Osmotic Propulsion: The Osmotic Motor

A model for self-propulsion of a colloidal particle—the osmotic motor—immersed in a dispersion of “bath” particles is presented. The nonequilibrium concentration of bath particles induced by a surface chemical reaction creates an osmotic pressure imbalance on the motor causing it to move. The ratio of the speed of reaction to that of diffusion governs the bath particle distribution which is employed to calculate the driving force on the motor, and from which the self-induced osmotic velocity is determined. For slow reactions, the self-propulsion is proportional to the reaction velocity. When surface reaction dominates over diffusion the osmotic velocity cannot exceed the diffusive speed of the bath particles. Implications of these features for different bath particle volume fractions and motor sizes are discussed. Theoretical predictions are compared with Brownian dynamics simulations.

Figure 1

The scaled osmotic velocity for a motor with a first-order reaction on half of its surface plotted against Da for various values of ${\varphi }_b(1+a/b{)}^2$. Here, $D_a=kT/6\pi \eta a$ is the Stokes-Einstein-Sutherland “diffusivity” of the motor [cf. Eq. (2)]. The theoretical predictions (curves) are compared with BD simulations (symbols). The solid curve corresponds to the fixed motor shown for comparison.

Figure 2

Density profiles in the symmetry plane of the osmotic motor at $\mathrm{Da}=100$. The four panels correspond to the four curves (from top to bottom) in Fig. 1. Red is low bath particle concentration and blue the uniform level far from the motor. The right half of the motor is reactive and its motion is from left to right.