Viscosity measurements at pressures up to 14 000 bar using an automatic falling cylinder viscometer

Irving, John Bruce (1977) Viscosity measurements at pressures up to 14 000 bar using an automatic falling cylinder viscometer. PhD thesis, University of Glasgow.

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The thesis describes a new method for measuring the viscosity of liquids in a pressure vessel capable of reaching 14 000 bar, and results are presented for six liquids at 30°C, up to viscosities of 3000 P.

The technique is based on the well-tried principle of a cylindrical sinker falling in a viscometer tube. It departs from earlier systems in that the sinker is retrieved electromagnetically rather than by rotating the whole pressure vessel, and the sinker is held by a semi-permanent magnet before a fall time measurement is made. The sinkers do not have guiding pins, but rely on self-centering forces to ensure concentric fall. Another novel aspect is that a sinker with a central hole to produce faster fall times has been introduced for the first time. An analysis for such a sinker is presented, and when the diameter of the hole is mathematically reduced to zero, the equation of motion for the solid sinker is obtained. The solution for the solid cylinder is compared with earlier approximate analyses. The whole cycle of operation - retrieval, holding, releasing, sinker detection, and recording is remotely controlled and entirely automated.

With unguided falling weights it is essential that the viscometer tube is aligned vertically. The effects of non-vertical alignment are assessed both experimentally and theoretically. An original analysis is presented to explain the rather surprising finding that when a viscometer tube is inclined from the vertical, the sinker falls much more quickly. The agreement between experiment and theory is to within one per cent.

From the analysis of sinker motion, appropriate allowances for the change in sinker and viscometer tube dimensions under pressure are calculated; these are substantially linear with pressure. The viscometer was calibrated at atmospheric pressure with a variety of liquids whose viscosities were ascertained with calibrated suspended-level viscometers. Excellent linearity over three decades of viscosity was found for both sinkers. A careful analysis of errors shows that the absolute accuracy of measurement is to within ±1.8 per cent.

The fall time of the sinker is also a function of the buoyancy of the test liquid. Therefore a knowledge of the liquid density is required, both at atmospheric pressure and at elevated pressures. The linear differential transformer method for density measurement formed the basis of a new apparatus designed to fit into the high pressure vessel. Up to pressures of 5 kbar measurements are estimated to be within ±0.14 per cent, and above this pressure uncertainty could be as high as 0.25 per cent.

The last chapter deals with empirical and semi-theoretical viscosity-pressure equations. Two significant contributions are offered. The first is a new interpretation of the free volume equation in which physically realistic values of the limiting specific volume, vo, are derived by applying viscosity and density data to the equation iso-barically, not isothermally as most have done in the past. This led to a further simplification of the free volume equation to a two constant equation.

The second contribution is a purely empirical equation which describes the variation of viscosity as a function of pressure: ln(η/ηo)t = A(eBP - e-KP) where no is the viscosity at atmospheric pressure, and A, B and K are constants. This 'double-exponential’ equation is shown to describe data to within experimental error for viscosities which vary by as much as four decades with pressure. It also describes the different curvatures which the logarithm of viscosity exhibits when plotted as a function of pressure: concave towards the pressure axis, convex, straight line, or concave and then convex. The many other equations in existence cannot describe this variety of behaviour.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Subjects: T Technology > T Technology (General)
Colleges/Schools: College of Science and Engineering > School of Engineering
Supervisor's Name: Barlow, Dr. A.J.
Date of Award: 1977
Depositing User: Mrs Marie Cairney
Unique ID: glathesis:1977-40932
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 14 Jan 2019 13:57
Last Modified: 14 Jan 2019 13:57
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