Boundary velocity slip of pressure driven liquid flow in a micron pipe

Abstract

The velocity slip of gas flow in a micron channel has been widely recognized. For pressure driven liquid flow in a macro pipe, the minute velocity slip at the wall boundary is usually neglected. With a decreasing scale in the cross section of the flow passage, the effect of velocity slip on flow and heat transfer behaviors becomes progressively more noticeable. Based on the three Hamaker homogeneous material hypotheses, the method for calculating the acting force between the solid and liquid molecular groups is established. By analyzing the forces exerted on the liquid group near the pipe wall, it is found that the active force arising from the rough solid wall can provide the component force to resist the shearing force and keep the liquid group immobile. Based on this a velocity slip criterion is proposed. Considering the force balance of a slipping liquid group, the frictional force caused by the solid wall can be obtained and then the velocity of the liquid group can be calculated using the derived coefficient of friction. The investigation reveals that, in a micron pipe, a small velocity slip may occur when the flow pressure gradient is relatively large, and will cause errors in the pipe flow estimates.