GB2574180A - Automatic rotational viscometer and rheometer - Google Patents

Abstract

In a viscometer, a cylindrical probe 4 is immersed into liquid 7 to depth 4b. The probe is rotated at constant speed and the torque measured. The immersion depth is increased in steps, and the measurement repeated at each step. By linear regression or graphical methods, the contribution of end effects arising from the base 6 of the cylinder, which may have a circular, conical or hemispherical profile, can be eliminated. Immersion depth may be set by means of a stepper motor or helical screw under computer control. Readings may be taken at multiple rotation speeds at each immersion depth. By knowing the diameter of cylindrical container 7a, upward displacement of liquid 7 may be accounted for as probe immersion is increased. A software package may control the measurements and analysis.

Description

Field of Invention

This invention relates to the measurement of the viscous and rheological properties of liquids and fluidly mobile pastes and slurries. The study of viscosity is generally understood to refer to the flow properties of liquids, often measured by the drag experienced by objects shearing through a liquid. Rheometry is the study of the complex behaviour of viscosity towards different rates of shear. This invention enables measurement of time-independent viscous behaviour via stable state testing over tens of seconds, and does not relate to time-dependent behaviour such as thixotropy, which can extend over minutes or hours.

Background of the Invention

Rotational viscometers and rheometers consist of a motor housing connected to a torque sensor that holds a probe or bob that can rotate in the test liquid, where any torque (twisting force) on the probe can be measured. Rotational viscometers and rheometers utilise probes of various geometries, of which the functional parts are wholly immersed in a viscous medium and rotated, experiencing viscous drag. This produces torque in the direction opposite to rotation. This torque can be measured by various methods well known in the art, including torque transducers, displacement transducers for spring devices, and electrical load on the driver motor. The viscosity at a particular rotational speed can be calculated from the torque if the probe has been calibrated in a liquid of known viscosity and socalled Newtonian flow, which is flow that obeys Newton's equation (and others) for viscous drag in a linear relationship relative to the shear rate. The viscosity thus measured is considered to be independent of rotational speed for Newtonian liquids, the standardisation and verification of which is carried out by capillary viscometry .

The probe can be of various geometries, including cylinders, flat discs, cone and plate, and T-bars. This invention covers the use of cylinders .

In theory, a purely cylindrical surface rotating in a viscous medium offers the opportunity to relate the shear rate (area per second) to the shear stress (torque), and thereby obtain the single viscosity point pertaining to those conditions, since the area of the cylindrical part of the surface can be precisely determined. Real cylinders, however, are enclosed by top and bottom surfaces, which are essentially circular. In the case of real probes, the bottom surface is provided with a conical or hemispherical surface, so that as the probe is immersed in a liquid, air is displaced and not trapped in a bubble below the probe. The upper surface is circular, conical or hemispherical and bears the shaft connecting the cylinder to the motor and torque sensor. In commercial versions of probes, the shaft is notched to provide a guide to immersion to the correct level in the test liquid. The upper and lower surfaces, along with the shaft connecting the probe to the motor, add an acceptable amount to the shear stress experienced by the cylindrical surface if the material being investigated has Newtonian characteristics.

If the latter is true, the probe's torque response to a viscous liquid can be calibrated using liquids of known viscosity. The same probe can then be used again to measure the viscosity of another liquid, using the calibration value to convert torque into viscosity.

If the material being investigated suffers from non-Newtonian flow such as so-called shear thinning or shear thickening, the contributions of torque from upper and lower surfaces and the shaft cannot be accepted for the most critical work. Shear thinning materials, such as many polymer solutions, experience a viscous drag that bears a reduced proportionality to shear rate as the latter increases, so that measuring the torque at different rotational speeds does not yield the same viscosity. Shear thickening materials, such as cornflour pastes, experience an increased proportionality to shear rate, and suffer the same problem. It should be emphasised here that even while the rotational speed is constant for any single test, parts of the probe's surface would, with certain geometries, experience different rates of shear because they are at different distances from the axis of rotation and thus moving at different linear velocities.

To understand the problem with circular, conical or spherical surfaces, refer to Figure 1. This shows the specific problem as it applies to circular discs, and therefore the general problem with these geometries. Since the whole disc rotates together, area (11) at radius (13) experiences more shear than area (12) at radius (14) because the parameter of area per second is larger. Therefore, for shear thinning materials, this part contributes proportionately less than it should per unit area to the overall torque. For shear thickening materials, area (11) at radius (13) contributes proportionately more per unit area. This problem is referred to in the literature for cylindrical viscometer probes as end corrections. See End Effect in Rotational Viscometers, Journal of Applied Physics 18, 988 (1947). The additional end effect resulting from the twisting of the sample liquid column between the bottom of the cylinder and the base of the container has been found (according to the literature) to be negligible for distances greater than 1 centimetre and viscosities greater than 1 poise and can be safely ignored for the purposes of this invention.

One accepted method to make end corrections is to provide two or more cylinder probes of different lengths but identical top and bottom geometries. The increased length of cylinder can then be related, graphically or by simple arithmetic, to the torque to eliminate end effects, thus enabling viscosity calculation at that single rotational speed. This method suffers from the necessity that the material must be measured two or more times with fresh probes of different lengths, entailing disconnection, reconnection and cleaning, along with immersion quality checking, all of which take operator time.

This problem can be overcome by using a probe that can be immersed to variable lengths, where the change in immersion length can be calculated as an increase in contact area with the test liquid, and this area increment used with the torque increment to obtain the viscosity. Variable immersion viscometers have been described in the literature and suggested as a means to eliminate end corrections. In Mechanics and Chemistry in Lubrication, (1985, Elsevier), page 74 and Figure 4-11 (a) and (b), the authors describe the mathematics necessary to eliminate end corrections, but do not describe the experimental set-up to any degree, therefore not enabling the practice .

Remington - Essentials of Pharmaceutics (Pharmaceutical Press, 2012) page 408, and Remington - The Science and Practice of Pharmacy, page 354 paragraph 36 and Figure 23-18 both suggest the fill level of the sample container could be adjusted for different immersion lengths, but this method would require observation of the immersed length with a travelling microscope: a time-consuming practice with inherent inaccuracies.

Disclosure of Invention

This invention overcomes those problems by providing a means to obtain the exact, functional surface area of the cylindrical surface rotating in the material, and thus the correct viscosity at the particular rotational speed, using only one cylinder. This invention also enables collection of data points with different cylinder immersion lengths, and at a range of rotational speeds, without disassembly, reassembly, re-immersion and repeated cleaning of the eguipment.

To achieve these improvements, this invention provides a motorised accurately measured movement of a single cylinder of constant diameter into the material, in steps, see Figure 2. The cylinder breaks the surface at (5), immersing a length (4b) in the material, such a length having been measured by a computer-controlled movement of the motor and sensor housing downwards while being supported by its stand. This movement of motor and sensor housing may be achieved by methods well known in the art, such as using stepper motors or driven helical screws. Readings of torque are taken at each further immersion of the cylinder probe into the sample liquid. Since the increased torque is directly linked to the extra length immersed and the rotational speed is constant for each test, end effects coming from the circular, conical or hemispherical base, and from the surface effect where the probe breaks the surface of the liquid, are entirely eliminated by regression calculation or graphical methods. The result is a correlation between the purely cylindrical surface area immersed and the torque.

This invention anticipates the use of various equations for viscosity calculation well known in the art, particularly inclusive of equations relevant to cylinders.

This invention also provides a cylindrical container of measured, constant internal diameter to hold the material sample for measurement. This may be insulated or provided with a bath to facilitate measurement at a controlled temperature. It may also be provided with a holed lid to prevent evaporation of any solvents present or ingress of unwanted atmospheric gases or vapours while allowing access to the shaft. Precise measurement of the probe and container are essential to this invention; see Method of Using the Invention.

Optionally, this invention also anticipates a software package to drive the viscometer and collect data, such software allowing for automatic viscometer control, data collection and operator cooperation .

This invention also anticipates a set of cylindrical probes of different diameters and of bottom geometry well known in the art, such as conical, to prevent the trapping of bubbles. Such a set is often found with commercial viscometers where large ranges of materials with widely different viscosities are to be measured.

This invention also anticipates that the motor can be of a type that provides precise speed control over a range of speeds. Typical for the industry, these speeds can include, for example, 0.5, 1.0, 2.5, 5, 10, 25, 50 and 100 revolutions per minute (rpm).

This invention also anticipates that the viscosity data points can be plotted against shear rate using logarithmic/linear or logarithmic/logarithmic axes in a software package (for example, a spreadsheet program like Microsoft's Excel) to obtain an approximation to a straight line as they appear on these graphs. By this means, the apparent slope of the line on log-linear or log-log graphs (or the best fit equation provided by Excel and other programs) can be taken as a measure of the non-linearity of the sample's viscous behaviour and therefore an indication of the degree of shear-thickening or shear-thinning experienced by the material. It must be emphasised that unless viscosity points are obtained that relate directly to a precise shear rate/torque relationship, such data plotting and correlation is futile because any other shear geometry is compromised by the presence of different shear rates and is therefore dependent on the exact geometry utilised. For example, this author has obtained many such correlations in log-log or loglinear graphs for polymer solutions tested with a horizontal disc viscometer such as a Brookfield RV type. While useful in a single laboratory, such data cannot be compared between different laboratories unless the conditions are identical. Correlations often produce two numbers from the graphs, whereas specifying apparatus types requires more data. Therefore, this invention enables an easier study and sharing between laboratories of this rheological behaviour than previously possible in a short length of time per test, and allows for experimentation on chemistry and other matters to behaviour .

Short test times are important contain volatile solvents that long test, causing thickening, atmospheric oxygen or carbon offset those problems, but the also preferable for accuracy.

concentrations, solvent blends, polymer obtain favourable rheological in rheometry. Polymer solutions often can become partially depleted during a

Other materials can become exposed to dioxide. A holed cover can partially shortest time for test completion is

Method of Using the Invention

In practice, a set of measurements may be taken as follows:

1. The cylindrical container of known internal diameter is filled to a given point with sample material and placed under the probe .

2. The probe is lowered into the sample until the conical or hemispherical point is well within the liquid and the liquid is wetting the cylindrical surface of the probe.

3. The probe is rotated at the lowest speed and the torque measured until it is steady for a fixed length of time.

4. The speed is then increased to the next higher setting, and the probe rotated again. This sequence is repeated at all the speed settings of the motor, obtaining the first set of data points for that length of immersion.

5. The motor is then stopped and driven downwards a precise distance, at a speed low enough to allow proper wetting of the cylinder so as to prevent air bubbles being drawn into the sample or onto the cylinder.

6. The rotational speed of the motor is then re-set to the slowest setting, and the entire process repeated through all the other speeds, as in paragraph 4 here.

7. The motor is then driven downwards again, and the entire process repeated according to paragraph 6 here. This is repeated for the entire length of the cylinder, or until four or more immersed lengths have been recorded.

8. As the probe is being driven downwards, it will displace a volume of liquid and the level of the sample will rise. Therefore, to know the exact length of immersion each time, the software will allow for entry of the probe's identity and will calculate the actual immersed length each time. For example, if the probe is driven down by 5.0 millimetres (mm), the probe diameter is 15 mm and the container's internal diameter is 60 mm, the liquid level will rise 1.25 mm and the actual extra immersion will be 6.25 mm. This parameter will be used with the radius of the probe to calculate the incremental area of immersion .

9. After all the measurements are collected, or at the point where at the fastest speeds, the torque would exceed the maximum for the sensor to handle, the data points can be either printed out or displayed for the operator to use, or imported into software for analysis. Although the data are collected during speed changes, they are collated over immersion areas and are plotted as X-Y graphs or calculated as regression lines, one for each speed. The X-Y graphs have the area of immersion as the independent variable (X-axis) and the torque as the dependent variable (Y-axis). The first data point for each speed may have to be discarded, as it corresponds to the probe having just broken the surface of the sample liquid, and end effects may need to stabilise by further immersion before a straight line may be obtained. An operator using graph paper can obtain the slopes manually. Alternatively, the linear regression formula yields the slopes (which will be in units of torque per unit area) after removing any non-linear part. Any person skilled in the art then has all the information necessary to calculate the viscosity at each rotational speed.

10. If required for rheometry study, the viscosity points can then be plotted against shear rate to obtain a curve that can generate pairs of numbers for each sample liquid via a curve matching algorithm. For example, if a logarithmic-linear relationship can be shown to be appropriate, an equation such as the form:

y = 46.88 log_e(x)+386 will provide two values, 46.88 and 386 to define the rheometric parameters for the liquid. Alternatively, a log-log relationship may provide a better match, giving a power equation of the form:

3 9 y = 185 X ' , producing two parameters of 185 and 1.39 for the liquid.

Description of Drawings

Figure	2 describes	the apparatus,	with numbered	details	as follows
(1)	Incremental	movement of motor and sensor	housing
(2)	Rotation of	motor shaft
(3)	To drive motor
(4)	Cylindrical	probe with (4a)	conical base	and (4b)	immersed

length (5) Surface effects (one of the end effects in the literature) (6) Variable shear at circular base (see Figure 2), (one of the end effects in the literature) (7) Sample of liquid, mobile paste or slurry. (7a) Container of known internal diameter. (7b) Holed lid (8) Minimum distance from base >1 centimetre (9) Known internal diameter

Figure 1	describes	the end	effect	of a circular	base
(10)	unit	of time
(11)	area	swept at	larger	radius
(12)	area	swept at	smaller radius
(13)	large	r radius	, with	a high shear rate
(14)	small	er radius	, with	a lower shear	rate

Claims (5)

1. A means for accurately increasing the functional length of an immersed cylindrical viscometer probe, so that the contribution of the non-cylindrical parts towards shear torque can be eliminated, thus enabling calculation of a strict shear rate to shear force relationship according to the viscosity equations known in the art.

2. A means to obtain a set of such measurements according to Claim 1 without the need to re-attach the probe on the viscometer.

3. A means to calculate the immersion length according to Claim 1 from the dimensions of the cylinder probe and the sample vessel.

4. A means according to Claim 1 to eliminate probe geometry in the measurement of viscosity so that correlation may be made between liquids tested in different laboratories based only on the shear rate and torque.

5. A means to obtain parameters via log-log or log-linear plotting and curve matching of the data points, such parameters having universal applicability and therefore standing on their own rather than being dependent on probe geometry.