The Viscosity of Liquids

Viscosity is the property of a fluid which characterizes its resistance to flow. It is often measured by timing the flow of a liquid through a cylindrical tube under the influence of gravity. In order to understand the definition of the viscosity, consider a fluid flowing between two large plane parallel plates (fig. 6.1). The velocity of the fluid in the direction of the flow, varies with position. It is at its maximum midway between the plates and decreases to zero between each plate on the basis of experimental observation. Now imagine that the fluid is made up of horizontal layers which are parallel to the plates. The movement of one layer with respect to another is retarded by a frictional force which is related to the fluid s viscosity. The origin of this friction is clearly intermolecular forces. 

In order to define the viscosity, one imagines a cylinder of thickness dx and radius r located on the central axis of the tube. The retarding force is proportional to the surface area of the cylinder involved in the flow and to the gradient of the 

If the radius of the tube is tq, integration of equation (6.3.3) gives the result that 

This shows that the forward velocity is a parabolic function of position in the tube varying from zero at the wall where r is equal to Tq, to the maximum value at the center of the cylindrical tube, where is equal to —ro(dP/dx)/(4r ). It is emphasized that equation (6.3.4) is only applicable to laminar or non-turbulent flow in a cylindrical tube. When a liquid flows under different geometrical boundary conditions, the relationship between the flux and the force is not the same. 

From equation (6.3.1), the SI units of viscosity are N s m or Pa s. In the older literature, the viscosity is cited in cgs units, that is, in dyn s cm. 1 dyn s cm is called a poise. Since one Newton is equal to 10 dynes, it follows that one poise is equal to 0.1 Pa s. At room temperature, liquids typically have viscosities of 1 cP, which corresponds to 1 mPa s. 

The mobile phase viscosity is an important characteristic of the mobile phase. It relates the mobile phase velocity and the inlet pressure required to achieve this velocity. After Darcy law [127], the mobile phase velocity, u, is proportional to the local pressure gradient  

Since vmder steady-state conditions B and Tj are constant, integration of Eq. 5.86 shows that u is proportional to the column pressure drop, AP 

As an example of calculation, assrnne the following values Unear velocity 0.10 cm/s, viscosity, 1.0 cP, coliunn length, 15 cm, particle size 10 im, and permeability constant, 1 x 10 . The pressure drop is 

It has also been shovm that the diffusion coefficients in a solvent are inversely proportional to its viscosity. The viscosity changes with temperature, composition, and the concentration of the feed. When the column is operated at a constant reduced velocity, v = udp)/Dj, the efficiency constant. The effect of a change of viscosity due to an adjustment in any of the parameters just Hsted will have Ht-tle effect on the pressure required to keep the reduced velocity constant (since the product of the viscosity and the diffusion coefficient remains constant) but it will markedly affect the retention times (which will increase with increasing viscosity) and, in preparative applications, the production rate. Thus, conditions under which the viscosity is low should be preferred. 

We review here the viscosity of the most common mobile phases, the factors that influence this viscosity, the temperature, the pressure, and the mobile phase composition, and we discuss two phenomena of practical importance in the preparative applications of chromatography (i) the dependence of the mobile phase viscosity on the concentration in feed components and the pressure excursion generated by the elution of high concentration bands of viscous feed and (ii) the occurrence of flow instabilities and fingerings due to the rapidly varying viscosity of the eluent. 

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Viscosity (See Sec. 5 for further information.) In flowing liquids the existence of internal friction or the internal resistance to relative motion of the fluid particles must be considered. This resistance is caUed viscosity. The viscosity of liquids usuaUv decreases with rising temperature. Viscous liquids tend to increase tlie power required by a pump, to reduce pump efficiency, head, and capacity, and to increase Friction in pipe lines. 

The viscosities of liquid metals vaty by a factor of about 10 between the empty metals, and the full metals, and typical values are 0.54 x 10 poise for liquid potassium, and 4.1 x 10 poise for liquid copper, at dreir respective melting points. Empty metals are those in which the ionic radius is small compared to the metallic radius, and full metals are those in which the ionic radius is approximately the same as tire metallic radius. The process was described by Andrade as an activated process following an AiThenius expression... 

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. 

Ohm s law, V=J R (voltage equals current times resistance), electricity has the same form as equation 9.1-14 which may be written as equation 9.1-15, where AP is the pressure differential, Q is the flow rate and resistance is given by equation 9.1-16, where t] is the viscosity of the fluid. Table 9.1-2 shows that the viscosity of liquids is highly temperature-dependent. Gases are much less temperature dependent because of the greater separation between molecules. If there are multiple discharge paths the equivalent resistance is the same as electrical resistors in... 

Mobility of Ions in D20. The viscosity of liquid D20 at room temperature has a value 1,232 times the viscosity of H20. Since the D2O and HaO molecules are so similar in other respects, we should expect the mobility of ions dissolved in D20 to be smaller than in H20. The conductivity of potassium chloride and potassium acetate was measured in mixtures of D20 and H20 up to a composition containing 97 per cent of D20.1 The values for ions in D2O, given in Table 7, were obtained by extrapolation from values obtained in the mixed solvent containing a few per cent of H20. As was expected, the conductivity in D20 was found to be smaller than in H20. But the change was not quite so great as the change in the viscosity, as is shown by the ratios in the last column of Table 7. We must conclude that, for some or all of the ions, the... 

In 1906, Einstein worked out a theory of the viscosity of a liquid which contains, in suspension, spherical particles which are large compared with the size of molecules of the liquid. The predictions of the theory are found to be in good agreement with the measured values of the viscosity of liquids containing colloidal particles in suspension. The presence of these obstacles increases the apparent viscosity of the liquid, and Einstein found1 that the increment is proportional to the total volume v of the foreign particles in unit volume, that is to say, the sum of the volumes of the particles that are present in unit volume of the liquid thus,... 

A typical liquid-crystal molecule, such as p-azoxyanisole, is long and rodlike (14). Their rodlike shape enables the molecules to stack together like dry, uncooked spaghetti they lie parallel to one another but are free to slide past one another along their long axes. Liquid crystals are anisotropic because of this ordering. Anisotropic materials have properties that depend on the direction of measurement. The viscosity of liquid crystals is least in the direction parallel to the long... 

Ely, J.U. and Tiner, R.L. "Hydraulic Fracturing Method Using Benzoic Acid to Further Increase the Viscosity of Liquid Hydrocarbon," US Patent 3,799,267(1974). 

Doolittle AK (1952) Studies in Newtonian flow III. The dependence of the viscosity of liquids on molecule weight and free space (in homologous series). J Appl Phys 23(2) 236-239... 

The viscosity coefficients at dislocation cores can be measured either from direct observations of dislocation motion, or from ultrasonic measurements of internal friction. Some directly measured viscosities for pure metals are given in Table 4.1. Viscosities can also be measured indirectly from internal friction studies. There is consistency between the two types of measurement, and they are all quite small, being 1-10% of the viscosities of liquid metals at their melting points. It may be concluded that hardnesses (flow stresses) of pure... 

Intrinsic resistance to dislocation motion can be measured in either of two ways direct measurements of individual dislocation velocities (Vreeland and Jassby, 1973) or by measurements of internal friction (Granato, 1968). In both cases, for pure simple metals there is little or no static barrier to motion. As a result of viscosity there is dynamic resistance, but the viscous drag coefficient is very small (10" to 10" Poise). This is only 0.1 to 1 percent of the viscosity of water (at STP) and about 1 percent of the viscosity of liquid metals at their... 

It has been claimed that biodesulfurization via the 4S pathway can also reduce viscosity. An application introduced by Environmental Bioscience Corporation included a method for reducing the viscosity of liquid-containing sulfur heterocycles [406] using biodesulfurization. The original patent application (Ser. No. 631642) was filed in US... 

A further empirical expression, due to Andrade, for the viscosity of liquid metals at their melting points, which agrees well with experimental data is... 

As in the case of the diffusion properties, the viscous properties of the molten salts and slags, which play an important role in the movement of bulk phases, are also very structure-sensitive, and will be referred to in specific examples. For example, the viscosity of liquid silicates are in the range 1-100 poise. The viscosities of molten metals are very similar from one metal to another, but the numerical value is usually in the range 1-10 centipoise. This range should be compared with the familiar case of water at room temperature, which has a viscosity of one centipoise. An empirical relationship which has been proposed for the temperature dependence of the viscosity of liquids as an Arrhenius expression is... 

The liquid state is a condensed state, so each molecule is always interacting with a group of neighbours although diffusing quite rapidly. As a result, although momentum through a shear plane still occurs, it is a small contribution when compared to the frictional resistance of the molecules in adjacent layers. It is the nature of this frictional resistance that we must now address and it will become clear that it arises from the intermolecular forces. The theories of the viscosity of liquids are still in an unfinished state but the physical ideas have been laid down. The first... 

Thickening agent. A hydrophilic substance used to increase the viscosity of liquid mixtures and solutions and to aid in maintaining stability of their emulsifying properties. 

Estimate the viscosity of liquid chromium at its melting temperature of 2171 K. 

Estimate the viscosity of liquid iron at 1600°C. The density of liquid iron at... 

Pyrogenic or fumed silica is a finely divided filler which is used as a thixotrope to increase the viscosity of liquid resins. 

Apf = the difference in density between liquid-phase and gas bubbles, g/cm3 4l = the viscosity of liquid-phase, g/cm s... 

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