Transport phenomena in the near-field region of Stefen flow

Abstract

Stefan flow is a transport phenomenon concerning the movement of one component of a multi-component mixture that is induced by the production or removal of the component at an interface. Fick’s law is often used to describe the transport phenomena in many physical and chemical processes. However, when the system scales down to the order of molecular mean free path, the influence of interface that is not considered in Fick’s law, cannot be neglected. To predict the transport phenomena in the near-field region, the Herz-Knudsen (HK) relation is often adopted, in which the near-field region controlled by the HK relation was assumed as a zero-thickness layer. Our theoretical analysis has shown that this assumption is less physically realistic. In this study, we derive the thickness of the near-field region through the analysis of the theoretical binary diffusion coefficient and corresponding mass flux. Based on the analysis, we propose a modified Fick’s law to describe the far-field and near-field regions separately. The validity of this modified Fick’s law and its difference from Fick’s law coupled with the HK relation are demonstrated by comparing the partial pressure distributions of binary mixtures, predicted by the two versions of Fick’s law and the Direct Simulation Monte Carlo (DSMC) method, due to the deposition of one component on a cold surface. The comparison results show that the modified Fick’s law outperforms the Fick’s law coupled with the HK relation in accuracy at high deposition coefficients for H2O/N2 mixture and in stability within the range of this study. Moreover, the situations when the modified Fick’s law is required are discussed. This study provides a more molecular-level insight into the transport phenomena in the near-field region of Stefen flow.