Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Flow through a circular tube with a permeable Navier slip boundary | Cox and Hill Nanoscale Research Letters 2011 6 389 http content 6 1 389 o Nanoscale Research Letters a SpringerOpen Journal NANO EXPRESS Open Access Flow through a circular tube with a permeable Navier slip boundary Barry James Cox and James Murray Hill Abstract For Newtonian fluid flow in a right circular tube with a linear Navier slip boundary we show that a second flow field arises which is different to conventional Poiseuille flow in the sense that the corresponding pressure is quadratic in its dependence on the length along the tube rather than a linear dependence which applies for conventional Poiseuille flow. However assuming that the quadratic pressure is determined say from known experimental data then the new solution only exists for a precisely prescribed permeability along the boundary. While this cannot occur for conventional pipe flow for fluid flow through carbon nanotubes embedded in a porous matrix it may well be an entirely realistic possibility and could well explain some of the high flow rates which have been reported in the literature. Alternatively if the radial boundary flow is prescribed then the new flow field exists only for a given quadratic pressure. Our primary purpose here is to demonstrate the existence of a new pipe flow field for a permeable Navier slip boundary and to present a numerical solution and two approximate analytical solutions. The maximum flow rate possible for the new solution is precisely twice that for the conventional Poiseuille flow which occurs for constant inward directed flow across the boundary. Introduction A body of evidence currently exists in the literature 1 2 that suggests that fluid flow rates in carbon nanotubes are considerably in excess of that predicted by the conventional Poiseuille flow field even taking into account a slip boundary condition. Some of this evidence has been re-appraised and certain errors in experimental measurements have been strongly suspected 3 . Despite
