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 dec...