Rapid mixing model

The Rapid Mixing Model. In this model (36, 46) it is assumed that the combined internal convective-diflFusive transports are so rapid that the droplet temperature is maintained spacially imiform but temporally varying. This represents the fastest internal heat transfer hmit and is relevant for less viscous fuels in which internal motion can be easily generated. The model is somewhat artificial in that the existence of nonradial convection, particularly the requirement for the external gas stream to generate internal circulation, invalidates the assumption of spherical S3onmetry. However, by comparing results from the present... 

When results of the rapid mixing model and the diflFusion limit model are compared, it is shown (Figures 3 and 4) that in the initial dropletheating dominated period, the former predicts a larger droplet size, a lower surface temperature, a larger H, a slower vaporization rate and a small flame size y, as would be expected since more heat is needed to heat the entire droplet. The reverse situation prevails in the subsequent vaporization-dominated period. 

The Rapid Mixing Model. In this model (50, 56, 60, 61) the concentration and temperatoe within the droplet are maintained spacially uniform but temporally varying. Since the droplet surface is continuously... 

The implicit assumption in the determinahon of Eqs. (5.42) and (5.45) is that the mass-and heat-transfer resistances within the droplet are null. This is a common assumphon that is based on the idea of quasi-stationary conditions within the droplet that often goes under the name of the rapid-mixing model. In the special case in which Bm is approximately constant, the right-hand side of Eq. (5.45) is constant, and thus the rate of change of the surface area is independent of the droplet diameter (i.e. the d evaporahon law). 

Alternatively, the thin-skin model, which assumes an infinite diffusion resistance with only a thin layer on the droplet surface being heated and evaporated, can be used. This second assumption is more appropriate for cases in which the droplet reaches its boiling temperature immediately after the start of the evaporation process. All the other approaches (such as the diffusion-limited model), which are recommended in the case of mulhcompo-nent droplets, require some form of spahal discretization inside the droplet, resulting in much higher computational costs. To close the set of equahons, it is necessary to describe the evolution of the droplet temperature Tp as discussed in Section 5.2.3. For example, upon including the effect of evaporation on the heat flux for the rapid-mixing model, the particle-enthalpy balance yields... 

Predicted plasma concentrations of a drug given by infusion (A), twice daily injection (B), or once daily injection (C). Model assumes rapid mixing in a single body compartment and a t1/2of 12 hours. 

Results of isotope ratio measurements from an earlier study that used a similar protocol to the one just described are shown in Figure 3. These curves show plasma Isotope levels for both the i.v.oral tracer, labelled as PTA and CTA respectively. It is generally accepted that isotopic enrichment, atom percent excess, of urine reflects that of plasma, and after the initial period of rapid mixing, urinary atom percent excess is used in lieu of plasma measurements. The curves drawn through the data are those generated using the proposed model for calcium kinetics. 

The combination of rapid mixing and fast detection systems allows cationic polymerisations to be followed on an even shorter time scale than with adiabatic calorimetry. Recent commercial stop-flow spectrophotometers have a dead time of about 15 msec, an improvement of more than one order of magnitude over previous home-made models. This implies that reactions with half lives of less than 100 msec can be analysed kinetically with a good degree of accuracy. Hi -vacuum techniques are not compatible with these instruments and all operations are therefore carried out in an inert atmosphere. 

The authors recognize that the generation of the observed uniform MORB He/ He from the residue of heterogeneous OIB sources is a potential problem. They propose that rapid mixing of the shallow asthenosphere may homogenize this shallow reservoir. Numerical modeling may provide a future test of this. 

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