Effect of a resistance-free tank on the resistance to gas transport in high vacuum tube

Abstract

The expression for the time lag in a cylindrical tube, into which a gas at very low flow rate enters at one end while the other end is connected to a resistance-free accumulation tank, has been derived assuming that the gas transport in the tube is a diffusive process. Assuming a constant diffusion coefficient of the gas in the tube allowed obtaining an analytical expression for the time lag using the concept of linear asymptotes and Laplace transformation of the governing partial differential equation. The obtained expression indicates that if the pressure response is monitored in the tube, the presence of the tank at the end of the tube would lead to a negative time lag in the tube. The time lag becomes more negative as the distance from the tank increases and the volume of the tank increases while the cross-sectional area of the tube decreases. The comparison of the model with the experimental data obtained in tests with nitrogen in which the pressure response to a step increase in feed pressure of membrane was monitored in the tube at two different distances from the membrane cell, indicates that the error due to resistance to gas transport in the tube on the experimental time lag of tested medium is even greater than that predicted by the model. This is because of the assumption of constant diffusion coefficient in the tube, which does not allow predicting the experimentally observed increase in the slope of the asymptote with the distance from the membrane cell.