Drag force of nanoparticles in the transition regime

Abstract

The transport properties of nanoparticles in gases have a widely practical application, including aerosol science, combustion, and micro- and nanoscale fabrication. A nanoparticle moving in a fluid is expected to experience a drag force, which determines the transport property of the particle. According to the Einstein relationship, the diffusion coefficient of a particle is inversely proportional to the drag force coefficient. However, in the transition regime, it is usually difficult to evaluate the drag force of suspended particles. A typical method is to extend the asymptotic solution of the free molecular or continuum limit to the transition regime. Based on gas kinetic theory, Li and Wang proposed a theoretical expression for drag force on nanoparticles in the free molecular regime, which is then extended to the entire range of Knudsen number following a semi-empirical approach. For nanoparticles, it is necessary to verify the theoretical predictions since the gas-particle non-rigid-body interactions have to be taken into account. In the present paper, the drag force on nanoparticles in the transition regime is investigated by using molecular dynamics (MD) simulations. To evaluate the drag force, a harmonic potential is employed to the nanoparticle to constrain its Brownian motion in our MD simulations. In the steady state, the drag force can be obtained by the balance between the drag and harmonic forces. It is found that the gas-particle non-rigid-body interactions have a significant influence on the drag force of nanoparticles. For weak gas-solid couplings, the MD simulation results could agree well with the prediction of Li-Wang theory. However, for strong couplings, there exists significant discrepancy between the MD simulation results and the theoretical results. Due to the gas-solid intermolecular interactions, gas molecules can be adsorbed on the nanoparticle surface, and after a time period, they may re-emit from the surface when they gained sufficient kinetic energy. Therefore, an adsorption-desorption equilibrium and an adsorption layer can be established on the particle surface. The adsorption layer enlarges the collision cross-sectional area and enhances the momentum transfer between gas molecules and the particle, and thus the drag. This can explain the inconsistent between the theoretical results and MD simulations. In this work, we introduce an adsorption ratio to evaluate the thickness of the adsorption layer. Then, the effective particle radius can be defined by the sum of particle radius and the thickness of the adsorption layer. By using the effective particle radius, the simulation values agree with the theoretical predictions much better. The results of this work provide insights for the application of nanoparticles in aerosol science.