Compressible liquid flow in nano- or micro-sized circular tubes considering wall–liquid Lifshitz–van der Waals interaction

Although nano- and micro-scale phenomena for fluid flows are ubiquitous in tight oil reservoirs or in nano- or micro-sized channels, the mechanisms behind them remain unclear. In this study, we consider the wall–liquid interaction to investigate the flow mechanisms behind a compressible liquid flow in nano- or micro-sized circular tubes. We assume that the liquid is attracted by the wall surface primarily by the Lifshitz–van der Waals (LW) force, whereas electrostatic forces are negligible. The long-range LW force is thus introduced into the Navier–Stokes equations. The nonlinear equations of motion are decoupled by using the hydrodynamic vorticity-stream functions, from which an approximate analytical perturbation solution is obtained. The proposed model considers the LW force and liquid compressibility to obtain the velocity and pressure fields, which are consistent with experimentally observed micro-size effects. A smaller tube radius implies smaller dimensionless velocity, and when the tube radius decreases to a certain radius Rm, a fluid no longer flows, where Rm is the lower limit of the movable-fluid radius. The radius Rm is calculated, and the results are consistent with previous experimental results. These results reveal that micro-size effects are caused by liquid compressibility and wall–liquid interactions, such as the LW force, for a liquid flowing in nano- or micro-sized channels or pores. The attractive LW force enhances the flow’s radial resistance, and the liquid compressibility transmits the radial resistance to the streaming direction via volume deformation, thereby decreasing the streaming velocity.