Viscosities worked examples

Problem 3.4(b) (Worked Example) Suppose you now mold a 1-cm-diameter spherical ball of 1,4-polyisoprene and place it on a flat surface at 25 °C and find that the time for it to sag to 90% of its original height is 10 minutes. Now you place the polyisoprene in a rheometer at 25°C to measure its viscosity, but the viscosity is too high to measure accurately, so you raise the temperature to lOO C and measure a zero-shear viscosity of 10 P. Use this information and that in Problem 3.4(a) to determine the viscosity of the gel in Problem 3.4(a), given that the gel density is = 3g/cm ... 

Problem 3.14 (Worked Example) Derive expressions for the shear viscosity and first and second normal stress coefficients in steady-state shearing of the Johnson-Segalman model, given by Eqs. (3-80) and (3-8 la). 

Problems and Worked Examples 6.1 through 6.5, at the end of this chapter, will sharpen your skills in obtaining simple, practical estimations of the viscosity, modulus, and relaxation time of hard-sphere suspensions. 

Problem 6.1 (Worked Example) Estimate the zero-shear viscosity of a suspension of hard spheres 100 nm in diameter at a volume fraction of [Pg.318]

Problem 6.7(a) (Worked Example) Estimate the first normal stress difference Ni for a suspension of long, thin particles (approximated as spheroids) with p = 100 and L = 0.1/ m, if the solvent viscosity is 1 P, the shear rate y is 100 sec, and the particle concentration is 0 = 0.001, which is in the dilute regime. 

Problem 6.8 (Worked Example) Estimate the steady-state uniaxial viscosity of a suspension of 0.1% by volume of rod-like particles L = 6 yum long and d = 10 nm in diameter in a Newtonian oil of viscosity 100 P at an extension rate of 1 sec . ... 

Problem 10.3(b) (Worked Example) Derive Eq. (10-31), the time- or strain-dependent shear viscosity in the absence of Frank elastic stresses. 

Worked Example the data shown in Figure 2.7 were obtained firom the constant pressure period of a pilot scale plate and fiiame filter press. Calculate the cake resistance given filter area 2.72 m, viscosity 10 Pa s, mass of dry cake per unit volume filtrate 125 kg m and filtrate pressure 3 bar. The ecific resistance by Equation (2.24) is 5.4x10 mkg The apparent medium resistance is 2.9xl0 m" by Equation (2.25). However, in this instance the medium resistance is a composite term including the resistance to filtrate flow due to the cake formed dtiring the... 

Worked Example the data diown in Figures 2.8 and 2,9 were obtained on a pilot scale plate and frame filter press, calculate the specific and medium resistances given filter area 2.72 m, viscosity 10" Pa s, mass of dry cake per unit volume filtrate 125... 

Worked example [using the data fi om Hermia 1993], reproduced below, calculate the pressure as a function of time needed to maintain a constant flow rate of 1 m mT h on candle fibers of radii 15 and 10 mm, and for a filter of planar geometry. Data pressure at end of precoating 0.1 bar, beer viscosity 0.003 Pa s, body feed dosage 1 kg mT precoat dosage 1.5 kg specific resistance lxlo m kg and filter aid bulk density 350 kg m.-. The maximum pressure available fi om the pmq> is 3.5 bar. Applying Equation (6.9) at various times provides the results tabulated in Table 6.4. 

It is also possible to simulate nonequilibrium systems. For example, a bulk liquid can be simulated with periodic boundary conditions that have shifting boundaries. This results in simulating a flowing liquid with laminar flow. This makes it possible to compute properties not measurable in a static fluid, such as the viscosity. Nonequilibrium simulations give rise to additional technical difficulties. Readers of this book are advised to leave nonequilibrium simulations to researchers specializing in this type of work. 

Metal- Working and Hydraulic Fluids. In the preparation of fluids for metal-working and hydrauflcs, the trend has been to replace organic-based materials with aqueous-based materials. Neodecanoic acid has found apphcation in these newer fluids as a corrosion inhibitor and a viscosity improver. For example, neodecanoic acid is used in an aqueous hydrauflc fluid concentrate for corrosion inhibition and improved antiwear properties (101), in the preparation of a thickened aqueous hydrauflc fluid to reduce viscosity loss (102), and in a water-soluble metal working oil to reduce corrosion (103). In a similar vein, neodecanoic acid has been used in antifreeze concentrates for corrosion inhibition (104). 

Few mechanisms of liquid/liquid reactions have been established, although some related work such as on droplet sizes and power input has been done. Small contents of surface-ac tive and other impurities in reactants of commercial quality can distort a reac tor s predicted performance. Diffusivities in liquids are comparatively low, a factor of 10 less than in gases, so it is probable in most industrial examples that they are diffusion controllech One consequence is that L/L reactions may not be as temperature sensitive as ordinary chemical reactions, although the effec t of temperature rise on viscosity and droplet size can result in substantial rate increases. L/L reac tions will exhibit behavior of homogeneous reactions only when they are very slow, nonionic reactions being the most likely ones. On the whole, in the present state of the art, the design of L/L reactors must depend on scale-up from laboratoiy or pilot plant work. 

The reported densities of ionic liquids vary between 1.12 g cm for [(n-QHi7)(C4H9)3N][(CF3S02)2N] and 2.4 g cm for a 34-66 mol% [(CH3)3S]Br/AlBr3 ionic liquid [21, 23]. The densities of ionic liquid appear to be the physical property least sensitive to variations in temperature. For example, a 5 degree change in temperature from 298 to 303 K results in only a 0.3 % decrease in the density for a 50.0 50.0 mol % [EMIM]C1/A1C13 [17]. In addition, the impact of impurities appears to be far less dramatic than in the case of viscosity. Recent work indicates that the densities of ionic liquids vary linearly with wt. % of impurities. For example, 20 wt. % water (75 mol %) in [BMIM][BF4] results in only a 4 % decrease in density [33]. 

Modification of filler s surface by active media leads to the same strong variation in viscosity. We can point out as an example the results of work [8], in which the values of the viscosity of dispersions of CaC03 in polystyrene melt were compared. For q> = 0.3 and the diameter of particles equal to 0.07 nm a treatment of the filler s surface by stearic acid caused a decrease in viscosity in the region of low shear rates as compared to the viscosity of nontreated particles more than by ten times. This very strong result, however, should not possibly be understood only from the point of view of viscometric measurements. The point is that, as stated above, a treatment of the filler particles affects its ability to netformation. Therefore for one and the same conditions of measuring viscosity, the dispersions being compared are not in equivalent positions with respect to yield stress. Thus, their viscosities become different. 

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