Cross sections concentration

From the above MC simulation results, a suppositional concentric square column structure is constructed, which is not observed in MC simulation (Yu et al., 2007a) but can be considered as a basic block of the CMSC structure. We plot the same four architectures together forming a close-packed structure in Figure 37. Under curved confinements, the topological CMSC structure can be considered as the cross-sectional concentric circle that truncates the four close-packed square columns with the exterior radii Rex, and the center is at the common corner of the four squares. Among the four square columns, the phase structures of... 

In this way, cross-sectional concentration profiles could be determined with fairly high accuracy [69],... 

Cross-sectional concentration profiles in a Y micro mixer... 

No details on mixer in [109]) [P 25] By use of confocal microscopy, cross-sectional concentration profiles were derived in a Y micro mixer (see Figure 1.58) [70]. At the top and bottom of the channel large fluorescent areas were found, while this region thinned in the channel center. The experimental images perfectly match the simulated concentration profiles. 

Figure 1.93 Cross-sectional concentration profiles for multi-lamination flow patterns in the rectangular interdigital micro mixer for various flow rates [20] (by courtesy ofAIChE).

Figure 1.159 Concentration profiles of an injected plug of Rhodamine B traveling over a four-groove structure in a micro channel at two different groove-to-channel mobilities rEOM and for an unstructured channel as reference case. This plot describes the axial broadening of the pulse signal. In addition, cross-sectional concentration profiles are given to analyze the corresponding impact on mixing [156] (by courtesy of RSC).

The material in the nip at any axial position has a uniform volatile concentration, C—i.e., the nip mixing is sufficiently intense to wipe out bulk cross-sectional concentration gradients which normally tend to develop through the combined action of surface depletion and the seemingly inevitable tendency for the flow to channel through the core of the advancing helical nip. 

All acquisition times listed are relative actual times will vary greatly with cross section, concentration, power, etc. 

Now bring into consideration the average (over the cross section) concentration. 

According to Equation 3.79, the validity of Equation 3.67 increases as the inlet is approached (the relative error decreases linearly). The fiiU model in Table 3.1 and its pseudo-homogeneous version described in Section 3.4 were solved numerically using gPROMS [122]. The numerically determined cross-sectional concentration averages from both cases allowed the calculation of 8, and this is compared with Equation 3.76 in Figure 3.5. 

The influence of a bend on the distribution of particles in a pipe cross-section of pneumatic conveying systems has been investigated numerically. The numerical model solved the finite-volume equations for the conservation of mass and momentum for two phases. It was evident that the cross-sectional concentration of the particles a few meters after a bend is not uniform and that the particles tend to concentrate around the pipe s wall. Various cross-sectional concentrations of particles were found for different pipe to bend radius ratios particles size and direction of gravity (i.e. horizontal to vertical flow, and horizontal to horizontal flow). Based on the (Efferent cross-sectional concentrations for different particle sizes, it was concluded that the paths taken by the particles after the bend were strongly dependent upon their sizes. As a consequence, segregation of particles downstream of a bend is expected. 

In the present study the two-fluid theory was used to model gas-particles flow in a pneumatic conveying system. Numerical simulations with various pipes to bend radius ratios and particle sizes have been conducted in order to predict the cross-sectional concentration of particles. A three dimensional (3D) simulation of gas-particle flow in a pipe system, comprising two bends and three straight sections, has been conducted. The orientation of the second straight section was either horizontal or vertical. The influence of the bend radius on the characteristic of the flow field was examined for three types of particle properties. 

A. Levy and D.J. Mason, The Effect of a Bend on the Particle Cross-Section Concentration and Segregation in Pneumatic Conveying Systems, Powder Technology, 98 (1998) 95-103. 

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