Drag on nanoparticles in a liquid: from slip to stick boundary conditions

Stokes' law with stick boundary conditions has been widely accepted for the transport of microscale particles in a liquid. For nanoparticles, however, the hydrodynamic boundary conditions become unclear. In this work, the drag force acting on nanoparticles suspended in a liquid and the hydrodynamic boundary coefficient were calculated by using molecular dynamics simulations. For weak interfacial couplings, slip boundary conditions can be used to describe the particle transport, whereas at strong interfacial couplings, the hydrodynamic boundary coefficient converges to a value greater than the prediction by Stokes' law. In the present paper, we propose a density accumulation length to determine the effective particle size, which makes Stokes' law valid for nanoparticles. For a copper nanoparticle suspended in an argon liquid, the density accumulation length increases to 0.32 nm with increasing solid-liquid coupling strength. Furthermore, it is found that there exists a transition from slip to stick boundary conditions as the solid-liquid intermolecular coupling strength increases. The results presented in this work provide guidance for the prediction and manipulation of the transport properties of nanoparticles in a liquid.