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Interaction of Active Janus Particles with Passive Tracers

In this study, we investigated the motion of active SiO2-Pt Janus particles in the 2D bath of smaller silica tracers dispersed in varying areal densities. The effect on the organization of the tracer particles around the active JPs was also explored. Our experiments indicate that the interaction between the tracers and the active JPs mainly depend on the nature of collision marked by the duration of contact. For all the concentration regimes, we have shown that the short time collisions do not have significant impact on the motion of active JPs, however, during moderate/long-time collisions tracer(s) can lead to a significant change in active JPs motion and even cause them to rotate. In the concentrated regime, our experiments reveal the emergence of a novel organizational behavior of the passive tracers on the trailing Pt and the leading SiO2 with a strong dependence on the nature of collision.


Introduction
Artificial active matter systems demonstrate the capability to perform non-equilibrium motion by utilizing the energy from their surroundings (1, 2). In doing so, they successfully mimic the motion of several micro-organisms such as bacteria (E. coli), sperm cells, etc (3). Therefore, studying the isolated and collective motion of such artificial active systems provides useful insights into the motion of their biological counterparts. In addition, these artificial systems have shown the capability to be useful in several potential applications such as drug-delivery, micro-machines, environmental remediation, biological sensing and imaging etc (4)(5)(6)(7)(8). Artificial active matter systems can be broadly classified in two categories i.e. Active Colloids (ACs) and Active Droplets (ADs), based on their propulsion mechanism. For ACs among the various strategies that have been devised over the years, the use of Janus particles (JPs) has been widely recognized (9). The two opposite sides of the JPs (spheres or rods) are of different chemical compositions (10,11). To make them ACs one side is usually coated with a reactive metal such as Pt or Pd, and the other side is of chemical gradient is generated by the particle itself, it is known as self-diffusiophoresis (15)(16)(17).
In the case of active droplets, self-propulsion is a resultant of Marangoni flow in the surrounding fluid which originates due to gradient in concentration of surfactant molecules along the interface felicitated by the continuous dissolution of droplet molecules in the bulk liquid (18,19).
For their successful use in most of the sought-after applications, it is critical to gain an in-depth understanding of their motion, both isolated and collective, under varied scenarios. This includes presence of nearby obstacles, external-flow and inert impurities. In the bulk of a simple Newtonian liquid, several experimental and analytical studies has established that such active JPs perform ballistic motion at short time scales which transitions to a random motion at long time scales (20). This transition is prompted by the Brownian fluctuation in the orientation of the JPs. In the vicinity of an impenetrable wall, the complex interplay of the wall-induced hydrodynamic interactions, the chemical activity, and gravity, cause JPs to align with their Janus plane being perpendicular to the wall (21)(22)(23)(24). Close to the wall, on exposure to shear flow, experiments have shown that these JPs can migrate upstream or perpendicular to the shear flow (25)(26)(27). The understandings of these wall-induced interactions have been further implemented to guide the motion of active JPs (28), capture the active JPs by stationary obstacles (29) and to sort them through well designed maze (30). So far very few studies have investigated the interactions of fast moving active JPs with mobile inert passive tracers (31). Most of these studies have discussed the 2D clustering behavior of the tracer particles with the light activated JP as the nucleating site (32)(33)(34), originated by the activity induced flow-fields in the vicinity of the wall. Recently, Hailing et al demonstrated the use of active JPs for directional locking and channel unclogging of silica beads in micro-channels (35). In a very recent study Katuri et al (36) by exploring the motion/structure of the passive tracers surrounding the active JPs, mostly immobile, map the activity induced hydrodynamic fields. The study indicated that the interactions between the tracers and active JPs are complex and dependent 3 on the state of active JP. Given the underlying rich physics, further experimental studies are warranted to explore the complex interactions between the tracers and motile active JPs under different scenarios. In this study, we dispersed active SiO2-Pt JPs in a bath of passive silica tracers under dilute, semi-dilute and concentrated regimes. The effect of passive tracers on the motion of active JPs and the complimentary effect on passive tracers' distribution is experimentally investigated.

Experimental Section
Janus Particles were synthesized using the drop-casting method as reported by Love et al (37).
Briefly, a dilute suspension of 5 µm SiO2 colloidal particles was prepared in Milli-pore water with a (1:3) ratio. The suspension was drop cast on a plasma-treated glass slide used as a substrate.
Plasma treatment was done to make the glass slide hydrophilic which helps in the uniform spreading of the particle suspension. The water was removed via slow evaporation which ensured the formation of the monolayer formed, confirmed via optical microscopy as shown in figure 1. A successful Pt coating and formation of Janus particles. To observe the particles, an optical cell was prepared by sandwiching two plasma-treated glass slides using a spacer (PDMS ring of height 2 µm). An appropriate amount of the 2 m SiO2 particle solution, used as passive tracers, was added to achieve different area fractions where N is the total number of particles in the frame, ap is the area of an individual particle and A is the total area. A small amount of the JPs solution was added to keep the JP concentration low. An appropriate amount of H2O2 aqueous solution was also added to achieve the overall H2O2 wt% as 0% and 3%. Finally, the optical cell was covered with a coverslip of (∼ 100 µm). The optical cell was then placed on the thermal stage mounted on the microscope stage for -imaging. A constant temperature of 25°C was maintained using the thermal stage.

Methodology
Since the particles are heavy, they sediment towards the bottom wall of the optical cell and move in the 2D X − Y plane with insignificant movement in the Z direction. Particles were imaged using FLIR camera with resolution (1pixel= 0.22 µm) equipped with Olympus Inverted Microscope. To allow the system to attain a constant temperature of 25°C a waiting period of 10 minutes was used after placing the optical cell on the thermal stage. Subsequently, movies for 5 − 10 mins were recorded at 20 fps. Afterward, particle tracking was done using MOSAIC plugin in Image-J that uses a correlation-based approach to obtain particle trajectories. The trajectories were analyzed for 100 sec to get the time-dependent X-Y data.
For Brownian particles, the mean square displacement (MSD) 2 L  is increasing linearly with time. The data were fitted using the equation Here, D is the short time scale Brownian Diffusivity of the particle at temperature T in a liquid with viscosity η. For active JPs, the MSD is parabolic in nature which was fitted with using the equation where v is the average propulsion speed v of the active JPs. The instantaneous velocity of the active JPs was used to compute the velocity autocorrelation function ( ) which was fitted using the equation: Here R  is the rotational time scale,  is the Dirac-delta function, and  is the angular velocity of the active JPs to capture the curvature in the trajectories, if any. A representative plot for C(t) with fitting has been shown in supporting figure 2.
The distribution of passive particles around the JPs was computed using the 2D radial distribution function ( )

Control Experiments
To first establish the validity of our experimental setup and protocols, we performed some control experiments, as discussed below:

Passive Motion
Appropriate amounts of 5 µm SiO2-Pt JP suspension and 2 µm SiO2 tracer particle suspension were mixed to achieve  passive JPs is due to their interaction with the surrounding passive tracers and the bottom wall. It was also seen that in absence of any activity, due to the density difference in the Pt and the SiO2 side, the Janus particles orient with the Pt side facing downwards. Next, to understand the distribution of tracer particles around the JP, we compute the 2D radial distribution function g(r). JPs during the process of two such collisions. Clearly, just before the collision the JP rotates away from the tracer particle, after which they rotate towards the tracer particle until the tracer detaches.
This behavior is also evidenced in representative time-lapse images shown in figure 3(e) and video S3 in the Supporting Information). During the initial approach, even when the particles are far-apart from a physical contact, the long ranged hydrodynamic interactions emerge. The tracer particle successfully modifies the flow-field in front of the active JP, causing it to rotate away from the passive tracer. This observation agrees with the recent analytical predictions made by Purushothaman and Thampi (39). Subsequently, when the passive tracer is attached to the active JP, it generates an asymmetry in the otherwise symmetric flow-field around the JP, causing the particle to rotate in the direction towards the tracer particle to conserve the overall angular momentum.
Our results indicate that despite the significant size difference and overall low concentration, smaller SiO2 particles no longer just act as tracer particles, instead, remarkably affect the motion of an active JP. The rotational behavior is similar to the previously reported study on smaller active JPs near the fixed obstacles. However, for the first time to the best of our knowledge, we have demonstrated the influence of a smaller movable tracer particle significantly affecting the motion of a bigger active JP.   |vinst. | >>0, despite the same 3wt % H2O2 concentration, the wake area (~ 90 m 2 ) in our experiments was found to be much more than 20 m 2 reported by Katuri et al. We also observed that during the motile state of the active JP, the wake resembles appearance with the comet-like pattern, wherein it is elongated along the velocity direction of the particle. On the other hand, during the rest state the wake resembled a fluid-like shape reported by Katuri et al.

Active JPs in the semi-dilute suspension of passive tracers
These differences emphasize that besides the chemical activity of the active JPs, their translation motion also plays a crucial role in enlarging the wake area. To further understand this, we investigated the wake disappearance time under different conditions. The plot shown in figure 6 indicates that for moderate time collisions where the tracer particles glide over the active JP and detach, the wake disappears in nearly similar time ~10s irrespective of the area of the wake. Figure   7(a) and 7(b), shows the time-lapse images of a wake disappearing gradually. The sequence of images indicates that as the active JP moves out of the wake, the peripheral tracer particles along the longer edges move perpendicular to the length of the wake to fill the void. confirms that due to the motility of the active JPs the depletion region is generated which the slow diffusing passive tracers are unable to fill instantly hence a void is developed. On the other hand, for the wakes formed by the long-time collisions, where the tracer particles remain stuck for longer times, the wakes disappear slowly (figure 7(b)) as the JP moves out of the area slowly due to its lesser speed. In the limiting case where the active JP are stuck, we expect the wake to persist as long the particle remains active.
The emergence of a wake on the Pt side is accompanied by the accumulation of passive tracers at the leading edge of the active JPs. We quantity this by computing the variation in g(r) at the front half. In   Figures 8(a) and 8(b), we demonstrate the average g(r) for the passive traces on the silica side about the center of an active JP. Figure 8(a) indicates that in the case of moderate-time collisions, the first peak at r=a of g(r) is significantly higher than the control case. The increase in the second peak at r=3a is not much and eventually at r=7a the g(r) nearly matches with the control case (here a is radius of the passive particle and r is measured from the surface of the JP). In case of long-time collisions, it is observed that similar to the moderate-time collision although at r=7a, g(r) approached the control Figure 7: (a) Representation of wake area. Time-lapse optical microscopy images for the wake area disappearing in concentrated passive tracer limit (b) Moderate time collision, t between images is ~2.21 sec, wake disappearance time ~8.85 sec (c) Long time scale collisions, t between images is ~5 sec, wake disappearance time ~20.1 sec. Scale in (b) and (c) corresponds to 5 µm.
15 case values, however the height of the second peak at r=3a is more pronounced. This confirms that the nature of collision affects the accumulation of passive tracers at their leading also.
Although the areal coverage of passive traces in the concentrated regime is not very high to achieve the jammed state. However, occasionally it was observed that when two active JPs moved in a manner which resulted in a finite approach velocity along the line joining their centers, the passive tracers in the intermediate region approached the jammed state. This local jamming of the tracer particles induces a long-range interaction between the active JPs forcing them to turn and change their direction of motion. As a result, the two JPs are unable to come in physical contact with each other, which however in the control case, in absence of intermediate passive tracers the active JPs are able to touch most of the time. This observation is further highlighted in the minimum approach distance Rmin between the active JPs in the two scenarios, shown in figures 9(a) and 9(b). In the concentrated regime, Rmin is much larger than the Rmin in the control case.