Integrated shear factor

Literature reports have used the following reactor parameters to correlate the effects of agitation intensity with cell injury in bioreactors agitator rpm, impeller tip speed, integrated shear factor and Kolmogorov eddy size. Additional parameters have been used for microcarrier bioreactors (discussed below). All correlations of cell injury with a bioreactor parameter should be used only qualitatively. These correlations are, at present, indicative of various trends or mechanistic hypotheses and should not be used for quantitative bioreactor scale-up. In addition, such correlations are applicable to the specific cell type, because different cell types are likely to exhibit different responses to fluid forces. 

The integrated shear factor (ISF), which is assumed to be (incorrectly, strictly speaking) a measure of the strength of the shear field between the impeller and the vessel wall, and may be somewhat more useful for scale-up purposes, is defined as ... 

Steady Flow in Packed Beds of Monosized Spherical Particles. Steady incompressible fully developed flow in porous media confined in a circular pipe can be treated with a single differential equation as given by equation 111. The inertial effects are only reflected in the shear factor term. Two purposes are served in this section to verify the integrity of the models presented earlier, including the passage model on shear factor and wall effects on the flow, and to show the flow behavior itself. The flow problem is solved numerically with a central difference method. An abundance of experimental data are available in the literature. However, we confine ourselves to the laminar flow regime for a packed bed of spherical particles. We make use of the latest available data presented by Fand et al. (110) for a packed bed with weak wall effects and the experimental data of Liu et al. (32). 

C = joint clearance D = diameter of lap area F = shear strength of brazed filler metal J = joint integrity factor of 0.8 L = length of lap area = IW(D-W) T ] / JFD T = tensile strength of weakest member th = thickness of thinner joint member W = wall thickness of weakest member... 

Materials selection process can be depicted in terms of Figure 1.40. Materials selection involves many factors that have to be optimized for a particular application. The foremost consideration is the cost of the material and its applicability in the environmental conditions so that integrity can be maintained during the lifetime of the equipment. When the material of construction is metallic in nature, the chemical composition and the mechanical properties of the metal are significant. Some of the important mechanical properties are hardness, creep, fatigue, stiffness, compression, shear, impact, tensile strength and wear. 

These velocity profiles are used to determine two key factors the average flow rate and the shear stress at the wall. The average velocity, v, is obtained using the following integral ... 

The legitimacy of employing Blasius type models for the shear stresses in stratified flows was checked in several studies. Kowalski made direct measurements of the Reynolds shear stress in the gas for horizontal stratified flow in pipes and found that the gas-wall friction factors are well approximated by the Blasius equation provided that the hydraulic diameter is utilized [64]. For the liquid phase, Andritsos and Hanratty [28] found that the use of the Blasius equation to calculate introduces some error. However, improvements achieved by using a more complicated model for which is based on velocity profile and eddy viscosity concepts, were found to be of mild effect on the integral flow characteristics. 

If the components are thermodynamically completely miscible, the minor component has to be distributed over the major component as homogeneously as possible, but no interfacial forces are involved. This type of mixing is called distributive mixing and the total shear, being the shear rates integrated over the time period during which this shear is active on the fluid element considered, is the most important factor. 

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