The motion of catalytically active colloids approaching a surface

Abstract

Catalytic microswimmers typically swim close to walls due to hydrodynamic and/or phoretic effects. The walls in turn are known to affect their propulsion, making it difficult to single out the contributions that stem from particle-based catalytic propulsion only, thereby preventing an understanding of the propulsion mechanism. Here, we use acoustic tweezers to lift catalytically active Janus spheres away from the wall to study their motion in bulk and when approaching a wall. Mean-squared displacement analysis shows that diffusion constants at different heights match with Faxén's prediction for the near-wall hydrodynamic mobility. Both particles close to a substrate and in bulk show a decrease in velocity with increasing salt concentration, suggesting that the dominant factor for the decrease in speed is a reduction of the swimmer-based propulsion. The velocity-height profile follows a hydrodynamic scaling relation as well, implying a coupling between the wall and the swimming speed. The observed speed reduction upon addition of salt matches expectations from a electrokinetic theory, except for experiments in 0.1 wt% H₂O₂ in bulk, which could indicate contributions from a different propulsion mechanism. Our results help with the understanding of ionic effects on microswimmers in 3D and point to a coupling between the wall and the particle that affects its self-propulsion speed.

Fig. 1. Acoustic tweezer experiments. (a) Close to the substrate, active particles significantly slow down upon the addition of salt. By observing self-propelled particles in bulk, we can determine whether these salt effects are wall-effects or if salt also affects the bulk behavior. The purple arrows represent the counter flows that occur near the wall. (b) Schematic drawing of the acoustic tweezers setup with acoustic node. (c) Three exemplary predictions of scattering patterns for a polystyrene particle at different z-heights with the corresponding radial intensity profile. This information is needed to connect the holographic signal to the distance from the focal plane. (d) Experimental scattering pattern snapshot with the radial intensity profile for a particle ≈10 μm above the substrate. (e) z-Coordinate trajectory for a passive particle that is lifted up with the acoustic tweezers and sediments twice.

Fig. 2. Influence of salt on the activity of catalytic microswimmers in both 2D and 3D. Trajectories of active particles for 2D experiments (a)–(d) and 3D experiments (e)–(h). All trajectories are plotted for 100 consecutive frames (with a frame rate of 18.9 fps corresponding to about 30 s) and have been moved to start in the same point.

Fig. 3. Height dependence of the diffusion coefficient and particle velocity. (a) For a single particle suspended in 0.1 wt% H₂O₂, the diffusion coefficient D normalized over the expectation value for D_bulk depends on the particle height above the substrate h normalized over the particle radius R. The evolution of D(h) over D_bulk follows the hydrodynamic model for the height-dependent diffusion derived by Faxén. (b) The single particle velocity v, however, is independent of the distance between particle and substrate for low activity (0.1 wt% H₂O₂), but becomes height-sensitive at higher activity (0.5 wt% H₂O₂), when the particle is closer than approx. 5 particle radii above the substrate. The dotted line in (b) serves to guide the eye. Shaded regions in all plots indicate the standard deviation between different particles under the same conditions. All shown experiments are in absence of salt.

Fig. 4. Salt affects active particles close to the surface and in bulk in a similar way. Diffusion coefficient D and particle velocity v both as a function of salt concentration for particles suspended in 0.1 wt% H₂O₂ ((a) and (b)) and 0.5 wt% H₂O₂ ((c) and (d)), respectively. Data obtained close to the substrate is indicated by blue spheres, and bulk data is indicated by green squares. D and v were obtained from a mean-squared displacement (MSD) analysis where lag times up to 1 s were considered. The dashed line in a and c indicates the expectation value from the Stokes–Einstein relation with T = 296 K and η = 0.9321 mPa s (water). Points plotted are median values and error bars indicate the first and third quartiles.

Fig. 5. Relative speed reduction comparison. The velocities relative to the velocity at c_NaCl = 0.1 mM as function of c_NaCl in bulk (a) and at the substrate (b) for two different fuel concentrations compared with the effective Henry's function for self-electrophoresis F_H(κa) (see footnote) following an electrokinetic theory outlined in ref. . Plotted points are median values and errorbars represent first and third quartiles.