(98av) Active Diffusiophoretic Motion of Submicron Swimming Colloids With Large Surface Reaction Rates and Solute Convection
Harnessing forces to propel colloidal particles as mechanical engines are central to the design of locomoting objects for nanocolloid assembly, for transport of biomolecules in targeted drug delivery and as roving vehicles for sensing and detection. One of the potential mechanisms is diffusiophoresis, a chemo-mechanical transduction mechanism in which a concentration gradient of solutes in a thin interaction layer (L=O(1-10)nm) applies an unbalanced intermolecular interaction on the colloid and ultimately brings about its motion in a particular direction. We study active diffusiophoretic motion (or self-diffusiophoresis) in which a partially coated colloid with catalyst consumes reactant from the environment and releases product in an irreversible first order reaction, creating solutal fields in both reactant and product across the colloid which sustains diffusiophoretic motion. As technological interest progresses towards miniaturization of the motors, it's crucially important to understand the dependence of the swimming velocity, U, on the particle radius, a. Here we focus on two factors which affect this dependence, the reaction rate and the solute advection.
Numerical solutions are obtained for the case in which only the reactant solute interacts with the colloid, with a potential interaction which decreases exponentially with the distance between the particle and the colloid. The hydrodynamics at small Reynolds number but finite Péclet number, the ratio of convective transport to diffusion (Pe=U'L/D, U' is the characteristic swimming velocity), is coupled with solute mass balance conservation. Our algorithm relies on an iterative method for obtaining the solute concentration field based on Galerkin finite elements in conjunction with an analytical solution we found for the hydrodynamics. The effect of the reaction rate is defined by the Damköhler number, Da, the ratio of the rate of reaction of solute to the diffusion (Da=kL/D, where k is the rate constant and D is the solute diffusion coefficient), and the effect of advection by the Péclet number.
When convection is negligible (Pe equals zero), we find that for small Da, the swimming velocity decreases as the particle radius becomes smaller. For finite values of Da, the scaled velocity is non-monotonic: For particle radii much smaller than L, the velocity increases with decreasing radius. For particle radii of order L, the velocity decreases with increasing radius. This leads to the interesting and technologically promising conclusion that if the reaction rate is fast enough, swimmers will increase their velocity as their size decreases, as long as their size does not approach the length scale of the intermolecular interaction. At any particle radius, the effect of advection is shown to decrease the swimming velocity due to a reduction in the gradient across the particle. Lastly, we evaluate the swimming velocity for all various values of the nondimensional groups illuminating the swimming velocity dependency on colloid size which is a critical issue for engineering and designing the next generation of "nanoengines".