Regimes comparisons

Droop, M.R. (1983) 25 years of algal growth kinetics - a personal view. Botanica Marina, 26, 99-112. Ducobu, H., Huisman, J., Jonker, R.R. and Mur, L.R. (1998) Competition between a prochlorophyte and a cyanobacterium under various phosphorus regimes Comparison with the Droop model. 

The result of Equation (22.30) is, under this assumption, the constant value of average solids velocity in the preloading regime. Comparison of the values calculated using a very simple Equation (22.30) and the values obtained by Roes and van Swaaij [4] for their experimental systems yields excellent agreement. Detailed discussion of this issue will be the subject of a future publication. 

The majority of polymer flow processes are characterized as low Reynolds number Stokes (i.e. creeping) flow regimes. Therefore in the formulation of finite element models for polymeric flow systems the inertia terms in the equation of motion are usually neglected. In addition, highly viscous polymer flow systems are, in general, dominated by stress and pressure variations and in comparison the body forces acting upon them are small and can be safely ignored. 

The comparison of analytical characteristics HPLC methods of determination of phenols with application amperometric and photometric detectors was caiiy out in this work. Experiment was executed with use liquid chromatograph Zvet-Yauza and 100 mm-3mm 150mm-3mm column with Silasorb C18 (5 10 p.m). With amperometric detector phenols were detected in oxidizing regime on glass-cai bon electrodes. With photometric detector phenols were detected at 254 nm. 

The turbulent regime for Cq is characterized by the section of line almost parallel to the x-axis (at the Re" > 500). In this case, the exponent a is equal to zero. Consequently, viscosity vanishes from equation 46. This indicates that the friction forces are negligible in comparison to inertia forces. Recall that the resistance coefficient is nearly constant at a value of 0.44. Substituting for the critical Reynolds number, Re > 500, into equations 65 and 68, the second critical values of the sedimentation numbers are obtained ... 

For a monolayer film, the stress-strain curve from Eqs. (103) and (106) is plotted in Fig. 15. For small shear strains (or stress) the stress-strain curve is linear (Hookean limit). At larger strains the stress-strain curve is increasingly nonlinear, eventually reaching a maximum stress at the yield point defined by = dT Id oLx x) = 0 or equivalently by c (q x4) = 0- The stress = where is the (experimentally accessible) static friction force [138]. By plotting T /Tlx versus o-x/o x shear-stress curves for various loads T x can be mapped onto a universal master curve irrespective of the number of strata [148]. Thus, for stresses (or strains) lower than those at the yield point the substrate sticks to the confined film while it can slip across the surface of the film otherwise so that the yield point separates the sticking from the slipping regime. By comparison with Eq. (106) it is also clear that at the yield point oo. 

A similar treatment applies for the unstable regime of the phase diagram (v / < v /sp), where the mixture decays via spinodal decomposition.For the linearized theory of spinodal decomposition to hold, we must require that the mean square amplitude of the growing concentration waves is small in comparison with the distance from the spinodal curve. 

Figure 5.3e shows the situation when the air velocity was increased to Ugs = 20 m/s. It is seen from this figure that the liquid bridges in churn flow disappeared and a liquid film formed at the side walls of the channel with a continuous gas core, in which a certain amount of liquid droplets existed. The pressure flucmations in this case became relatively weaker in comparison with the case of the churn flow. The flow pattern displayed in Fig. 5.3f indicates that as the air velocity became high enough, such as Ugs = 85 m/s, the liquid droplets entrained in the gas core disappeared and the flow became a pure annular flow. It is also observed from Fig. 5.3f that the flow fluctuation in this flow regime became weaker than that for the case shown in Fig. 5.3e, where Ugs = 20 m/s. 

Fig. 5.15 Comparison between the experimental flow patterns obtained by Triplett et al. (1999a) and the experimental flow regime transition lines of Damianides and Westwater (1988) representing their 1 mm diameter cireular test section. Reprinted from Triplett et al. (1999a) with permission...

This flow regime map can be compared with other maps developed previously for air-water two-phase flow in small-diameter horizontal and vertical channels. Figure 5.21a-d shows comparisons with the results of Damianides and Westwa-ter (1988), Fukano and Kariyasaki (1993), Triplett et al. (1999a) and Zhao and Bi (2001 a), respectively. The solid lines represent the flow regime transition boundaries observed in the 1 mm diameter channels and the flow regime names in parentheses are those given by the respective authors. 

The styrene conversion versus reaction time results for runs in the laminar flow regime are plotted in Figure 8. Both the rate of polymerization and the styrene conversion increase with increasing flow rate as noted previously (7). The conversion profile for the batch experimental run (B-3) is presented as a dashed line for comparison. It can be seen that the polymerization rates for runs with (Nj e e 2850 are greater than the corresponding batch polymerization with a conversion plateau being reached after about thirty minutes of reaction. This behavior is similar to the results obtained in a closed loop tubular reactor (7J) and is probably due to an excessively rapid consumption of initiator in a... 

Ozin, Hanlan, and Power, using optical spectroscopy (49,121). In view of the marked temperature-effect observed for the cobalt system, we shall focus on this cluster system here. Evidence for cobalt-atom aggregation at the few-atom extreme first came from a comparison of the optical data for Co Ar — 1 10 mixtures recorded at 4.2 and 12 K (see Fig. 4). A differential of roughly 8 K in this cryogenic-temperature regime was sufficient to cause the dramatic appearance of an entirely new set of optical absorptions in the regions 320-340 and 270-280 nm (see Fig. 4). Matrix variation, from Ar, to Kr, to Xe, helped clarify atom-cluster, band-overlap problems (see Fig. 5). 

Figure 6 shows the comparison between the present solutions and those from Venner et al. [40] and Holmes [41] for smooth EHL contacts in full-film regime. The central and minimum film thicknesses are listed in Table 3. From Fig. 6 and Table 3, it can be seen that as long as in full-film EHL regime the solutions from the present model are in good agreement with those by Venner et al. and Holmes. 

Figures 9 and 10 compare the him thickness and pressure prohles from the present model with the results calculated by Venner et al. [42] obtained under the same conditions. The comparison in Fig. 9 is made for the cases of transverse stationary sinusoidal waviness while Fig. 10 is for longitudinal waviness. Again, the results exhibit a good similarity. The good agreements in solutions from different researchers conhrm that the numerical schemes implemented in the present model are reliable, at least for the analyses in full-hlm EHL regime.

Due to lack of deterministic solutions of mixed lubrication in the literatures, it is difficult to conduct a direct result comparison in the mixed lubrication regime. Considering the fact that at the ultra-low speed mixed lubrication would transit to the boundary lubrication or lubricated contact... 

The present formula Eq. (126) is tested in comparison with the Bixon-Jortner perturbation theory in the weak electronic coupling regime [109]. The Arrhenius plot is shown in Fig. 23, where the electronic coupling Had is taken... 

This model breaks down when hv becomes small in comparison to k T, as the potential becomes so soft that the atoms will no longer be located at a specific site but diffuse over the surface. In this intermediate regime the atoms move around in a potential... 

Table 1.3 Comparison of miscellaneous dimensionless groups characterizing different hydrodynamic regimes in macroscopic vessels and micro reactors.

Figure 3.49 Comparison of yields of a micro reactor and monolithic reactors, both operating in the same flow regime [2],...

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