Dynamics of Marangoni-Driven Elliptical Janus Particles

TL;DR

This work addresses how particle shape and size influence Marangoni-driven self-propulsion of camphor-Janus particles at an air–water interface. It combines experiments on elliptical Janus disks with a minimal 2D reaction–diffusion–mechanical model that couples camphor transport to surface-tension gradients, producing force and torque under anisotropic drag. The main findings show that circular Janus particles translate straight while elliptical ones undergo circular motion, with the radius $R$ decreasing and angular velocity $\omega$ increasing as the eccentricity $e$ grows; a bistable regime appears near the transition, and phase diagrams in $(\alpha,\kappa)$ delineate conditions for stable circular motion. The study demonstrates that geometry and surfactant dynamics control chemo-mechanical feedback in active matter, offering design rules for Marangoni-driven micromachines and sensor devices, and sets the stage for exploring collective behaviors of multiple 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.

Figures (5)

• Figure 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 Figs. (b), (c) and (d), A denotes the camphor-infused active part and P the passive part. In Figs. (c) and (d), the black dots represent the released camphor molecules.)
• Figure 2: (a) - (e) Trajectory of centre of mass of Janus particle for different shapes. (a) shows a straight path, while (b)--(e) show almost circular trajectories with radius $R$. (b) $R = (2.585 \pm 0.184)~\mathrm{cm}$; (c) $R = (1.599 \pm 0.105)~\mathrm{cm}$; (d) $R = (1.213 \pm 0.056)~\mathrm{cm}$; (e) $R = (0.888 \pm 0.028)~\mathrm{cm}$; (See Movie1) (f) shows the variation of angular speed $\omega$ and radius $R$ with eccentricity $e$. The average $\omega$ and $R$ are computed over ten cycles.
• Figure 3: (a-d) shows 4 different shapes from circle to elongated ellipse, depicting distinct trajectories from straight-line to circle (also see Movie2).Fig. (e) shows how the angular velocity $\omega$ and the radius $R$ change upon changing the shape of the particle. For this case, $\alpha = \alpha_0,~$ and $\kappa = 0.2 \frac{\gamma_0 f_0}{\alpha_0}$
• Figure 4: The figure shows that the $\alpha, \kappa$ determine the trajectory of the particle of eccentricity $e=0.93 ~~(a = 1.25~a_0 ,~b=0.46~a_0)$ in the steady state (in units of $\alpha_0$ and $\kappa_0 = \gamma_0 f_0 / \alpha_0$). The white-dotted curve gives a rough boundary for the ratio $2\pi\alpha/\omega$ near 1. When this happens, the circular trajectory is disturbed, and the particle deviates to a complex trajectory.
• Figure 5: The radius $(R)$ and $\omega$ of the particle is plotted by changing $\alpha$ and $\kappa$. Since the surface tension dip due to the surfactant depends on $\kappa$, increasing it increases both the radius $R$ and $\omega$.