Typical fluid viscosities

Typical fluid viscosities for various materials and typical shear-rate ranges for their processing operations are shown in Tables 3.10 and 3.11 (Macosko, 1994). 

Viscosity is measured in poise. If a force of one dyne, acting on one cm, maintains a velocity of 1 cm/s over a distance of 1 cm, then the fluid viscosity is one poise. For practical purposes, the centipoise (cP) is commonly used. The typical range of gas viscosity in the reservoir is 0.01 - 0.05 cP. By comparison, a typical water viscosity is 0.5 -I.OcP. Lower viscosities imply higher velocity for a given pressure drop, meaning that gas in the reservoir moves fast relative to oils and water, and is said to have a high mobility. This is further discussed in Section 7. 

Permeability (k) is a rock property, while viscosity (fi) is a fluid property. A typical oil viscosity is 0.5 cP, while a typical gas viscosity is 0.01 cP, water being around 0.3 cP. For a given reservoir, gas is therefore around two orders of magnitude more mobile than oil or water. In a gas reservoir underlain by an aquifer, the gas is highly mobile compared to the water and flows readily to the producers, provided that the permeability in the reservoir is continuous. For this reason, production of gas with zero water cut is common, at least in the early stages of development when the perforations are distant from the gas-water contact. 

The field unit for permeability is the Darcy (D) or millidarcy (mD). For clastic oil reservoirs, a good permeability would be greater than 0.1 D (100 mD), while a poor permeability would be less than 0.01 D (10 mD). For practical purposes, the millidarcy is commonly used (1 mD = 10" m ). For gas reservoirs 1 mD would be a reasonable permeability because the viscosity of gas is much lower than that of oil, this permeability would yield an acceptable flowrate for the same pressure gradient. Typical fluid velocities in the reservoir are less than one metre per day. 

Power Consumption of Impellers Power consumption is related to fluid density, fluid viscosity, rotational speed, and impeller diameter by plots of power number (g P/pN Df) versus Reynolds number (DfNp/ l). Typical correlation lines for frequently used impellers operating in newtonian hquids contained in baffled cylindri-calvessels are presented in Fig. 18-17. These cui ves may be used also for operation of the respective impellers in unbaffled tanks when the Reynolds number is 300 or less. When Nr L greater than 300, however, the power consumption is lower in an unbaffled vessel than indicated in Fig. 18-17. For example, for a six-blade disk turbine with Df/D = 3 and D IWj = 5, = 1.2 when Nr = 10. This is only about... 

Consider each of the fluids for which the viscosity is shown in Fig. 3-7, all of which exhibit a typical structural viscosity characteristic. Explain why this is... 

A general expression can be found by combining these two cases (Melis et al., 1999). In these expressions, kB is the Boltzmann constant, T is the fluid temperature (Kelvin), ji is the fluid viscosity, y is the local shear rate, and a is an efficiency factor. For shear-induced breakage, the kernel is usually fit to experimental data (Wang et al., 2005a,b). A typical form is (Pandya and Spielman, 1983) as follows ... 

Cross-flow filters behave in a way similar to that normally observed in crossflow filtration under ambient conditions increased shear-rates and reduced fluid-viscosity result in an increased filtrate number. Cross-microfiltration has been applied to the separation of precipitated salts as solids, giving particle-separation efficiencies typically exceeding 99.9%. Goemans et al. [30] studied sodium nitrate separation from supercritical water. Under the conditions of the study, sodium nitrate was present as the molten salt and was capable of crossing the filter. Separation efficiencies were obtained that varied with temperature, since the solubility decreases as the temperature increases, ranging between 40% and 85%, for 400 °C and 470°C, respectively. These workers explained the separation mechanism as a consequence of a distinct permeability of the filtering medium towards the supercritical solution, as opposed to the molten salt, based on their clearly distinct viscosities. 

The rate at which the momentum transfer takes place is dependent on the rate at which the molecules move across the fluid layers. In a gas, the molecules would move about with some average speed proportional to the square root of the absolute temperature since, in the kinetic theory of gases, we identify temperature with the mean kinetic energy of a molecule. The faster the molecules move, the more momentum they will transport. Hence we should expect the viscosity of a gas to be approximately proportional to the square root of temperature, and this expectation is corroborated fairly well by experiment. The viscosities of some typical fluids are given in Appendix A. 

Step coverage — From the process flow schematics shown previously, it is apparent that printed transistors inherently have substantial topology within their cross-sectional structure. As a consequence, step coverage becomes an important parameter in process optimization. Given the large steps (typically several tens of nm or more) and the use of relatively thin subsequent layers, it is important that the layers cover each other adequately liquids must be able to coat the vertical sidewaUs of steps during a multilayer print process. This places constraints on fluid viscosity, evaporation rate, wetting, etc. 

Tcmpgrature. The effect of operating temperature on the permeate flux is usually significant due to the change of fluid viscosity with temperature. In liquid-phase processing, the permeate flux increases as the temperature increases primarily due to viscosity or solid solubility. Liquid viscosity generally decreases as the temperature increases. Furthermore, the solubility of suspended solids also typically increases with increasing temperature. 

The region of the flow above the plate bounded by 5 in which the effects of the viscous shearing forces caused by fluid viscosity are fell is called the velocity boundary layer. The boundary layer iliickiiess, 8, is typically defined as the distance) from the. surface at which u = 0.99F. 

Time-Independent Non-Newtonian Fluids. Time-independent non-Newtonian fluids are characterized by having the fluid viscosity as a function of the shear rate (or shear stress). However, the fluid viscosity is independent of the shear history of the fluid. Such fluids are also referred to as non-Newtonian viscous fluids". Figure 1 shows a typical shear diagram for the various time-independent non-Newtonian fluids. 

Starting with simulations of fluid with viscosity 100 Pa.s, further simulations were carried out for fluids with viscosity 10 Pa.s, 1 Pa.s and 0.001 Pa.s. Initially all simulations were carried out for 40 x 40 grids. Typical predicted results are shown in Figs 6.21 and 6.22. It can be seen that fluid viscosity has a pronounced influence on fluid dynamics. As the viscosity decreases, the penetration depth of the incoming jet increases, leading to circulatory flow within the domain. For lower viscosity fluids, much sharper profiles exist within the solution domain. It will be of interest... 

Power Consumption of Impellers Power consumption is related to fluid density, fluid viscosity, rotational speed, and impeller diameter by plots of power number (g P/pN Df) versus Reynolds number (D Np/p). Typical correlation lines for frequently used impellers operating in newtonian liquids contained in baffled cylindrical vessels are presented in Fig. 18-17. These curves may be used also... 

These relationships are valid for isolated bubbles moving under laminar flow conditions. In the case of turbulent flow, the effect of turbulent eddies impinging on the bubble surface is to increase the drag forces. This is typically accounted for by introducing an effective fluid viscosity (rather than the molecular viscosity of the continuous phase, yUf) defined as pi.eff = Pi + C pts, where ef is the turbulence-dissipation rate in the fluid phase and Cl is a constant that is usually taken equal to 0.02. This effective viscosity, which is used for the calculation of the bubble/particle Reynolds number (Bakker van den Akker, 1994), accounts for the turbulent reduction of slip due to the increased momentum transport around the bubble, which is in turn related to the ratio of bubble size and turbulence length scale. However, the reader is reminded that the mesoscale model does not include macroscale turbulence and, hence, using an effective viscosity that is based on the macroscale turbulence is not appropriate. 

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