Laminar flow slurries

Suspensions of fine sohds may have pseudoplastic or plastic-flow properties. When they are in laminar flow in a stirred vessel, motion in remote parts of the vessel where shear rates are low may become negligible or cease completely. To compensate for this behavior of slurries, large-diameter impellers or paddles are used, with (D /Df) > 0.6, where Df is the tank diameter. In some cases, for example, with some anchors, > 0.95 Df. Two or more paddles may be used in deep tanks to avoid stagnant regions in slurries. 

Settling slurries cannot be pumped in laminar flow. Turbulence must exist to prevent the solid particles from settling. Settling slurries should be pumped through pipelines at velocities which just prevent the solid particles from settling. This results in the minimum pressure drop across the pipeline. 

With this background of non-Newtonian behavior in hand, let us examine the viscous behavior of suspensions and slurries in ceramic systems. For dilute suspensions on noninteracting spheres in a Newtonian liquid, the viscosity of the suspension, r)s, is greater than the viscosity of the pure liquid medium, rjp. In such cases, a relative viscosity, rjr, is utilized, which is defined as rjs/rjL. For laminar flow, is given by the Einstein equation... 

Naphthali-Sandholm method, 404 dgorithm flowsketch, 411 Nitric acid reactor, 576 Nitrogen fixation, 574,578,588 Nitrotoluene isomers separation, 544 Noncatalytic reactions with solids, 595 Non-Newtonian liquids, 100, 103-109 Bineham. 104.105.107-109 dilatant, 103, 104 laminar flow, 108,109 pressure drop in lines, 106, 109 pseudoplaslic, 103, 104 rheopectic, 104,105 slurries, 71 thixotropic, 104-106 viscoelastic, 105, 106 Notation, 672 NPSH, pumps, 133,146 centrifugal pumps, 146 positive displacement pumps, 134, 135 various pumps, 144 NRTL equation, 475... 

An exception to the generally observed drag reduction in turbulent channel flow of aqueous polymer solutions occurs in the case of aqueous solutions of polyacrylic acid (Carbopol, from B.F. Goodrich Co.). Rheological measurements taken on an oscillatory viscometer clearly demonstrate that such solutions are viscoelastic. This is also supported by the laminar flow behavior shown in Fig. 10.20. Nevertheless, the pressure drop and heat transfer behavior of neutralized aqueous Carbopol solutions in turbulent pipe flow reveals little reduction in either of these quantities. Rather, these solutions behave like clay slurries and they have been often identified as purely viscous nonnewtonian fluids. The measured dimensionless friction factors for the turbulent channel flow of aqueous Carbopol solutions are in agreement with the values found for clay slurries and may be correlated by Eq. 10.65 or 10.66. The turbulent flow heat transfer behavior of Carbopol solutions is also found to be in good agreement with the results found for clay slurries and may be calculated from Eq. 10.67 or 10.68. 

Figure 5-12 displays the spectra of the Doppler signal for laminar flow at the recycle slurry line at the SRC-II pilot plant at various pump speeds (flow velocities). The characteristics of these spectra are (a) considerable energy concentration at low frequencies (the nature of this high-energy concentration... 

Figure 9.1.3 shows the measured velocity profile in a 51 mm circular glass tube determined by laser doppler velocimetry for the laminar flow of a non-Newtonian colloidal slurry with a mean velocity of 1.37 m s (Park et al. 1989). The particles are 1-2 m transparent silica spheres with a mean particle size of 1.13 /um based on number and 1.79 /am based on volume, the volume fraction (f> = 0.14, and the fluid is a mixture of an organic solvent and mineral oil with an index of refraction matched to that of the particles. 

Figure 15.5 shows a plot of the friction factor versus the Reynolds number as defined in Eq. 15.10. Because the Reynolds number has been defined by Eq. 15.10, the laminar-flow data must fall on the line shown. For flow at Reynolds numbers greater than 2000, two possible kinds of behavior are known. All slurries and many polymer solutions are represented by the solid curve in Fig 15.5. These do not seem to significantly suppress the turbulent behavior of the fluid. However, some polymer solutions and polymer melts, particularly those which show distinct viscoelastic behavior (such as rubber cement) obey the curves shown dotted at the right in Fig. 15.5. Visual observation [7] indicates that for these fluids the turbulence in the fluid is much less than it would be for a newtonian fluid at the same Reynolds number.

The rheological behaviour of a coal slurry (1160kg/m ) can be approximated by the Bingham plastic model with Tq = 0.5 Pa and /ng = 14mPa-s. It is to be pumped through a 400 mm diameter pipe at the rate of 188kg/s. Ascertain the nature of the flow by calculating the maximum permissible velocity for laminar flow conditions. 

Determine the critical velocity for the upper limit of laminar flow for a slurry with the following properties, flowing in a 150 mm diameter pipe. 

The following laboratory results are available for laminar flow of this slurry in small diameter tubes. 

In a simple casting unit, a Newtonian viscous slurry and a laminar flow can be assumed, the thickness of the dry tape, h, shown in Fig. 4.34, is given by ... 

All the above-mentioned models have been usually developed for the nonturbulent region. There is a dearth of information about non-Newtonian behavior at the turbulent level, mainly perhaps due to the fact that most of the practical applications (pumping, flow and mixing of slurries, etc.) lie in laminar flow regime. 

A mud slurry is draining in laminar flow from the bottom of a large tank through a 5 m long horizontal pipe with a 1 cm inside diameter. The open end of the pipe is 5 m below the level in the tank. The mud is a Bingham plastic with a yield stress of 15 N/m, an apparent viscosity of 0.06 kg/m/s, and a density of 2000 kg/m. At what velocity will the mud slurry drain from the hose ... 

First, if we ignore the filter medium and consider only the cake itself, the pressure drop versus liquid flow relationship is described by the Ergun equation [Equation (6.15)]. The particle size and range of liquid flow and properties commonly used in industry give rise to laminar flow and so the second (turbulent) term vanishes. For a given slurry (particle properties fixed) the resulting cake resistance is defined as ... 

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