Viscosity
المؤلف:
Peter Atkins، Julio de Paula
المصدر:
ATKINS PHYSICAL CHEMISTRY
الجزء والصفحة:
ص665-667
2025-12-17
53
Viscosity
The formal definition of viscosity is given in Section 21.4; for now, we need to know that highly viscous liquids flow slowly and retard the motion of objects through them. The presence of a macromolecular solute increases the viscosity of a solution. The effect is large even at low concentration, because big molecules affect the fluid flow over an extensive region surrounding them. At low concentrations the viscosity, η, of the solution is related to the viscosity of the pure solvent, η0, by , η=η0(1+[η]c+· · · )
The intrinsic viscosity, [η], is the analogue of a virial coefficient (and has dimensions of 1/concentration). It follows from eqn 19.22 that
Viscosities are measured in several ways. In the Ostwald viscometer shown in Fig. 19.10, the time taken for a solution to flow through the capillary is noted, and compared with a standard sample. The method is well suited to the determination of [η] because the ratio of the viscosities of the solution and the pure solvent is propor - tional to the drainage time t and t0 after correcting for different densities ρ and ρ0:
(In practice, the two densities are only rarely significantly different.) This ratio can be used directly in eqn 19.23. Viscometers in the form of rotating concentric cylinders are also used (Fig. 19.11), and the torque on the inner cylinder is monitored while the outer one is rotated. Such rotating rheometers (some instruments for the measure ment of viscosity are also called rheometers) have the advantage over the Ostwald viscometer that the shear gradient between the cylinders is simpler than in the capillary and effects of the kind discussed shortly can be studied more easily. There are many complications in the interpretation of viscosity measurements. Much of the work is based on empirical observations, and the determination of molar mass is usually based on comparisons with standard, nearly monodisperse sample. Some regularities are observed that help in the determination. For example, it is found that θ solutions of macromolecules often fit the Mark–Kuhn–Houwink–Sakurada equation:
[η] =KMva
In some cases, the flow is non-Newtonian in the sense that the viscosity of the solution changes as the rate of flow increases. A decrease in viscosity with increasing rate of flow indicates the presence of long rod-like molecules that are orientated by the f low and hence slide past each other more freely. In some somewhat rare cases the stresses set up by the flow are so great that long molecules are broken up, with further consequences for the viscosity.
Fig. 19.10 An Ostwald viscometer. The viscosity is measured by noting the time required for the liquid to drain between the two marks.
Fig. 19.11 A rotating rheometer. The torque on the inner drum is observed when the outer container is rotated.
Fig. 19.12 The plot used for the determination of intrinsic viscosity, which is taken from the intercept at c = 0; see Example 19.5.
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