Macroscopic continuity, flow rate

The above equations can be used to predict the output 1/ in the effluent from a continuous-flow gas-liquid contractor. Let the flow rate of phase a be F. Then, a macroscopic balance at a steady state leads to the equation ... 

On the basis of the considered macroscopic flow pattern, the dominant circulation flows (/ c and Fc/2) subdivide the reactor into three parallel levels, where each level is then divided into Nc/3 equally sized compartments of equal volume Vc = Vr/Nc. Every compartment is modeled as a nonstationary ideal continuous stirred tank reactor, with a main inlet and outlet flow, which connects the given compartment with adjacent compartments on the same level, and secondary exchange flow rates accounting for the turbulent mixing with adjacent compartments laying on the upper and/or lower level (Fig. 7.3). 

Microfluidic generation of polymer particles starts from the emulsiflcation of liquid monomers, oligomers, or polymers. This step is followed by polymerization, cross-linking, or physical gelation of the molecules compartmentalized in droplets. Dimensions of polymer microbeads are predetermined by the dimensions of precursor droplets, which are in turn controlled by the geometry and dimensions of microchannels in MF droplet generator, the mechanism of droplet formation, the macroscopic properties of the droplet and continuous phases, and the relative volumetric flow rates of the continuous and droplet phases. 

Consider a continuous crystallizer of volume V, as shown in Figure 6.4.2(a). A feed stream having a particle (crystal) number density function ra/(rp) (which is also the population density function), volumetric flow rate Qf and species i mass concentration enters the crystallizer continuously. Product stream 1, having a particle (crystal) number density function n (tp), volumetric flow rate Qi and species i mass concentration Pf, leaves the crystallizer continuously. The particle (crystal) number density function n rp) in the well-mixed crystallizer is the same throughout the crystallizer. The macroscopic population balance equation for a stirred tank separator may be written using equations (6.2.60) and (6.2.61) as follows ... 

The relations discussed above can be applied directly to homogeneous deformations of a body in which the strains are the same everywhere in the sample and the macroscopic deformation of the sample is essentially the same as that of any infinitesimal element of it. In many deformation geometries commonly used for experimental measurements, however, such as torsion between coaxial cylinders, torsion of a cylindrical rod, flow through a tube, flexure, etc., the magnitudes of the strains and rates of strain vary from point to point. Application of the equations of continuity and motion and integration over the sample geometry are then necessary to relate external forces and displacements to the viscoelastic functions. For some cases, if the deformations are small, the geometry is no real complication ... 

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