 2\nd\nD\n3\n2s\n1/8\n\n\n−\n  \n. When b = 4, the prediction decreases by a factor of 0.5.\nFor the estimation of diffusion coefficient D , it is estimated by the Stokes-Einstein model\ns\nas D =k T /(6r) . On the basis of previous works on polyethylene glycol (Biophysical\ns B b\njournal 95, 1590–1599; Membranes 8, 23), we assume the hydrodynamic radius r of our\nsurfactant poly(ethylene glycol) diacrylate 400 to be 0.5 nm, giving a diffusion coefficient of\n~10-10 m2 s-1. The Stokes-Einstein model is most accurate for spherical particle in a continuous\nsolvent where the particle is much larger than the solvent molecules. However, diffusion of\nsurfactant violates the ideal prerequisite as polymer chain is not rigid sphere, size of polymer\nis not significantly small than that of water molecules, boundary condition for polymer chain\nmay not be no-slip, and interaction between polymer chains happens. These factors contribute\nto deviation in the estimation of diffusion coefficient. For example, the actual diffusion\ncoefficient may be cD which gives\ns\nR\nl\n~ c 1 4\nd\nD\n3\n2s\n1/8\n\n\n−\n  \n. When c = 16, the prediction decreases\nby a factor of 0.5.\nBy analysing the simplification in derivation of Equation S2, we propose that the intercept\nin Figure 2e is potentially due to simplification in the assumption of spreading cessation and\nestimation of diffusion coefficient.\nOur modification to the manuscript: To explain that the intercept is potentially due to\nsimplification in the assumption of spreading cessation and estimation of diffusion coefficient,\nin the Manuscript, we added sentences (Page 22, Lines 5-7); in the Supplementary Materials,\nwe added sentences (Page 2, Lines 11-14).\nComment 6:\n5. The major concern with Fig. 2f is that the spread in the data is too great to reach any\nmeaningful conclusion. In fact, on apparent inspection, a line with a higher slope seems to be\na better fit than the line with slope $1/3$.\nOur response: We thank the reviewer for pointing this out. In previous Figure 2f, data from\ndroplets of different compositions are plotted, causing a wide spread. To obtain a reliable\nrelationship, we perform experiments using only one composition (aqueous solution of 0.375\nwt% sodium alginate and 25 wt% PEGDA400). Droplets’ sizes are controlled through different\nnozzles. For a specific type of nozzle, experiments are repeated 5 times so that error bars\ndenoting standard deviation are provided. As shown in Figure R5, the data are distributed much\ncloser to a fitting line whose slope is roughly 1/3.\nFigure R5 (updated Figure 2f in the Manuscript). The maximum propulsion velocity U\nmax\nas a function of the motor radius R . The red line is the fitting line. Error bars denote standard\nm\ndeviation of 5 experiments. The droplet is aqueous solution of 0.375 wt% sodium alginate and\n25 wt% PEGDA400. The liquid bath is 1 wt% calcium chloride aqueous solution.\nOur modification to the manuscript: In the Manuscript, we updated Figure 2f through only\none composition (aqueous solution of 0.375 wt% sodium alginate and 25 wt% PEGDA400)\nand repeated experiments.\nComment 7:\n6. The definition of efficiency is still unclear. I did not understand what the authors mean by\n`per unit mass of surfactant'. Can the authors please explain how they calculate this quantity?\nOur response: We thank the reviewer for giving us the opportunity to clarify the definition of\nefficiency. Unlike conventional definition of efficiency, that is, work output divided by energy\ninput, the efficiency used in our manuscript is firstly defined by Steve Granick and Bartosz A.\nGrzybowski (ACS Nano 11, 10914–10923). In their work, they define it as “the particle’s\nmaximum kinetic energy per unit mass of expended fuel”. The particle’s maximum kinetic\nenergy is calculated based on the maximum propulsion velocity as m U 2m\nax\n2 where m is the\ninitial total mass of motor which includes mass of motor matrix and loaded fuel. The total mass\nof fuel (surfactant) m loaded in their metal-organic framework motor is measured using the\nf\nthermogravimetric analysis. As a result, the efficiency is calculated as\nm ax\nm U 2m\nax\n2 m\nf\n  . In our\nwork, we calculate the efficiency by following their definition. For example, for a motor of\ninitial total mass m = 0.01 g wherein mass of surfactant is m = 0.0025 g, we measure its\nf\nmaximum velocity to be 890 mm s-1, then its efficiency is m U 2m\nax\n2 m\nf\n= 1584.2 μJ g-1.\nOur modification to the manuscript: In the Manuscript, we added sentences (Page 10, Lines\n4,5) to explain the definition of variables in the equation of efficiency.\nWe would like to thank the reviewer once again for expending so much time and effort in\nproviding a review which has helped us to improve the clarity and specificity of our manuscript.\nResponse to Reviewer\nReviewer 2:\nComment:\nI have gone through the authors' replies to my previous round of comments. I am satisfied with\ntheir replies. I think the manuscript has achieved the quality and rigour necessary for\npublication in Nature Communications. Hence, I recommend the manuscript for publication.\nOur response: We sincerely thank the reviewer for his/her recommendation for publication of\nour manuscript. We thank the reviewer for expending so much time and effort in providing a\nreview which has helped us to improve the clarity and specificity of our manuscript."}]

Decision letter