Viscosity coefficients measurement

Viscosity coefficients measured in these geometries when n is immobilised by boMiesowicz viscosities. (Note, that in the literature a variety of alternative notations are common in particular the definitions of r i and r 2 are frequently interchanged.) If the orientation of n is fixed in an arbitrary direction with respect to v and Vv, then the effective viscosity coefficient is given by a linear combination of the Miesowicz viscosities, and another viscosity constant Tju, which cannot be visualised in a pure shear-flow ... 

For n perpendicular to the interface, the effective viscosity coefficient measured is some combination of Tip, Tip and tij3. 

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... 

Brillouin scattering of laser light in liquids has been studied by several authors. Shapiro etal. 233) measured hypersonic velocities in various liquids and obtained a Brillouin linewidth of 0.011 cm" in methylene chloride but of less than 0.002 cm in benzene, carbon disulfide and chloroform. The broadening of the Brillouin components arises from damping of thermal phonons and is closely connected with the viscosity coefficient of the medium. From the measured linewidths, the lifetimes of the phonons responsible for Brillouin scattering at 89 45 were calculated to be 4.8 x 10 sec for methylene chloride and 7.6 x 10 sec for toluene. 

When water passes through a polymer network, a frictional resistance arises between water and the network. What happens to the transport phenomenon of water through the network if the polymer network approaches its critical temperature This is a naive but very important question. Tokita et al. carried out a friction coefficient measurement of NIPA gel as a function of temperature [87]. They found that the friction coefficient f normalized by the solvent viscosity rj, f/t, changed more than three orders of magnitude by approaching... 

Table 7. Measurements of the Fredericks transition in the magnetic field 71) (H = critical field, r = relaxation time, kn = splay elastic constant, yl = twist viscosity coefficient...

Viscosity A measure of the resistance of a liquid to flow. It is properly the coefficient of viscosity, and expresses the proportionality between shear stress and shear rate in Newton s law of viscosity. 

These data were obtained by estimating the chain expansion factor a from viscosity and osmotic second virial coefficient measurements, through the combined use of equations (10) and (11). These results tend to confirm the main predictions of the theory presented by the above mentioned authors both as regards the steep decrease in with... 

Supercritical Alkanes. Figure 5 compares diffusion coefficients for reverse micelles diffusion coefficients measured in liquids generally decrease by 10 to 15 percent as pressure is increased to 400 bar, and show the expected systematic increase as alkane length decreases (and viscosity increases). 

Note that the turbulent viscosity parameter has an empirical origin. In connection with a qualitative analysis of pressure drop measurements Boussinesq [19] introduced some apparent internal friction forces, which were assumed to be proportional to the strain rate ([20], p 8), to fit the data. To explain these observations Boussinesq proceeded to derive the same basic equations of motion as had others before him, but he specifically considered the molecular viscosity coefficient to be a function of the state of flow and not only on the system properties [135]. It follows that the turbulent viscosity concept (frequently referred to as the Boussinesq hypothesis in the CFD literature) represents an empirical first attempt to account for turbulence effects by increasing the viscosity coefficient in an empirical manner fitting experimental data. Moreover, at the time Boussinesq [19] [20] was apparently not aware of the Reynolds averaging procedure that was published 18 years after the first report by Boussinesq [19] on the apparent viscosity parameter. 

Unfortunately, there are relatively few data for transport coefficients measured under high pressure from which the coefficient (3 In rijdT)v can be calculated. Table I compares the isobaric and isochoric temperature coefficients of viscosity and binary diffusion for a number of liquids. It will be seen that the isochoric temperature coefficients are considerably smaller than those observed at constant pressure. The data of Jobling and Lawrence28 indicate that (d In rj/dT)v is more nearly proportional to (1/T2) than is (d In t]jdT)P. This observation is confirmed in an analysis of viscosity data for a number of hydrocarbons made by Simha, Eirich, and UUmann.31 The small number of substances studied and the shortness of the temperature range covered, however, do not enable us to assume a logarithmic dependence of the isochoric viscosity as a generally valid relationship. 

Lubricants have a nonlinear viscosity coefficient against temperature. At very low or very high temperature this nonlinearity can create significant measurement failures. A careful analysis will show this effect within the transmission chain. Sticking is the worst case. It can happen that frozen water makes a short cut in torque sensors. In most cases damping factors are based on the electrical filter circuits (Fig. 7.12.13). 

The order parameter S is a very important quantity in a partially ordered system. It is the measure of the extent of the anisotropy of the liquid crystal physical properties, e.g., elastic constants, viscosity coefficients, dielectric anisotropy, birefringence, and so on. S is temperature dependent and decreases as the temperature increases. The typical temperature dependence of S is shown in Figure 1.16. 

Sometimes when dealing with a fluid that contains a dispersed particle phase that cannot be considered a component, we treat the suspension fluid as a continuum with a constitutive relation that is modified because of the presence of the particles. An example to be discussed in Chapter 5 is Einstein s modification of the Newtonian viscosity coefficient in dilute colloidal suspensions due to hydrodynamic interactions from the suspended particles. As with molecular motions, the modified coefficient may be determined from measurements of the phenomenon itself by using results from analyses of the particle behavior in the fluid as a guide. These ideas are further expanded upon in Chapter 9 where the behaviors of concentrated suspensions of colloidal and non-colloidal particles are examined. 

Q The diffusion coefficient measured in water at 20 ° C for the protein lysozyme is about 10.4x I0 " m s . What is / s for this molecule, given that the viscosity of water at 20 Cis 1.002X 10 Nsm A Rearranging the above equation ... 

Viscosity is a property of liquids which describes their resistance to flow. Glycerol is a more viscous fluid than water, which is more viscous than acetone (nail polish remover). Viscosity is quantified by a viscosity coefficient, rj. Table 5-3 lists some representative values measured at 20 °C. Glycerol, whose viscosity is about the same as maple syrup, is over 1000 times more viscous than... 

The viscosity coefficient of gases may be determined from measurements of the rate of fiow through a capillary tube of known radius under a given pressure difference, and from the result the mean free path, I, may be calculated. For simple gases at atmospheric pressure it is of the order 10- cm. It varies inversely as the pressure, and long before the highest vacuum given by a modern pump is reached it exceeds the dimensions of ordinary small-scale laboratory apparatus. 

We shall now discuss the application of the Ericksen-Leslie theory to some practical problems in viscometry. Probably the first precise determination of the anisotropic viscosity of a nematic liquid crystal was by Miesowicz. He oriented the sample by applying a strong magnetic field and measured the viscosity coefficients in the following three geometries using an oscillating plate viscometer ... 

The viscosity coefficients may also be determined by studying the reflexion of ultrasonic shear waves at a solid-nematic interface. The technique was developed by Martinoty and Candau. A thin film of a nematic liquid crystal is taken on the surface of a fused quartz rod with obliquely cut ends (fig. 3.7.1). A quartz crystal bonded to one of the ends generates a transverse wave. At the solid-nematic interface there is a transmitted wave, which is rapidly attenuated, and a reflected wave which is received at the other end by a second quartz crystal. The reflexion coefficient, obtained by measuring the amplitudes of reflexion with and without the nematic sample, directly yields the effective coefficient of viscosity. 

The integrated intensity gives the elastic constants while the half width yields It is therefore possible to measure the viscosity coefficients from an analysis of the scattered light using appropriate geometries. 

The hydrodynamic equations of the classical nematic ( 3.1) are applicable to the N, phase as well. There are six viscosity coefficients (or Leslie coefficients) which reduce to five if one assumes Onsager s reciprocal relations. A direct estimate of an effective value of the viscosity of from a director relaxation measurement indicates that its magnitude is much higher than the corresponding value for the usual nematic. 

However, the measurable strain shear correlates with the well-known external gradient g that gives another effective viscosity coefficient ... 

Vosburgh and co-workers have reported for LiCl in some aliphatic alcohols up to butanol and Sobkowski and Mine have reported the same quantity for HCl in alcohols up to w-propanol. For both electrolytes increases as the number of carbons increase in the alcohol. Venkatasetty and Brown have measured the viscosities of Lil, NH4I and BU4NI in butanol at 0, 25 and 50°C and attempted to fit the data to the Jones-Dole equation. " Although measurements were made in relatively dilute solutions, deviations from linearity were observed over the concentration range studied and viscosity coefficients were not evaluated. 

---