Dynamics of Marangoni-driven elliptical Janus particles

Abstract

We investigate the spontaneous motion of an elliptical Janus particle, driven by Marangoni forces, on a water surface to understand how particle shape and size influence its dynamics. The Janus particle is one-half infused with a substance such as camphor, which lowers the surface tension upon release onto the water surface. The resulting surface tension gradient generates Marangoni forces that propel the particle. For fully camphor-infused (non-Janus) particles, previous studies have shown that motion occurs along the short axis of the ellipse. However, for Janus particles, our experiments reveal a much richer steady-state dynamics, depending on both the particle's eccentricity and size. To understand these dynamics, we develop a numerical model that captures the connection between the spatio-temporal evolution of the camphor concentration field and the Marangoni force driving the particle. Using this model, we simulate the motion of particles with varying eccentricities—from nearly circular to highly elongated shapes. The simulations qualitatively reproduce all the trajectories observed in experiments and provide insights into how particle geometry influences the dynamics of chemically driven anisotropic particles. With the help of the numerical model, we compute a full phase diagram characterising the dynamical states as a function of surfactant properties.

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I. Introduction

The generation of spontaneous motion is a key feature in active matter systems. In nature, microbial swimmers such as E. coli propel themselves by rotating or beating their flagella.¹ Other species, such as M. xanthus, glide on soft hydrogel substrates using a combination of mechanisms other than swimming.² In addition, a thin layer at the air–water interface (aquatic surface monolayers), which has distinct physicochemical properties, accommodates a rich ecosystem for microbes and insects that move on the interface.^3,4 Inspired by these naturally occurring self-motile systems, a large class of artificially motile colloidal systems has been synthesised by various means.^5–14 One of the common ways to realise chemically active colloidal particles is by using Janus colloidal particles, with unequal chemical properties that provide a head–tail asymmetry.^5,7,15 These unequal chemical properties create local variations in temperature or chemical potential, which induce local flows and result in a directed motion of the particle.

In the recent past, the surfactant–water system has served as a prototype of such chemo-mechanical transducers, capable of providing directed motion of suspended particles. In these systems, spontaneous motion is generated due to Marangoni flow due to surface tension gradients, generated by adding chemicals that temporarily reduce surface tension¹⁶ and such Marangoni-driven self-propulsion is achieved by a variety of mechanisms.^17–24 Among the wide variety of Marangoni propellers, one of the most common and extensively studied systems exhibiting spontaneous motion is the camphor–water system. The self-propulsion of camphor on water has fascinated researchers for decades, with the earliest studies dating back more than two centuries.²⁵ More recently, a series of studies on camphor systems have displayed a variety of collective phenomena, including rotational, translational, and oscillatory movements.^{18,20,26–35} To complement these experiments, theoretical analyses have also been conducted on such systems.³⁶

In these experiments, typically, a small paper disk infused with camphor is placed on the surface of water. As camphor molecules diffuse over the interface, they gradually reduce the local surface tension. A slight asymmetry in the camphor concentration, usually caused by a random perturbation, breaks the symmetry of the surface tension gradient and sets the disk in motion along a particular direction. The movement of the disk acts as positive feedback on the asymmetric distribution of camphor, leading to a comet-like camphor profile around the moving disk. Single-particle^29,37 and collective dynamics of circular disks have exhibited oscillations,³⁸ synchronisations,^39–44 aperiodic bursts,⁴⁵ kinetic arrest, and cluster flow of the particles. On the other hand, the polar symmetry of camphor concentration can be broken by the geometry of the paper disk. For instance, experiments on elliptical particles, completely dipped in camphor, have shown directed motion always in the direction of their short axis.⁴⁶ Another effective way to break the polar symmetry of the camphor disk is to infuse camphor only on a portion of the disk, rather than coating it completely. This can be done systematically by making Janus camphor disks of circular and elliptical shapes, by coating only one side of their symmetric axis.

Here, we experimentally study the dynamics of such an elliptical and circular Janus particle on the air–water interface, created by an asymmetric coating of camphor on the disk. The experiments show that the qualitative features of the particle are completely different compared to the non-Janus system, and their dynamics depend on the shape (measured by the eccentricity) of the Janus particle. Furthermore, we built a minimal theoretical model that captures the essential features of the particle dynamics. This model takes into account the dynamics of the camphor molecule, as well as the particle. We numerically solve this model and systematically study the dynamics of the Janus particle by varying the particle shape, size, and specific properties of the surfactants.

II. Experiments

A. Method and preparation

For the experiments, Janus-like particles were prepared from an A4 paper sheet by drawing ellipses of varying eccentricities. The length of the major axis 2a was fixed at 1.9 cm, while the length of the minor axis 2b was systematically decreased, starting from 2b = 1.9 cm, 1.6 cm, 1.4 cm, 0.8 cm and 0.6 cm, as illustrated in Fig. 2(a)–(e). To create Janus-like particles, one half of each ellipse (the half separated by the minor axis, as illustrated in Fig. 1(b)) was painted with a 0.5 M camphor–ethanol solution using an acrylic marker pen.⁴⁷ After painting, the particles were allowed to dry for about 2 minutes to enable evaporation of ethanol, leaving camphor deposited only on the painted half of the particle surface. Each particle was then gently placed approximately at the center of the surface of deionized (DI) water contained in a circular Petri dish with diameter, D = 26.5 cm. The Petri dish was filled with DI water of volume, V = 600 ml, creating a water height of about 2 cm. Separate experiments were conducted for each particle size mentioned above.

Fig. 1 (a) Experimental setup. (b) Schematic of an elliptical Janus particle with major axis 2a and minor axis 2b. (c) Anti-clockwise rotation of the Janus particle. (d) Clockwise rotation of the Janus particle. (In (b)–(d), A denotes the camphor-infused active part and P the passive part. In (c) and (d), the black dots represent the released camphor molecules.)

The entire experimental set-up was operated under UV light illumination to enhance visualization, since the two ends of the elliptical particles contain white circular spots that reflect UV light effectively. To minimize air interference and ensure accurate dynamics, the system was enclosed in a large acrylic glass box (see Fig. 1). The room temperature was maintained at (23 ± 1) °C throughout all experiments. The particle dynamics on the water surface were recorded using a GoPro camera set to 60 frames per second and 1080p resolution. The captured videos were analysed using IMAGEJ software, while further analysis, such as estimation of trajectories and angular velocities, was performed with Python programming.

B. Experimental results

When the Janus particle is placed on the surface of the water, it starts to move at the air–water interface. This motion arises due to the fluid flow induced by the solutal Marangoni effect,²⁰ which results from a surface tension gradient created by the camphor coating applied to one half of the particle. Depending on the particle size and shape, the Janus particles exhibit two distinct modes of motion. The circular Janus particles (a ≃ b) move in a straight path on the water surface, whereas the elliptical Janus particles display circular trajectories which are also periodic. In our experiments, the major axis was kept fixed at 2a = 1.9 cm, while the minor axis 2b was varied as 1.6, 1.4, 0.8, and 0.6 cm. For perfect circular particles, (2a = 2b = 1.9 cm), the particle moves in a straight line (Fig. 2(a)), until the motion gets interrupted by the edges of the Petri dish. However, when 2b < 2a, the particle follows a circular path as shown in Fig. 2(b)–(e). We also observe that as b decreases, the radius of the particle's circular path decreases monotonously, as shown in Fig. 2(b)–(e). In Fig. 2(f) the mean angular velocity ω and radius of the particle trajectories are calculated. It is evident that as the radius of the circle decreases, the angular speed of the elliptical Janus particle increases (Fig. 2(f)). At the beginning of each experiment, the particle exhibits high activity and speed, often causing it to collide with the container boundary. Therefore, we neglected this transient phase (about 60 seconds) of motion and analyzed only the portion of the experiments in which the particle's motion became stable and far from the boundary. It is known that a relatively high concentration of camphor in the solution leads to strong surface tension gradients and consequently a high initial velocity. In our experiments, this resulted in more frequent interactions with the boundaries and longer transient periods before the particle reached steady motion. At the same time, the camphor concentration must be sufficiently high to generate propulsion of the particle. Taking these factors into account, we used a 0.5 M camphor solution for all experiments reported in this study. Also, being a finite system, the particle dynamics gradually slows down. Therefore, the averages are calculated over a time-window where such variations are negligible. In the case of a circular Janus particle, its symmetry ensures that the net force generated by the active region acts through the center-of-mass of the particle. As a result, the particle moves along an almost straight trajectory (Fig. 2a), although the release of camphor molecules is stochastic in nature. However, for an elliptical Janus particle, the stochastic release of camphor molecules causes the net force to deviate from the center-of-mass, producing a torque that induces rotation. As the minor axis 2b decreases, the variation from a straight trajectory can be qualitatively understood as follows. When the shape becomes asymmetric, the net force shifts further away from the centre-of-mass, leading to a stronger torque. Beyond a certain threshold value of 2b, this torque becomes very large, and the particle exhibits a nearly pivoted rotational motion. We observe that the direction of rotation of the elliptical Janus particle is random, as shown in Fig. 1(c) and (d). However, once the particle begins to rotate, it maintains its rotational direction until it collides with a boundary.

Fig. 2 (a)–(e) Trajectory of the centre of mass of Janus particle of different shapes. (a) shows a straight path, while (b)–(e) show almost circular trajectories with radius R_s (see Movie S1). (f) Variation of average angular speed ω_s and average radius R_s with eccentricity e. For each eccentricity, four independent experiments are conducted. The mean values of ω_s and R_s (●) are computed by averaging over ten cycles per experiment. The error bars represent the standard deviation calculated over different experiments.

III. Numerical model

A. Model description

To study the observed rotational dynamics of the elliptical Janus particle on the surface of water due to Marangoni forces, we follow the two-dimensional framework proposed by Kitahata et al.⁴⁶ We assume that the concentration field c(r,t) of the camphor on the surface evolves according to the equation:where D is the diffusion coefficient of camphor on the surface, α is the degradation rate of camphor molecules, and f(r_c,χ) denotes the source term. In this context, the source term indicates the camphor-coated half of the Janus particle, which can be defined as:where r_c and χ(t) denote the centre-of-mass and orientation of the particle and Ω(r_c) represents the camphor-coated half of the particle.

The surface tension γ is known to be a decreasing function of camphor concentration. The functional form can be linear⁴⁶ or non-linear.¹⁸ However, for small c(r,t), the functional form approximately follows a linear decrease in surface tension. Therefore, we assume,

γ(c,r,t) = γ₀ − κc(r,t), (3)

where γ₀ is the surface tension of pure water, and κ is a positive constant. The particle experiences a net Marangoni force F arising from surface tension gradients along its boundary Ω_rc, which is given by the relation,Since we are studying the dynamics of Janus particles, the torque τ about r_c is separately calculated,where n is the outward normal on the particle boundary. These relations qualitatively capture force and torque due to the Marangoni effect. The net force and torque calculated for the particle are incorporated in the dynamical equations of particle position and alignment,Due to the anisotropic shape of the particle, it is necessary to consider the parallel and perpendicular components of the velocity, v_‖ and v_⊥, such that the net velocity of the particle . Also, the angular velocity . Since we study the dynamics of a single particle, long-range, non-local hydrodynamic interactions and the evolution of the surrounding flow field are not included in the model. The effects of local hydrodynamics are captured by the local drag coefficients, η_‖, η_⊥ and η_θ, which are the parallel, perpendicular, and rotational drag coefficients, respectively.

As observed in the experiments, the type of trajectory displayed by the particle depends on the particle shape. One of the reasons for the dependence is that the distribution of forces and torques due to the Marangoni effect depends on the shape of the particle contour, as evident in eqn (4) and (5). Another important aspect that determines the trajectory is the anisotropic drag experienced by the particle on the water surface due to its shape. However, an exact estimation of these drag coefficients for partially submerged particles is challenging.^48–53 On the other hand, neglecting the anisotropy in drag will lead to an incorrect estimation of the particle trajectories.³⁶ Various combinations of translational and rotational drag give rise to different trajectories, like stationary states, rotational modes, and motion along the short axis. So, a proper relationship between these drag coefficients with the particle's shape and size needs to be established to capture the experimental observations correctly.

In this study, we adopt a simplified approach by estimating the drag coefficients for a spheroid immersed in a bulk fluid, characterized by its major and minor axes, a and b, respectively. This approach follows previous theoretical^54–56 and experimental⁵⁷ studies on circular and rod-like particles. Although the long-ranged hydrodynamic behaviour is qualitatively different for 2D and 3D systems, in ‘dry’ active matter systems such bulk drag coefficients are employed in 2D simulations that only consider local viscous drag. Moreover, the drag coefficient for spheroids captures the orientation dependence of local translational and rotational drag and qualitatively reproduces the experimental observations. The drag coefficient η for a spheroid is split into parallel η_‖ (parallel to the major axis), perpendicular η_⊥ (perpendicular to the major axis), and rotational η_θ (rotation of the body axis about the centre-of-mass) such that,

η_{‖ or ⊥} = 6πζbG_‖or ⊥ (8)

η_θ = ζV₀G_θ (9)

Here, V₀ is the volume of the particle, which for a spheroid is given by and ζ denotes the effective viscosity of the medium. To capture the anisotropy in friction for prolate particles, we use the Perin frictional factors G_‖, G_⊥ and G_θ for parallel, perpendicular and angular friction coefficients, defined in terms of p = a/b,

Putting this expression for translational and rotational drag coefficients in eqn (6) and (7) completes the description of the numerical model used.

To simulate the system, the particle is initially kept at the centre of a square box of size L = 15a₀ with periodic boundary conditions, with grid spacing dx, dy = 0.05a₀ with a₀ being the unit of length. The particle releases camphor from its body, which has a degradation rate α. In simulations to specifically study the effect of particle shape, we keep α = α₀, which is kept as the unit of inverse time. The diffusion coefficient of camphor D was found to have a negligible impact on single-particle dynamics over a range of 0.2a₀²α₀ to 10a₀²α₀. Therefore, we set D = 2.5a₀²α₀ for all subsequent simulations [SI (Fig. S1)]. For the current analysis of varying particle shape, κ is set to . The simulations were run for 10⁵ time steps with Δt = 2 × 10⁻⁴α₀⁻¹ achieving a steady state after 4 × 10⁴ time steps. The instantaneous camphor concentration c is calculated numerically by integrating the discretised version of eqn (1) using Euler's method. Subsequently, the reduction in surface tension γ and the instantaneous force and torque on the particle are calculated. Finally, the particle position and orientation are updated by numerically solving eqn (6) and (7) using Euler's method. Simulations for Janus particles were conducted by systematically varying the particle shape, degradation rate α, and effective Marangoni strength, κ. Each set of parameter values was simulated up to seven different initial realisations.

B. Numerical results

Initially, the coupled evolution of the camphor concentration field and the particle dynamics was simulated for an elliptical particle, which is completely coated with camphor. The simulation has successfully reproduced the previously established result⁴⁶ and verified that when the particle is fully camphor-coated, any initial torque generated by asymmetries in the camphor distribution decays over time. As a result, the system invariably relaxes to a state of persistent translational motion along the short axis, which represents the stable steady state for such particles.

1. Effect of particle shape. Having established this baseline, we next turned to the case of Janus particles, in which only one-half of the particle is coated with camphor. First, we systematically investigated how the particle's trajectory depends on its shape. To probe the effect of geometry, we varied the eccentricity e of the elliptical particle by fixing the semi-major axis a and gradually decreasing the semi-minor axis b from a down to 0. The limit a = b corresponds to a circular particle (e = 0). In this isotropic case, our simulations show that the only stable trajectory is a straight line, characterized by a vanishing angular velocity ω_s = 0 [Fig. 3(e), region I, and Fig. 3(d)]. This result is consistent with the experimental observation.

Fig. 3 (a)–(d) Four different shapes with eccentricities e = 0.97, 0.87, 0.54, and 0.28, depicting distinct trajectories from circle to straight-line (also see Movie S1). (e) shows how the steady state angular velocity ω_s and the radius R_s change upon changing the shape of the particle. For this case, α = α₀ and .

As the eccentricity e is increased, however, a qualitatively different behavior emerges. Beyond a certain critical value of e—which itself depends on the absolute size of the particle a—a new stable solution arises. In this case, the particle executes a circular trajectory with a steady state, finite angular velocity ω = ω_s, either in the clockwise or in the counter clockwise direction (Fig. 3(a)–(c) and region III in Fig. 3(e)). Close to this transition point from a straight to a circular trajectory, the system passes through an intermediate bistable regime (region II in Fig. 3(e)), where both the straight-line solution (ω = 0) and the circular solution (ω = ω_s) are stable for different runs. In this bistable window, the outcome depends sensitively on initial conditions and initial perturbations. The system may settle into either persistent translation or sustained rotation for the same parameter values. In Fig. 3(e), we compute the steady-state angular velocity ω_s and the radius of the circular trajectory, R_s, as a function of e and for three different values of a. As shown in Fig. 3(e), within region III, the angular velocity ω_s increases monotonically with eccentricity e, reflecting the fact that the torque experienced by the particle grows with the degree of asymmetry in the underlying camphor distribution. In addition to ω_s, the radius of the trajectory R_s also reaches a steady state. Within the bistable region (region II in Fig. 3(e)), we observe that for small e, the circular trajectories are comparatively large in radius (Fig. 3(c)), whereas increasing e systematically reduces the radius, as illustrated in Fig. 3(a)–(c). This trend is followed for all values of a (Fig. 3(e)) and is consistent with the trend observed in the experiments (Fig. 2(f)). It should also be noted that both ω_s and R_s are also determined by the size of the particle. Larger sized particles (with larger a) show a smaller ω_s and higher R_s for the same value of e, as evident in Fig. 3(e). We have systematically analyzed the relation between R_s and a for a fixed e (Fig. S2). For all values of e we observe that R_s increases monotonously with a. Note that, we have neglected fluctuations in eqn (6) and (7) and the dynamics is completely deterministic. However, we have also introduced Gaussian white noise in both the dynamical equations and studied the effect by systematically varying its strength (Fig. S3). The results show that the circular trajectories are robust to the noise strength comparable to the magnitude of Marangoni forces.

Both the experiments and the simulations show that an increase in particle eccentricity e leads to an increase in ω_s and a decrease in R_s. This observation can be rationalized by considering the particle geometry. As the eccentricity increases (achieved here by reducing the semi-minor axis b while keeping the semi-major axis a fixed), the perimeter of the camphor-coated region shrinks. This reduction lowers the net driving force F, according to eqn (4). At the same time, the enhanced asymmetry in camphor release associated with larger e sustains a comparatively stronger torque, since the decay of torque with eccentricity is slower than that of the force. Since the force F determines the steady linear velocity v_s and the torque τ determines the angular velocity ω_s, this effect is reflected as an increase in ω_s with e. Furthermore, the steady-state trajectory radius is determined by the ratio , which also increases as a result. In the asymptotic limit of highly elongated particles, the radius approaches a finite lower bound of R_s ≈ a/2.

2. Effect of chemical properties. Regarding the surfactant field, α represents the degradation (sublimation) rate of the surfactant, while κ quantifies the reduction in water surface tension caused by the surfactant. Both parameters play a crucial role in determining the type of dynamics exhibited by the particle. At this stage, it is useful to introduce certain characteristic length scales of the system. For a stationary particle, the spread of camphor governed by the reaction–diffusion eqn (1) is given by . However, due to initial perturbations, the particle begins to move with a speed v, which eventually reaches a steady constant value. As discussed earlier, the steady-state speed v_s depends on the particle size, geometry, and parameters α and κ. While moving at speed v_s, the particle leaves behind a surfactant trail of characteristic length [see Fig. 3(d)]. Owing to its asymmetry, the particle follows a curved trajectory, whose radius R_s is determined by the ratio of F to τ in the steady state. Tracing this curved path, the particle eventually returns to its initial position, thereby forming a circular trail. If the trail length is shorter than the circumference of the circle 2πR_s, the particle encounters no camphor trace at the starting point and thus continues along the same circular path. In contrast, if the trail length is comparable to or larger than the circumference, the particle experiences a modified surfactant field after one revolution, causing it to deviate from the circular trajectory. So we get a condition for a stable circular path: 2πR_s ≫ l₂ or 2πα/ω_s ≫ 1. When 2πα/ω_s < 1, the existing camphor concentration can deviate the particles from a circular trajectory. In Fig. 4, we plot a phase diagram for a fixed e in the κ − α space. The color code indicates the dimensionless parameter 2πα/ω_s. The white-dashed curve indicates 2πα/ω_s = 1 and it roughly separates the darker region in the phase diagram where the two length scales (2πR_s and l₂) become comparable, and the particle deviates from the circular trajectory.

Fig. 4 The figure shows that the α and κ determine the trajectory of the particle of eccentricity e = 0.93 (a = 1.25a₀, b = 0.46a₀) in the steady state (in units of α₀ and κ₀ = γ₀α₀/f₀). The white-dashed curve gives a rough boundary for the ratio 2πα/ω_s near 1. When this happens, the circular trajectory is disturbed, and the particle deviates to a complex trajectory (see Movie S2). All the experimental observations fall on the right side of the white-dashed curve.

In addition to the change in radius of the circular trajectory, both α and κ change the surface tension and thereby the Marangoni force and torque acting on the particle. For a given value of e, ω_s and R_s are determined by α and κ viaeqn (3)–(7). In Fig. 5, we show how R_s and ω_s changes as a function of κ for different α. Our analysis shows that the radius of the trajectory monotonously increases with κ and an increase in α causes a decrease in R_s for all values of κ (Fig. 5(a)). The angular velocity ω_s also increases monotonously with κ. However, the dependence on α is more prominent for higher κ, as shown in Fig. 5(b).

Fig. 5 The radius R_s (a) and angular velocity ω_s (b) of the particles at steady state are plotted by changing α and κ. Since the surface tension dip due to the surfactant depends on κ, increasing it increases both the radius R_s and ω_s.

IV. Conclusions

In this work, we have experimentally studied the self-propulsion of an elliptical Janus camphor particle at the air–water interface and examined how its shape controls its motion. Experiments show a straight trajectory for circular Janus particles and a circular trajectory for elliptical Janus particles. Experiments also reveal that as the particles become more elongated, the radius of the circular trajectory decreases and its angular velocity increases.

The experimental findings are rationalized using simulations that reveal distinct dynamical regimes that emerge as both particle geometry and surfactant parameters are varied and it qualitatively reproduces the experimental observations. As the particle becomes more elongated, a bistable regime appears: depending on initial conditions, the particle either moves straight or follows a circular path with a well-defined angular velocity. At larger eccentricities, the bistability disappears, and the particle reliably moves in circles, with angular velocity increasing as eccentricity increases. The radius of this circular motion decreases with eccentricity because the camphor-coated perimeter becomes smaller, reducing the net propulsive force faster than the torque. This imbalance—weakening force but comparatively persistent torque—produces tighter circular paths for more elongated particles. Finally, comparing the trail length with the curvature radius clarifies when stable circular trajectories occur. This leads to a simple division of the (α, κ) parameter space into regions that support clean circular motion and those where the particle deviates from it. We note that the effect of particle shape on Marangoni-propelled particles that are fully infused with camphor has been studied previously.^46,58,59 In addition, theoretical studies of rigidly connected camphor-infused particles have predicted circular motion.⁶⁰ However, the present study demonstrates experimentally and numerically that circular motion can also arise in Janus particles and that this motion can be controlled by tuning the aspect ratio of the particles.

We note that the numerical model does not explicitly consider the fluid velocity or flow-induced mixing of camphor. The spreading of camphor is not a pure diffusive process, although many previous studies have incorporated an effective diffusive term in the dynamical equation governing the camphor concentration. The Marangoni flow generated at the interface induces convective transport of camphor molecules; therefore, a more general description should include an advective (convective) contribution.^61,62 Nevertheless, under certain conditions—particularly at long time scales—the spreading can be effectively approximated as diffusive.⁶³ In this sense, the diffusive spreading assumed in eqn (1) should be regarded as a large-time approximation to the underlying spreading dynamics. Another important assumption taken in this study is that the viscous drag in eqn (6) and (7) is assumed to be linear to the respective velocity terms, an assumption valid for motion at low Reynolds numbers. Although this assumption may cause quantitative differences compared to experimental results, it was widely used in theoretical models, since it captures the essential qualitative features of the dynamics.^46,64–67 Despite these simplifications, our simulations qualitatively reproduce the experimentally observed trajectories, demonstrating that the interplay between the surfactant field and particle geometry is sufficient to explain the behaviors. The hydrodynamic effects due to the wall are not important as long as the particle is far from the wall of the Petri dish. These results highlight how geometric asymmetry amplifies or suppresses chemo-mechanical feedback, thereby enabling or destabilizing specific modes of motion. By systematically varying geometric parameters such as eccentricity and aspect ratio, we show that particle shape directly modifies the balance of Marangoni forces and torques, thereby selecting or switching between distinct modes of motion. As a next step, one can study the collective dynamics of multiple Janus particles to understand the types of interactions and their effects on collective motion. The interparticle interactions in such systems are expected to be more complex and challenging to model than those in typical dry active matter, as they can be influenced by both fluid flows and capillary effects. In addition, connecting such particles into chains can also reveal novel dynamical states.^68–70

This study opens pathways to control Marangoni-driven particles solely by adjusting their properties, such as shape, size, and surfactant nature and concentration. Similar attempts are made with particles by tuning other environmental properties such as airflow, evaporation gradients, confinement, and surface-tension landscapes to guide the trajectories of these systems and achieve effective external control. By tuning these environmental fields, one can guide trajectories, switch dynamical modes,⁷¹ or even trap particles within localized regions.⁷²

Beyond offering insight into fundamental active matter physics, our findings may inform the design of future self-propelled micromachines, environmental sensors, and soft-robotic elements that operate under autonomous, fuel-driven, and symmetry-broken conditions.

Conflicts of interest

There are no conflicts to declare.

Data availability

The source data for the figures are available in the following repository: https://zenodo.org/records/18046397?token=eyJhbGciOiJIUzUxMiJ9.eyJpZCI6ImZhZTJhNmUzLWY0MDMtNGQxMi05NDQ1LThhYmNlMjIzNjZjMiIsImRhdGEiOnt9LCJyYW5kb20iOiI4Y2JkNDZkZGI3Y2JiZjJlNGYzNDFmMmM2ZTRhOTk5OCJ9.Z1OriVehmVmLun5Dp7LME_zInaWulr0yBA1YlPfDwzbg0PIKqi1-CBfs_GqDEKpc9JTmgFhudBgfbQtqEnm31g.

Supplementary information (SI): Movie S1: the effect of the shape of the particle – comparison between experiment and theory. Movie S2: simulation movie showing the effect of α and κ for a fixed eccentricity e = 0.93. See DOI: https://doi.org/10.1039/d5sm01270h.

Acknowledgements

PP acknowledges financial support from the SERB, Department of Science and Technology (DST), India, under Grant No. CRG/2022/001541.

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Footnote

† These authors contributed equally.

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