Viscosity of liquids and glasses

The shear stress applied to the top plate via the tangential force is r = Ft/A. For Newtonian fluids, it is found that the velocity gradient dv/dx is proportional to the shear stress1, the constant of proportionality being the viscosity of the fluid. Viscosity is thus defined  

A highly viscous fluid is thus one that does not shear rapidly under a large shear stress. Using MKS units, viscosity has units of [kg/(m s)] or Pascal-seconds2. Viscosity, in older literature, was expressed using the CGS unit poise = [g/(cm-s)] 1 Pa-s = 10 Poise. 

The viscosity of a gas increases with temperature due to increased kinetic interaction between molecules, which in turn causes increased viscous drag . The viscosity of a liquid decreases with temperature due to increased thermal energy, decreasing the activated barrier for one atom to slip around its neighbors, or perhaps equivalently, the increased thermal en- 

1 Note that for solids behaving elastically, the shear strain is proportional to the shear stress. For Newtonian fluids, the shear strain rate (velocity gradient) is proportional to the shear stress. 

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Most previous work has been reviewed by Grace (G13) and Schiigerlet al. (in D5). Botterill (B12) and Hetzler and Williams (H8) correlated the apparent viscosity of liquid- and gas-fluidized systems, applying a free-volume theory which may be used successfully for glass-forming (polymeric) liquids. Saxton et al. (S3) proposed another approach to a free-volume theory. They compared theoretical expectations with the experimental data obtained in liquid-fluidized systems. Their extension to gas-fluidized systems (in cgs units) became, for sand. 

The viscosity of liquid silicates such as drose containing barium oxide and silica show a rapid fall between pure silica and 20 mole per cent of metal oxide of nearly an order of magnitude at 2000 K, followed by a slower decrease as more metal oxide is added. The viscosity then decreases by a factor of two between 20 and 40 mole per cent. The activation energy for viscous flow decreases from 560 kJ in pure silica to 160-180kJmol as the network is broken up by metal oxide addition. The introduction of CaFa into a silicate melt reduces the viscosity markedly, typically by about a factor of drree. There is a rapid increase in the thermal expansivity coefficient as the network is dispersed, from practically zero in solid silica to around 40 cm moP in a typical soda-lime glass. 

The differences between the values of viscosity, rj, and liquid surface energy, ctlv, of metals and glasses are of importance because the ratio orv/ 1 is of major significance in determining spreading rates (see equation (2.4)) and flow rates in capillaries (see equation (10.1)). For glassy materials, the ratio is less, and... 

For measurements of viscosity of molten salts and glasses at high-temperatures, several methods were proposed. The selection of a particular method depends in general on the viscosity of the liquids to be measured. A broad dispersion of experimental results reflects substantial experimental difficulties connected with viscosity measurement. In general, in the measurement of viscosity of molten salts the method of torsional pendulum is most frequently used, while in the measurement of viscosity of liquids, such as molten glasses, the falling body and the rotational methods are most suitable. Methods for viscosity measurement of liquids with a very high viscosity (above 10 Pa s) will not be described here. 

The most common viscosity test is the kinematic viscosity method (ASTM D445, IP-71, DIN 51566 and ISO 3104). Note that lubricant viscosity is discussed in detail in the next chapter. The kinematic viscosity is the product of the time of flow and the calibration factor of the instrument. The test determines the kinematic viscosity of liquid lubricants by measuring the time taken for a specific volume of the liquid to flow through a calibrated glass capillary viscometer under specified driving head (gravity) and temperature conditions. The test is usually performed at a lubricant temperature of 40°C and/or 100°C to standardize the results obtained and allow comparison among different users. 

The chemically inert character of sulfur hexafluoride is responsible for the almost complete lack of exchange of fluorine atoms between SFe and HF (249). It does react with hot alkali metals, however, and a study has been made of the rate of reaction of Na atoms with SF6 gas using the sodium diffusion flame technique. The rate constant at 247° is 2.23 X 10-1 cm mole-1 sec-1 and the energy of activation for the reaction SF6 + Na — SF6 + NaF, is about 37 keal. A film of sodium on a glass wall does not react with SF at room temperature. The reaction sets in at about 200° (57). The fluorides, SF , SF4, and S2F2, have no effect upon the viscosity of liquid sulfur in the range 180-195° (93). Sulfur hexafluoride forms a solid hydrate which has a crystal constant of 17.21 A. It decomposes just above 0° (285). 

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