Interfacial aggregation of self-propelled Janus colloids in sessile droplets

Living microorg anisms in confined systems typically experience an affinity to populate boundaries. The reason for such affinity to interfaces can be a combination of their directed motion and hydrodynamic interactions at distances larger than their own size. Here we will show that self-propelled Janus particles (polystyrene particles partially coated with platinum) immersed in droplets of water and hydrogen peroxide tend to accumulate in the vicinity of the liquid/gas interface. Interestingly, the interfacial accumulation occurs despite the presence of an evaporation-driven flow caused by a solutal Marangoni flow, which typically tends to redistribute the particles within the droplet's bulk. By performing additional experiments with passive colloids (flow tracers) and comparing with numerical simulations for both particle active motion and the fluid flow, we disentangle the dominating mechanisms behind the observed interfacial particle accumulation. These results allow us to make an analogy between active Janus particles and some biological microswimmers concerning how they interact with their environment.

Figure 1

Active Janus colloids in an evaporating sessile droplet with 10% hydrogen peroxide, under an atmosphere of 75% relative humidity, after 2000 seconds. Particle positions are obtained in three dimensions using their defocused image, and the droplet geometry is obtained from side view imaging.

Figure 2

(a) Average mean squared displacement (MSD) of Janus catalytic particle solution in the bulk of a 15% ${\mathrm{H}}_2{\mathrm{O}}_2$ solution. Fitting the parameters of the model in Eq. (1) yields $v_p=$ 2.9 $\mu \mathrm{m}$/s and ${\tau }_R=$ 19 s. (b) A selection of the active Janus particles trajectories used for assessing their self-propulsion velocity and rotational diffusion. These trajectories are obtained close to the bottom of a large container. Only the XY positions are taken into account to compute the MSD shown in (a). (c) When the Janus particles are suspended in water, they tend to sediment to the bottom of the container, and there the only motion observed is Brownian, as shown in the plot. The trajectories shown here have been collected for about 5 minutes, the same time as in (b).

Figure 3

(a) Distribution of particle average distances to the liquid/air interface in a 40 minute experiment in the absence of evaporation. The shift of the distribution to the left side is a clear sign of the accumulation of active Janus particles in the vicinity of the interface. (b) The distribution of self-propelled particle's vertical displacements (in the gravity axis) is symmetrical and centered at $dz=0$. Janus active particles in this size range are not observed to suffer from gravitaxis and consequently, it cannot be invoked to explain the interfacial particle accumulation in our results.

Figure 4

(a) A random selection of numerically computed trajectories of self-propelled particles are shown within a confined boundary resembling a droplet. The droplet interface is represented by a quarter of a circle centered at $r=0$ (not shown in the Figure) and with a radius $r=R$. (b) The graph shows the probability distribution as a function of the distance to the interface ($1-r/R$) of the particles at four instants of the simulation: Initially ($t=0$) particles are randomly distributed. Shortly after the simulation starts certain interfacial accumulation can be observed at $r=R$, which keeps increasing until the end of the simulation, at $t_{\mathrm{end}}=1.5t_{dp}$, where $t_{dp}$ is the time taken by a phoretic particle to travel one droplet radius. Certain accumulation at the solid substrate bottom surface can also be observed.

Figure 5

Active and passive colloids in an evaporating droplet under identical conditions: (a) Trajectories of active Janus colloids, 10% ${\mathrm{H}}_2{\mathrm{O}}_2$, and RH=75% (b) Trajectories of passive colloids at the same conditions, 10% ${\mathrm{H}}_2{\mathrm{O}}_2$and RH=75%.

Figure 6

Distribution of particle distances to the liquid/air interface in evaporating droplets at RH = 75%. (a) Active Janus colloids in the first period of the evaporation process (from $t=0$ s up to $t/t_D=$ 0.13, corresponding to $t/t_{dp}=0.83$). Newly deposited droplets typically fairly homogeneous bulk concentration with particle-depleted interfaces, similarly with passive colloids in (b). (c) Active Janus colloids accumulate notably at the droplet's interface in only $t/t_D=0.26$. Interestingly, passive colloids also tend to accumulate at the interface [see (d)] but to a lesser degree. The receding interface in evaporating droplets explains the accumulation in the passive colloids and the stronger rate in the active ones.

Figure 7

Probability distributions of $dz-dh$, where $dz$ is the distance traveled in the gravity axis by (a) an active Janus particle and (b) a passive colloidal tracer within its lifetime. $dh$ is the distance covered by the droplet's apex while evaporating in an environment at RH = 75%. In the inset one can see that $dz$ and $dh$ are correlated by plotting both independently against the particle lifetime $t/t_{st}$, with $t_{st}$ being the time taken for a particle to travel its own diameter. Janus active particles, due to their vicinity to the liquid-gas interface, manifest a stronger correlation than passive colloids, which tend to remain recirculating within the droplet's volume dragged by the evaporation-driven flow.