Micro-homogeneity

Thus the method allowed precise information on the micro-homogeneity of formerly and more recently prepared materials that could not be obtained with most classical analytical approaches. The limitation of SS-ZAAS, however, because of its... 

SoNNTAG TM, Rossbach M (1997) Micro-homogeneity of candidate RMs characterized by particle size and homogeneity factor determination. Analyst 122 27-31. 

A micro-homogeneity study was carried out by solid sampling ZETAAS for Pb and Zn which showed that the material may be considered as homogeneous for these two elements at levels of 10 mg (Pb) and 87 mg (Zn) and above [31]. 

BRITTLE NECKING MICRO- HOMOGENEOUS FRACTURE NECKING DEFORMATION... 

Solutions are micro-homogeneous mixtures the composition of which may vary within certain limits of saturation. 

The characteristic of a micro-homogeneous mixture is that its constituents cannot be separated by mechanical methods, such as sedimentation or filtration. In the nomenclature of physical chemistry, a true solution is monophasic, all its constituents being present as part of the same physical state, or phase. 

Fig. 5.30 Comparison of the two-phase frictional pressure gradient between micro-channel data and homogeneous flow model predictions using different viscosity formulations. Reprinted from Kawahara et al. (2002) with permission...

Similar void fraction data can be obtained in micro-channels and conventional size channels, but the micro-channel void fraction can be sensitive to the inlet geometry and deviate significantly from the homogeneous flow model. 

Using the properties of water Li and Cheng (2004) computed from the classical kinetics of nucleation the homogeneous nucleation temperature and the critical nu-cleation radius ra. The values are 7s,b = 303.7 °C and r nt = 3.5 nm. However, the nucleation temperatures of water in heat transfer experiments in micro-channels carried out by Qu and Mudawar (2002), and Hetsroni et al. (2002b, 2003, 2005) were considerably less that the homogeneous nucleation temperature of 7s,b = 303.7 °C. The nucleation temperature of a liquid may be considerably decreased because of the following effects dissolved gas in liquid, existence of corners in a micro-channel, surface roughness. 

A new approach was developed by Lee and Mudawar (2005a) to improve the accuracy of pressure drop prediction in two-phase micro-channels. Since the bubbly and churn flow patterns are rarely detected in high-flux micro-channel flow, the separated flow model was deemed more appropriate than the homogeneous. 

Kawahara et al. (2002) presented void fraction data obtained in a 100 pm micro-channel connected to a reducing inlet section and T-junction section. The superficial velocities are Uqs = 0.1-60m/s for gas, and fAs = 0.02-4 m/s for liquid. The void fraction data obtained with a T-junction inlet showed a linear relationship between the void fraction and volumetric quality, in agreement with the homogeneous model predictions. On the contrary, the void fraction data from the reducing section inlet experiments showed a non-linear void fraction-to-volumetric quality relationship ... 

Bowers and Mudawar (1994a) performed an experimental smdy of boiling flow within mini-channel (2.54 mm) and micro-channel d = 510 pm) heat sink and demonstrated that high values of heat flux can be achieved. Bowers and Mudawar (1994b) also modeled the pressure drop in the micro-channels and minichannels, using the Collier (1981) and Wallis (1969) homogenous equilibrium model, which assumes the liquid and vapor phases form a homogenous mixture with equal and uniform velocity, and properties were assumed to be uniform within each phase. 

A detailed description of AA, BB, CC step-growth copolymerization with phase separation is an involved task. Generally, the system we are attempting to model is a polymerization which proceeds homogeneously until some critical point when phase separation occurs into what we will call hard and soft domains. Each chemical species present is assumed to distribute itself between the two phases at the instant of phase separation as dictated by equilibrium thermodynamics. The polymerization proceeds now in the separate domains, perhaps at differen-rates. The monomers continue to distribute themselves between the phases, according to thermodynamic dictates, insofar as the time scales of diffusion and reaction will allow. Newly-formed polymer goes to one or the other phase, also dictated by the thermodynamic preference of its built-in chain micro — architecture. 

Stresses acting on micro-organisms in (a) to (c) are derived on the premise that the flow forces originate from the turbulent motion of the carrier medium. In almost all cases, turbulence is assumed to be locally isotropic and homogeneous which greatly simplifies the analysis and allows the application of the Kolmogoroff s theory of turbulence to the problem [81]. The Kolomogoroff micro-scale of turbulence,... 

Other key features in the analysis of pore structure are the length scales associated with the various micro- (nano)-scale obstacles and pores, the possible larger-scale variations in structure, and the averaging domain over which information is needed [6,341,436], The hterature refers to analysis of homogeneous and heterogeneous porous media, where homogeneous refers to media with no variation in physical properties (e.g., porosity, diffu-... 

In a micro reactor, there is much more surface available than in standard reactors [18]. Thus, surface-chemistry routes may dominate bulk-chemistry routes. In this context, it was found sometimes micro-reactor routes can omit the addition of costly homogeneous catalysts, since the surface now undertakes the action of the catalyst. This was demonstrated both at the examples of the Suzuki coupling and the esterification of pyrenyl-alkyl acids. 

For fast reactions Da becomes large. Based on that assumption and standard correlations for mass transfer inside the micro channels, both the model for the micro-channel reactor and the model for the fixed bed can be reformulated in terms of pseudo-homogeneous reaction kinetics. Finally, the concentration profile along the axial direction can be obtained as the solution of an ordinary differential equation. 

In the following, the impact of the micro-channel diameter on the temperature rise due an exothermic gas-phase reaction is investigated. For simplicity, a homogeneous reaction A —> B of order n with kinetic constant k is considered. Inside the micro channel, the time evolution of the radially averaged species concentration c and temperature T is governed by the equations... 

In order to exemplify the potential of micro-channel reactors for thermal control, consider the oxidation of citraconic anhydride, which, for a specific catalyst material, has a pseudo-homogeneous reaction rate of 1.62 s at a temperature of 300 °C, corresponding to a reaction time-scale of 0.61 s. In a micro channel of 300 pm diameter filled with a mixture composed of N2/02/anhydride (79.9 20 0.1), the characteristic time-scale for heat exchange is 1.4 lO" s. In spite of an adiabatic temperature rise of 60 K related to such a reaction, the temperature increases by less than 0.5 K in the micro channel. Examples such as this show that micro reactors allow one to define temperature conditions very precisely due to fast removal and, in the case of endothermic reactions, addition of heat. On the one hand, this results in an increase in process safety, as discussed above. On the other hand, it allows a better definition of reaction conditions than with macroscopic equipment, thus allowing for a higher selectivity in chemical processes. 

Another exception to the known mechanisms of conventional chemistry may arise when dominance of surface reactions is achieved in micro reactors. This holds for all catalytic reactions on solid contacts. Beyond that, it was shown that some formerly homogeneous bulk reactions may become heterogeneous when carried out in a micro reactor owing to the very large surface-to-volume ratio [155,171,172],... 

GP 11] ]R 19] The suppression of explosive homogeneous gas-phase reactions is not due simply to thermal quenching as a result of the heat losses from a micro reactor, but rather to radical quenching [9]. The micro reactor will therefore be safe even when heat losses from the reaction micro channel are reduced by design modifications. 

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