Solids bulk viscosity

Several different expressions have been derived for solids pressure, solids shear viscosity and solids bulk viscosity, employing different approximations and assumptions while applying the kinetic theory of granular flows. Some of the commonly used equations are described below (see Gidaspow, 1994 and a review given by Peirano, 1998) Solids pressure ... 

While bulk viscosity is a relatively obscure property of a liquid or a solid... 

The physical properties of spray-dried materials are subject to considerable variation, depending on the direction of flow of the inlet gas and its temperature, the degree and uniformity of atomization, the solids content of the feed, the temperature of the feed, and the degree of aeration of the feed. The properties of the product usually of greatest interest are (1) particle size, (2) bulk density, and (3) dustiness. The particle size is a function of atomizer-operating conditions and also of the solids content, liquid viscosity, liquid density, and feed rate. In general, particle size increases with solids content, viscosity, density, and feed rate. 

The relationship between the isoviscosity rj and the him thickness is shown in Fig. 28 in which is calculated according to Eq (5) from the experimental data as shown in Fig. 25. When the him is thicker than 25 nm, the isoviscosities of hexadecane with or without LC remain a constant that is approximately equal to the bulk viscosity. As the him becomes thinner, their isoviscosities increase at different extents for different additives. When the him thickness is about 7 nm, the isoviscosity of pure hexadecane is about two times its bulk viscosity, about three times for CP, four times for CA, six times for CAL, and more than ten times for CB. Thus, it can be concluded that the addition of a polar compound into base oil is a beneht to the formation of thicker solid-like layer. 

Bulk solids, dispersion in a liquid, 24 157 Bulk superconducting joints, 23 844 Bulk superconductors, 23 870 Bulk viscosity, 22 717-718 Bulk weigher, 26 247 Bulky rayon, 22 261-262 Bullion, silver, 22 643, 644-645, 647, 649-650... 

Fig. 2.17 Frequency dependence of dynamic shear moduli computed using a model for the linear viscoelasticity of a cubic phase based on slip planes, introduced by Jones and McLeish (1995). Dashed line G, solid line G".The bulk modulus is chosen to be G — 105 (arb. units). The calculation is for a slip plane density AT1 - 10 5 and a viscosity ratio rh = = 1, where rjs is the slip plane viscosity and t] is the bulk viscosity. The strain...

The gas phase viscosity is defined by the temperature and the gas composition through a semi-empirical function. For the solid phase shear viscosity, we (cf., 14) use semi-empirical relations based upon the viscometric measurements of Schugerl (21). The solid phase bulk viscosity is, at present, inaccessible to measurement consequently, we define it to be a multiple of the shear viscosity. 

At even lower temperatures, some unusual properties of matter are displayed. Consequently, new experimental and theoretical methods are being created to explore and describe chemistry in these regimes. In order to account for zero-point energy effects and tunneling in simulations, Voth and coworkers developed a quantum molecular dynamics method that they applied to dynamics in solid hydrogen. In liquid helium, superfluidity is displayed in He below its lambda point phase transition at 2.17 K. In the superfluid state, helium s thermal conductivity dramatically increases to 1000 times that of copper, and its bulk viscosity drops effectively to zero. Apkarian and coworkers have recently demonstrated the disappearance of viscosity in superfluid helium on a molecular scale by monitoring the damped oscillations of a 10 A bubble as a function of temperature. These unique properties make superfluid helium an interesting host for chemical dynamics. 

The bulk viscosity of polymer solution is an important parameter also when polymers are being used as suspending agents to maintain solid particles in suspension by prevention of settling (see Chapter 7) and when they are used to modify the properties of liquid medicines for oral and topical use. 

Bulk viscosity accounts for resistance of solid body to dilation and can be given as... 

We could use a simplified form of rj z) = ri f z). Here is the bulk viscosity, and /(z) can be experimentally determined. Here, z is the distance normal to the solid surface. A partial justification for the above functional form can be drawn from the temperature dependence of the surface diffusion coefficient and the bulk viscosity,or the fly stiction correlation with the bulk viscosity. To develop a rigorous hydro-dynamic model, we need better rheological data and more details are given in the following section on Rheology Measurement. 

The solid phase bulk viscosity is calculated from (4.92) ... 

Effect of Solids. The presence of dispersed particles can increase or decrease aqueous foam stability. One mechanism for the stability enhancement is the bulk viscosity enhancement that results from having a stable dispersion of particles present in the solution. A second stabilizing mechanism is operative if the particles are not completely water-wetted. In this case, particles would tend to collect at the interfaces in the foam where they may add to the mechanical stability of the lamellae. 

In the coke drum, foaming occurs. As the bulk viscosity of the resid increases and solids form, a stable foam front forms, and it rises higher in the drum as the coke level rises. If left unchecked, the foam will reach near the top of the coke drum and potentially go overhead, or foam-over . The consequences of a foam-over are immediate and disastrous. The transfer line from the coke drum to the fractionator becomes fouled with coke particles. As the solids reach the fractionation tower, the suction screens in the bottom of the tower become plugged. Finally, the finer particles of coke that pass through the suction screens will... 

The two second-order equations (58) and (59) yield four solutions for to. The first solution is a seismic wave in which the fluid and solid compress almost in phase. However, since the fluid is normally an order of magnitude more compressible than the solid, fluid flow is induced and the shear and bulk viscosities give rise to attenuation. This attenuation is minor for low frequency waves and much greater for high frequency waves. 

Let us first recall the general fact that whenever a second phase is dispersed in a solvent this should lead to an increase in the bulk viscosity. A solid theoretical description of this effect was first given by Einstein, who derived a formula that describes the increase in viscosity as a function of the volume fraction O of dispersed material for the case of compact spherical particles that have a sticlQ surface (no-slip condition) [23,24] ... 

It has been established that the viscosity of the boundary film (i bf) is considerably greater than the bulk viscosity (r bik)> by a factor of more than 5. According to Eqs. (VI.1)-(VI.3), an increase in viscosity will lead to an increase in the time for approach of two solid bodies and hence will affect the kinetic adhesion." ... 

The bulk viscosity accounts for the resistance of the solid phase against compression. There exists a commonly accepted formula derived from kinetic theory, see e. g. Gidaspow (1994). 

The fact that the effective viscosity is intermediate between that of solvent and polymer solution can be rationalized as follows. Within the depletion layer, the viscosity is expected to follow the polymer density distribution [289] and it gradually increases from the solvent viscosity at the solid surface to the bulk viscosity far from the particle. Therefore, as a particle difliises, the hydrodynamic resistance force is also in between the two limits. Fan et al. [294, 295] derived analytical expressions for the friction felt by a sphere when it moves through a macromolecular medium, and showed that the friction is strongly reduced compared to Stokes law. This means that depletion-induced slip effects facilitate protein transport through crowded media. 

Ceramic Dispersions. Ceramic is a nonmetallic inorganic material. Ceramic dispersions are the starting material for many applications. The use of detergents or surfactants enhances the wetting ability of the binder onto the ceramic particles and aids in the dispersion of ceramic powders in liquids. As dispersants, they reduce bulk viscosity of high-solid slurries and maintain stabUity in finely divided particle dispersions. Bi-block surfactants help agglomeration of the ceramic particles. In wastewater treatment, detergents are used in ceramic dispersions to reduce the amount of flocculents. 

Figure 11.25 Shear viscosity of the composite, G, normalized by the bulk viscosity of the matrix, K, as a function of the volume fraction of inclusions (0.6 times the number fraction). Calculations by finite element method (A), self-consistent model (solid line), and Hashin-Shtrikman lower bound (dashed line) are shown. (From Ref. 39.)...

Not only surfactant molecules may diffuse in advance of the wetting front. Spreading of pure liquids by surfaee diffusion of molecules from a micro-doplet over a solid surface was comprehensively studied using microellipso-metric measurements [29-34]. It has been observed that on the top of the first monolayer, a second and subsequent layers form, and the corresponding coefficients of surface diffusion were calculated. For liquid polydimethylsi-loxan (PDMS) on a hydrophobed silicone wafer, coefficients of surface diffusion in the first monolayer grow with decreasing molecular mass M of the PDMS from = A x 10 cm /s for M = 28,400 to 7 x 10 cm /s for M = 6700. Correlation between the values and bulk viscosity of the liquid PDMS have been established. 

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