Weighted average total strain

Table 10.2 Weighted Average Total Strain (WATS) for Three Rhomboidal Mixing Heads...

As a simple example of the calculation of the weighted average total strain (WATS) consider the laminar flow of a Newtonian fluid in a pipe of length L and radius R. The velocity profile gives the local velocity v at radial position... 

Since the mass flow rate of material between radial positions r and r+dr can be written as Inpvrdr the weighted local strain is 2npvrdr(AvrLIR v). Finally the weighted average total strain follows as ... 

Figure 11.14 Weighted average total strain (WATS) for a single-screw extruder " ...

Tadmor and Pinto [207] used the weighted average total strain (WATS) to describe mixing performance in the non-homogeneous flow field of a single screw extruder. This is defined as ... 

Here, Pcz>/ P>gd/ o are constant for the whole pattern (taken at zero value of the wave vector Sq of the first peak). The integral breaths found from the experimental diffraction profiles allow calculation of the surface-weighted (Ds) and volume-weighted (Dy) domain size and a mean-square (Gaussian) strain, s, which is the total strain averaged over infinite distance ... 

Mullen et al. (1989) reported that Bacillus cereus, B. subtilis, E. coli and P. aeruginosa were able to sorb an average of 89% of the total Ag+ and 12-27% of the total Cd2+, Cu2+ and La3+ from a ImM solution. Using polyacrylamide-entrapped cells of Brevibacterium sp strain PBZ, Simine et al. (1998) measured a sorption capacity of 40 mg g-1 and 13 mg g-1 dry biomass for Pb and Cd, respectively. Hall et al. (2001) isolated two bacterial strains of P. syringae that were tolerant to 1000 mg L-1 Cu. Similarly, Amoroso et al. (2001) were able to obtain Streptomyces spp. strains R22 and R25 with a high tolerance to Cr from sediments of the Sail River, Argentina. The cells of R22 and R25 could accumulate 10.0 and 5.6 mg Cr g-1 dry weight, respectively, from a concentration of 50 mg Cr mL 1. Cell fractionation studies with strain R22 showed that most of the chromium... 

The form of N. A further point of interest in eqn. (14.9) is the material property N, which measures the resistance of the mixture of A and B to change of shape or volume. It will be recalled that in forming eqns. (14.7), the components A and B were treated as geometrically independent it was assumed that component A responds to s according to its viscosity N, that component B responds separately according to its viscosity AT , and that the total effect is a weighted sum or average of these two separate strain responses. We should consider whether this is the best of possible approaches, as follows. 

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