Entry lengths concentration

The entrance length z/d for a fully developed velocity profile, for a concentration profile, or for a corresponding thermal entry length are given as 0.05 Re, 0.05 Re Sc, 0.05 Re Pr, respectively. The symbols are summarized in Table 11. 

The micro-PIV measurement reported in this experiment was carried out with a 4x objective lens. With a CCD sensor size of 6.3 x 4.8 mm, the size of an image pixel is 2.475 pm and the size of the measured area is 1584 x 1188 pm. Fluorescent particles with a diameter of 3 pm were used to trace the flow. A microchannel with the cross section of 910 x 50 pm and the length of 5 mm was used. The liquids used in the experiment were the aqueous NaCl solution (concentration 10 " M) and aqueous glycerol (volume concentration 24 %). The integration area is 32 x 32 pixels. Previous studies showed that the entry length of liquid flow in microchannel was very short [11]. The measurement was taken at 1 mm downstream of the entrance thus stable velocity field was obtained. 

For internal flows, concentration boundary layers develop from both top and bottom surfaces and develop into two regions as shown in the figure concentration entry length and concentration fully developed regions similar to hydrodynamic internal flow as shown in Figure 6.14. 

Concentration entry length and fully developed region for internal flow in a charmel. 

Concentration entry length (L J The length required for the dimensionless concentration profile to become fully developed. 

Because of the thinness of the boundary layer, mass transfer in the entry region is very rapid, with Sherwood numbers in excess of 1000 attained near the tubular entrance (Figure 5.2). As we move away from the entrance in the downstream direction, the boimdary layer gradually thickens, and the Sherwood number diminishes with the one-third power of axial distance x. Eventually it levels off and attains a constant value as the fully developed region is reached (Figure 5.2 and 5.3). Table 5.2 lists some of the relevant Sherwood numbers obtained in ducts of various geometries and constant wall concentration. The quantity x/d is referred to as the "entry length."... 

Influent water enters one end of the pressure vessel and travels longitudinally down the length of the vessel in the feed transport layer. Direct entry into the permeate transport layer is precluded by sealing this layer at each end of the roll. As the water travels in a longitudinal direction, some of it passes in radially through the membrane into the permeate transport layer. Once in the transport layer, the purified water flows spirally into the center collection tube and exits the vessel at each end. The concentrated feed continues along the feed transport material and exits the vessel on the opposite end from which it entered. 

Prior to the degradation of many organic compounds, a period is noted in which no destruction of the compound is evident. This time interval is designated as an acclimation period or, sometimes, an adaptation or lag period [93-98]. It may be defined as the length of time between the addition or entry of the compound into an environment and evidence of its detectable loss. During this interval, no change in concentration is noted, but then the disappearance becomes evident and the rate of destruction often becomes rapid. 

It turned out that for all the polymeric amphiphiles of the (EO) -(PO)m-(EO) type there was an increase in enantioselectivity compared with the reaction without amphiphile. Moreover, the ratio of the length of the (PO) block compared with the (EO) block seemed to determine enantioselectivity and activity and not the cmc (critical micelle concentration). A (PO) block length of 56 units works best with different length of the (EO)n block in this type of hydrogenation [30]. for the work-up of the experiments, G. Oehme et al. used the extraction method, but initial experiments failed and the catalyst could not be recycled that way. To solve this problem the authors applied a membrane reactor in combination with the amphiphile (EO)37-(PO)5g-(EO)37 (Tab. 6.1, entry 9) [31]. By doing so, the poly-mer/Rh-catalyst was retained and could be reused several times without loss of activity and enantioselectivity by more than 99%. 

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