Relaxation effects in the transition from streamline to turbulent flow in tubes and in micropores

The lowest value ( Re )́ of the Reynolds number at which isothermal streamline flow breaks down has been determined experimentally for the flow of nitrogen and of carbon dioxide through copper tubes and through thin porous disks of copper and of nickel. The mean pressure in the experiments has been from 1 to 70 atm of nitrogen and from 1 to 42 atm of carbon dioxide. The pressure difference was from 0.0005 to 0.04 atm across the tubes and from 0.02 to 0.94 atm across the porous disks. The temperature was room temperature throughout (18 to 20° C). In most experiments ( Re )́ has been the same for both gases under different conditions of pressure and of pressure difference but under some circumstances ( Re )́ for nitrogen was different from that for carbon dioxide (for the same tube or for the same porous disk) and also ( Re )́ for carbon dioxide varied with the mean pressure; it is shown that this unusual behaviour occurs when the relaxation length for equilibrium between the bending vibration of the carbon dioxide molecule and the translational motion of the molecule is between 0.1 and 0.6 times the radius of a pore in the porous material; furthermore, it is argued that ( Re )́ CO 2 > ( Re )́ N 2 when the bulk of the carbon dioxide is heated relative to the vibrational mode, whereas ( Re )́ CO 2 < ( Re )́ N 2 when it is cooled. Heating results from friction in the gas, cooling occurs as a consequence of the expansion of the gas.