Dissipation specific power

For plant cell suspensions cultivated in shake flasks, Huang et al. [45] used the energy dissipation rate as a correlating parameter for system response. Specific power input was calculated using the empirical correlation proposed by Sumino et al. [46] and subsequently employed in other applications [47,48] ... 

The specific power dissipated by agitators in the liquid, eagit, was measured by a strain gauge mounted on the impeller shaft. The total specific power e dissipated in the liquid by the agitator and the rising bubbles was calculated as e = eagjt + pgvs. The volumetric mass transfer coefficient and interfacial area were measured by the Danckwerts plot method described in detail in Part I. 

The overall volumetric mass transfer coefficients measured by pure oxygen absorption were expressed as a function of the total specific power dissipated in the liquid as follows ... 

Thus, for Newtonian fluids, the pressurization capability of the optimized JMP is eight times that of the SMP, and for non-Newtonian fluids, the ratio exhibits a minimum at n = 0.801 and rises to 11.59 at it — 0.25 whereas, the flow rate at fixed pressure rise for Newtonian fluids is 81 2 — 2.83 times in JMP as compared to SMP, and for non-Newtonian fluids with n = 0.25 it rises to 7.25. Clearly, the JMP configuration is about an order of magnitude more efficient then the SMP one. Moreover, the specific power input in a JMP configuration for Newtonian fluids is one-half that of the SMP, and for n — 0.25, it is one-fifth the corresponding ratios for specific power dissipated into heat are, one-quarter and 1/25, respectively. 

A useful way of describing the forcing of estuarine sedimentary processes is in terms of the specific dissipation (watts/square meter), which will be a function of both time and location throughout the estuary. Direct, systematic measurements of the specific power are not likely to be available for many (if any) estuaries, so estimates of the specific power must be based on the characteristics of the forcing mechanisms. The most im-... 

The mean shear rate in laminar flow depends on the kinematic viscosity, v of the fluid, and the specific power dissipation, e, expressed in W kg T... 

The specific power dissipation is proportional to the flow rate and the pressure drop. The pressure drop through open channels with laminar flow is given by the Hagen-Poiseuille equation [20] ... 

On the basis of Equation 4.25, the mixing time in microchannels with different diameters between 50 and 1000 pm was estimated to be a function of the specific power dissipation. Physical properties correspond to water at room temperature and atmospheric pressure. Because of the damping effect of the logarithmic function, the influence of the f e-number diminishes and the mixing time can be estimated with the simplified relation in Equation 4.26 (see Figure 4.13). 

Figure 4.13 Predicted (Equation 4.25) and experimentally determined mixing time as function of the specific power dissipation. (Experimental values taken from Ref. [15]. Adapted with permission from Elsevier.)...

Estimate the mixing time and the specific power dissipation in a cylindrical channel with a diameter of df= 1mm, a linear velocity of u = 0.2m- s". Z) j = 10 m s" -, v = 10" m s . Calculate the mixing time and specific power dissipation for a channel with dj = 0.5mm supposing the same volumetric flow. 

It follows for the specific power dissipation in circular tubes ... 

The mixing time in the microchannel as a function of the specific power dissipation is shown in Figure 4.31. The experimental results are in good agreement with the empirical relation (Equation 4.27) shown in Figure 4.13. 

Figure 4.31 Mixing time as function of specific power dissipation. Experimental results taken from Example 4.4. Solid line prediction with Equation 4.27.

If the mixing time obtained experimentally in all micromixers is related to the specific power dissipation, the empirical relation given in Equation 4.27 is found. 

The present chapter aims to be complementary to the studies and reviews already published to present theoretical basis elements for the understanding of mixing principles in laminar flows, mainly developed in micromixers. Among different characterization techniques of mixing efficiency, this chapter more specifically focuses on the chemical test method, called the Villermaux-Dushman reaction, that we have developed over many years and which is named in memory of Professor Jacques Villermaux. It will be shown how to obtain the mixing time and how to relate it to operating parameters such as the Reynolds number of the flow and the specific power dissipation per unit mass of fluid. A non-exhaustive comparison of several micromixers will be presented. 

Figure 6.5 Theoretical mixing time versus specific power dissipation in microchannels of different diameters (water, Sc =1000).

For micromixers for which experimental pressure drop data are available, it is possible to estimate the specific power dissipation from Equation (6.4) between the inlet and the outlet pressure measurement points. It is assumed here that the estimated specific power contributes to mixing, which is a rough estimation because of the pressure drop induced by the micromixer pipe connections. In Figure 6.9 is plotted the mixing time with respect to the specific power dissipation for several mixers. The experimental mixing times scale fairly well as a power law of the... 

Figure 6.9 Evolution of the mixing time in different micromixers versus specific power dissipation. Influence of the energetic mixing efficiency.

It has been shown in this chapter how to characterize mixing efficiency in micromixers and particularly how to relate mixing time to relevant operating parameters such as the Peclet number and the specific power dissipation. In spite of a low mixing energetic efficiency, micromixers can mix in a few milliseconds, much faster than conventional mixers. 

The viscous dissipation is a specific power consumption, i.e., power per unit volume. In S.I. units it is expressed in Watts per cubic meter [W/m ]. The heat fiux away from the polymer melt is determined by the heat fiux from the melt to the barrel and screw. If the screw is neutral the heat fiux to the screw is usually small and can be assumed to be negligible. If screw cooling is used, this assumption will not be correct. The heat fiux (heat flow per unit cross-sectional area) for cooling the polymer melt is determined by Fourier s law of conductive heat transport ... 

Often the mean specific power dissipation per unit liquid mass is used as a parameter to indicate the intensity of turbulence. It is defined as... 

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