ReoCue A Surface Loading Rheometer Abstract This paper describes a new rheometer for measuring rheological properties of fluids. The instrument uses the technique of surface loading which makes it possible to determine viscosity and elasticity of low moduli fluids even at small volumes of fluid samples. Examples given are whole blood and plasma in relation to erytrocyte volume fraction and hemoglobine, prediction of ESR from blood and plasma viscosity and, finally, kinetic effects in human saliva. Introduction By causing an oscillation system containing the sample to perform free oscillations and by measuring the damping and frequency shift of the oscillations caused by the sample, rheological properties of the sample can be determined. The rheometer described has a high accuracy even at viscosities as low as 1 mPas at sample volumes less than 1 ml due to its low self-damping and poses a strong alternative to conventional capillary viscometry. It may also provide a measure of viscoelastic properties of liquids where common rheometers fail due to violation of the gap loading condition. Theory The theory behind the instrument is the following. Assume that a hollow cylinder whose inner radius is R and whose inner height is H is suspended by a torsion wire along its axis. The spring constant of this construction is Iomega^2 , wherein I is the moment of inertia and omega the angular frequency, as the oscillation system with the empty cylinder performs free torsional oscillations. The free torsional oscillations are damped owing to the damping in the torsion wire and the other suspension means. The damping is defined by the logarithmic decrement lambda as lamda =1/n ln(An/A1) wherein n is the number of periods of the oscillation and An is the amplitude of of the oscillation in the nth period and A1 is the amplitude in the first period of oscillation. If the cylinder is filled with fluid and the oscillation system is caused to perform free oscillations, the damping of the oscillation will be greater than in the case of an empty cylinder. As the cylinder oscillates, the oscillation will penetrate into the fluid in the cylinder.The penetration depth delta is determined by the viscosity Eta , the density of the fluid D and the angular frequency omega according to the equation delta=(eta/D)^0.5. By selecting a suitable oscillation frequency, a penetration depth delta of a low viscosity fluid can be obtained, which is much smaller than the radius R of the cylinder. In this case the fluid in the centre of the cylinder will be immovable during the torsional oscillations and the fluid between the cylinder wall and the immovable portion of the fluid will be subject to shear. The shearing action promotes the damping of the oscillation. The damping caused by the shearing motion can be measured, and on the basis of the damping the viscosity of the fluid can be determined. For a viscous fluid the following relationship applies (1), provided that the penetration depth delta is much smaller than the radius R and the height H: Eta=k(lamda -lamda0) ^2,wherein lamda and lamda0 are the logarithmic decrement in oscillation with and without fluid in the cylinder, and k is a calibration constant. By measuring the damping and the relative frequency shift, the dynamic viscosity eta' and the storage modulus G' can be determined for a slightly elastic sample according to equationscontaining the relative damping and the relative frequency shift (2). These equations constitutes a lowest order solution to the general problem. Recent considerations towards a numerical approach to the general solution has been given by Kleinman (3). The working of the ReoCue is best examplified by some case studies from different applications in the medical field. Human blood and plasma Human blood is a non-Newtion fluid with a flow curve which is strongly dependent on the volume fraction of erythrocytes (4). In what follows all measurements have been carried out at an oscillation frequency of 8.5 Hz. A larger study has been carried out at the Lund University hospital, Bohlin et.al (5) where the ReoCue has been used to measure the viscosity of whole blood and its plasma on 122 patients both healthy and ill. Figure 2 below show the ratio of blood viscosity to its plasma viscosity plotted against the EVF value of the blood (in parts per 1000). The solid line is a fitted Krieger-Dougherty equation with c = 0.6 and k = 2.5.
Figure 2. Ratio of blood viscosity to plasma viscosity vs volume fraction of erythrocytes (EVF). The solid line is a fitted Krieger-Dougherty equation with c= 0.6 and k = 2.5. Figure 3 shows whole blood viscosity plotted against hemoglobine for the 122 patients.
There is a potential for large scale clinical use of blood viscosity if a correlation with the erythrocyte sedimentation rate (ESR) could be established, Bohlin (6). We show in Figure 4 how the ESR values can be succesfully predicted with over 95% explained variance for a subset of all males with ESR>10 of the patient study.
Saliva is a complex fluid of rather low viscosity but containing macromolecules responsible for the active role of saliva in lubrication and film formation. The ReoCue is well suited for saliva since it can work at the combination of low viscosity and small sample volumes. Another feature that appear interesting is that the ReoCue actually only probes the sample near the wall of the cell. This makes it ideal for an empirical study of how macromolucles in the saliva moves toward the wall of the cell after recently having been introduced with the bulk fluid in the cell. The kinetics of a 1 ml saliva sample is shown in Figure 5 below.A doubling of the 'viscosity' is seen during the first 10 minutes (7).
Figure 5. Human saliva kinetics during the first 10 minutes after freshly being inserted into the rheometer 1 ml cell. Conclusion We have described a new rheometer for measuring rheological properties of fluids of low dynamic viscosity where also a small volume of sample is required. Application of the instrument on body fluids such as blood, plasma and saliva have been examplified. References
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