Solid dynamic viscosity

Other parameters that may be defined in dynamic shear rheology are the viscous dynamic viscosity, rj = G"/o, and the solid dynamic viscosity, tj" = G Ico. 

The relationship of isoviscosity calculated by Eq (5) and a distance apart from the solid surface is shown in Fig. 7. For different kinds of solid materials with different surface energy, the isoviscosity becomes very large as the film thickness becomes thinner. It increases about several to more than ten times that of bulk fluid when it is close to the solid surface. In the thick film region, the isoviscosity remains a constant, which is approximately equal to the dynamic viscosity of bulk liquid. Therefore, the isoviscosity of lubricant smoothly... 

Dynamic techniques are used to determine storage and loss moduli, G and G respectively, and the loss tangent, tan 6. Some instruments are sensitive enough for the study of liquids and can be used to measure the dynamic viscosity rj. Measurements are made as a function of temperature, time, or frequency, and results can be used to determine transitions and chemical reactions as well as the properties noted above. Dynamic mechanical techniques for solids can be grouped into three main areas free vibration, resonance-forced vibrations, and nonresonance-forced vibrations. Dynamic techniques have been described in detail (242,251,255,266,269—279). A number of instruments are listed in Table 8. Related ASTM standards are listed in Table 9. 

Rheometric Scientific markets several devices designed for characterizing viscoelastic fluids. These instruments measure the response of a liquid to sinusoidal oscillatory motion to determine dynamic viscosity as well as storage and loss moduli. The Rheometric Scientific line includes a fluids spectrometer (RFS-II), a dynamic spectrometer (RDS-7700 series II), and a mechanical spectrometer (RMS-800). The fluids spectrometer is designed for fairly low viscosity materials. The dynamic spectrometer can be used to test solids, melts, and liquids at frequencies from 10-3 to 500 rad/s and as a function of strain amplitude and temperature. It is a stripped down version of the extremely versatile mechanical spectrometer, which is both a dynamic viscometer and a dynamic mechanical testing device. The RMS-800 can carry out measurements under rotational shear, oscillatory shear, torsional motion, and tension compression, as well as normal stress measurements. Step strain, creep, and creep recovery modes are also available. It is used on a wide range of materials, including adhesives, pastes, mbber, and plastics. 

Equation (2) may be used for the rate constant k of a chemical reaction or applied to the diffusion coefficient in liquid or solid phases or to the fluidity of liquids (reciprocal of dynamic viscosity) or to the specific electrical conductivity of semiconductors. 

Gallium(III) bromide is a hygroscopic, white solid which sublimes readily and melts at 122.5° to a covalent, dimeric liquid. The solid is ionic and its electrical conductivity at the melting point is twenty-three times that of the liquid.5 The vapor pressure of the liquid at T°K is given by the equation log p(mm.) = 8.554 — 3129/T and the heat of dissociation of the dimer in the gas phase is 18.5 kcal./mol.3 At 125° the liquid has the following properties 5,6 density, 3.1076 dynamic viscosity, 2.780 c.p. surface tension, 34.8 dynes/cm. and specific conductivity, 7.2 X 10-7 ohm-1 cm.-1 Gallium(III) bromide readily hydrolyzes in water and forms addition compounds with ligands such as ammonia, pyridine, and phosphorus oxychloride. 

This section draws heavily from two good books Colloidal Dispersions by Russel, Seville, and Schowalter [31] and Colloidal Hydrodynamics by Van de Ven [32] and a review paper by Jeffiey and Acrivos [33]. Concentrated suspensions exhibit rheological behavior which are time dependent. Time dependent rheological behavior is called thixotropy. This is because a particular shear rate creates a dynamic structure that is different than the structure of a suspension at rest. If a particular shear rate is imposed for a long period of time, a steady state stress can be measured, as shown in Figure 12.10 [34]. The time constant for structure reorganization is several times the shear rate, y, in flow reversal experiments [34] and depends on the volume fraction of solids. The viscosities discussed in Sections 12.42.2 to 12.42.9 are always the steady shear viscosity and not the transient ones. 

For viscoelastic fluids, the formalism of a viscous fluid and an elastic solid are mixed [31]. The equations for the effective viscosity, dynamic viscosity, and the creep compliance are given in Table 12.4 for a viscous fluid, an elastic solid, and a visco-elastic solid and fluid. For the viscoelastic fluid model the dynamic viscosity, >j (tu), and the elastic contribution, G (ti)), are plotted as a function of (w) in Figure 12.31. With one relaxation time, X, the breaks in the two curves occur at co. 

FIGURE 12.32 Shear moduli and dynamic viscosities measured for silica spheres at = 0.46, a = 28 2nm, O + a = 76 2nm(Mellemaetal. [68]). The broken lines correspond to the infinite shear viscosities (de Kruif et al. [43]) and the solid curves to the frequency dependence predicted by the visco-elastic fluid model of Table 12.4 with the measured values of 170,171 , and Gi. Redrawn from Russel et al. [31]. Reprinted with the permission of Cambridge University Press. 

Experience shows that convection heal transfer strongly depends on the fluid properties dynamic viscosity p., thermal conductivity k, density p, and specific heat c, as well as the fluid velocity V. It also depends on the geometry and the roughness of the solid surface, in addition to the type of fluid flow (such as being streamlined or turbulent). Thus, we expect the convection heat transfer relations to be rather complex because of the dependence of convection on so many variables. This is not surprising, since conveclion is die most complex mechanism of heat transfer. 

Here, k, Cp, p, and p are, respectively, the thermal conductivity, specific heat at constant pressure, density, and dynamic viscosity of the convective fluid V is the relative velocity between fluid and solid and L is a geometry dependent, characteristic length dimension for the system. Note that the Pr is composed exclusively of fluid properties and that the Re will increase in direct proportion to the relative velocity between fluid and solid surface. Example applications are shown in Fig. 2. 

Three forces act on a gaseous bubble in free liquid (without a solid phase) gravitational force (G = mg = Vpog) Archimedes force (F = Vpg) and the resistant force of the medium defined by Stake s law (R = bTiqroVo), where, g = acceleration due to gravity, ro = radius of bubble, V = volume of bubble, po = density of gases in bubble, p = density of liquid, q = dynamic viscosity of liquid, Vq = speed of bubble at equilibrium of the three forces. 

An aerodynamic interaction between the gas and the solids, mainly controlled by the dynamic viscosity of the gas and the elasticity of the packed solids. 

Let us consider a solid spherical particle of radius o in a translational Stokes flow with velocity U and dynamic viscosity /i (Figure 2.1). We assume that the fluid has a dynamic viscosity /z. We use the spherical coordinate system. R, 9, ip with origin at the center of the particle and with angle 0 measured from the direction of the incoming flow (that is, from the rear stagnation point on the particle surface). In view of the axial symmetry, only two components of the fluid velocity, namely, Vr and Vg, are nonzero, and all the unknowns are independent of the third coordinate [Pg.58]

Drops and bubbles. Axisymmetric shear flow past a drop was studied in [474,475], We denote the dynamic viscosities of the fluid outside and inside the drop by p and p.2- Far from the drop, the stream function satisfies (2.5.3) just as in the case of a solid particle. Therefore, we must retain only the terms with n = 3 in the general solution (2.1.5). We find the unknown constants from the boundary conditions (2.2.6)-(2.2.10) and obtain... 

In clinical studies, Tamaoki and colleagues [35] examined the effect of clarithromycin on sputum production and its rheological properties in patients with chronic lower respiratory tract infections. Clarithromycin was given at 100 mg twice daily for 8 weeks and compared with placebo. They showed that clarithromycin almost halved sputum volume, and that the percent solids of the sputum increased, with no effect of placebo. Elastic modulus (O ) significantly increased (at 10 Hz), whereas dynamic viscosity (h ) remained unchanged (Fig. 9). The reduction of sputum production and the corresponding increase in... 

The relative permeability k of water is assumed to be a function of the degree of water saturation and porosity, the relative permeability of air kra being a function of the degree of saturation only. K is the intrinsic permeability and p" the dynamic viscosity of the fluid in question, v is the (Lagrangian) velocity of the solid skeleton, p denotes the matrix suction (p =p -p ). The non-linear capillary pressure - saturation relation after Seker (1983) is used... 

FIGURE 6.19 (Upper panel) Steady-state shear viscosity versus shear rate (soUd symbols), dynamic viscosity versus frequency (open symbols), and transient viscosity calculated from Eq. (6.65) versus the inverse of the time of shearing (solid line). (Lower panel) Dynamic storage and loss modulus master curve for the same entangled polybutadiene solution (Roland and Robertson, 2006). 

FIGURE 6.30 Dynamic viscosity (squares), steady-state shear viscosity (circles), and the transient viscosity calculated using Eq. (6.65) (solid lines) for a linear (Mw = 389 kg/mol) and a highly branched (Mq/ = 1080 kg/mol) with 21 branches per chain and a branch Mq = 52.7 kg polyisobutylene (Robertson et al., 2002). 

---