Analysis of weakly compressible fluid flow in nano/micro-size circular tubes considering solid wall force

Aiming at the problem that fluid flow in nano/micro-size tubes deviates from the Hagen-Poiseuille law but the mechanism remains unclear to date, this paper focuses on fluid flowing in a nano/micro-size circular tube considering the weak compressibility of the fluid and the tube wall action. The tube wall action was introduced into the momentum equations as a wall force, the hydrodynamic vorticity-stream equations were derived, and the first-order perturbation solutions of pressure and velocity were obtained. It is found that there exists zero-order radial pressure. Due to the influence of wall-fluid interaction, the first-order radial pressure increases and the first-order velocity decreases. The dimensionless volume flow rate deviates from an uncompressible fluid due to the compressibility of the fluid and the tube wall force. The deviation of the dimensionless volume flow rate from Poiseuille flow increases with the increasing of compressible coefficient and ion concentration in the liquid acted with the tube wall, and increases with the decreasing of the tube diameter. The liquid cannot flow when the tube diameter is less than a certain size. This paper reveals that the mirco-scale effect of nano/micro-size is resulted from the compressibility of the fluid and the tube wall force together.