The Steady-State Flow of Gas Through Glass Capillary Tubes

Abstract

This paper describes experimental procedures for the calibration ofcapillary tubes to be employed as comparison standards in gas flow-ratemeasurements and considers several types of flow which were observed in thecalibration of seven capillaries of varying diameter. It is shown that undercertain experimental conditions deviations from Poiseuille flow are observedwhich may not be attributed to turbulence, and that this flow behavior may bedescribed empirically by introducing the classical kinetic energy correctioninto the Poiseuille equation.

Introduction

Techniques have been developed for the measurement of the volume rate offlow of nitrogen through glass capillary tubes as a function both of thedifferential pressure applied and of the absolute gas pressure. Capillary tubesthus calibrated are frequently used to determine the rate of gas flow through aporous sample in the measurement of slip-corrected permeability. The purpose ofthis note is to describe the calibration procedure and to discuss some observeddeviations from the ideal flow behavior predicted by the Poiseuilleequation.

Experimental Procedure

The volume flow rate of nitrogen as a function of the differential pressurewas determined experimentally for a series of seven glass capillary tubes ofvarying diameter. As is shown in Table 1, the capillary radii in the seriesranged from 0.004 cm for Kl to 0.07 cm for K7. The capillary tubes were cutfrom capillary tubing purchased on special order from several manufacturers andthe bore radii were determined by microscopic measurement. The gas volume flowrate was measured for each capillary tube at a series of differential pressuresin the range from 0 to 3 cm of mercury and at average absolute pressures of1.0, 2.5, 4.0, and 6.0 atm.

Experimental Procedure for Small Capillaries

A schematic diagram of the apparatus used to calibrate the three smallestcapillaries, Kl, K2, and K3, is shown in Fig. 1. By means of a standard RuskaInstrument Corp. volumetric pump (equipped with a synchronous motor drive, twostages of gear reduction, and a quick-change lathe gear box), nitrogen wasdisplaced by mercury from a metal cell immersed in a constant-temperature bath.The pump, the line to the cell, and a part of the cell were filled withmercury. As mercury was forced into the cell, it displaced nitrogen whichpassed through the capillary tube being calibrated and into a large containerwith a volume of approximately 30 liters.

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