Steady nanocapillary flow: Micropolar approach vs classical models

Abstract

The peculiarities of nanocapillary flows are studied in the framework of Newtonian and micropolar fluid models. The classical problem of a steady flow driven by a constant pressure gradient is formulated for a cylindrical nanocapillary with a radius much smaller than its length. All possible boundary conditions (slip, no-slip, and stick-slip) are exploited for the model of the Newtonian fluid, and two alternative boundary value problems (hyper-stick and no-slip with nonzero spin) are considered for the micropolar fluid model. Parametric studies of the considered analytical solutions are fulfilled. The flow rate is calculated for the considered boundary value problems and compared with the experimental data known in the literature. Real material constants known for water are used in the analysis. It is demonstrated that the classical approach fails to explain simultaneously two experimental effects known for nanocapillaries: retardation of flow in a capillary with smooth walls and acceleration of flow in a capillary with rough walls. The explanation is given in the framework of a micropolar fluid model, which is the natural extension of the Newtonian fluid model.