Similarities hydrodynamic

This is based on the flow and specific energy produced by the pump at its best efficiency point of performance following the approach stated by Wisclicenus Any fixed value of the specific speed describes a combination of operating conditions that permits similar flow conditions in geometrically similar hydrodynamic machines. ... 

The elimination or estimation of the axial dispersion contribution presents a more difficult problem. Established correlations for the axial dispersion coefficient are notoriously unreliable for small particles at low Reynolds number(17,18) and it has recently been shown that dispersion in a column packed with porous particles may be much greater than for inert non-porous particles under similar hydrodynamic conditions(19>20). one method which has proved useful is to make measurements over a range of velocities and plot (cj2/2y ) (L/v) vs l/v2. It follows from eqn. 6 that in the low Reynolds number region where Dj. is essentially constant, such a plot should be linear with slope Dj, and intercept equal to the mass transfer resistance term. Representative data for several systems are shown plotted in this way in figure 2(21). CF4 and iC io molecules are too large to penetrate the 4A zeolite and the intercepts correspond only to the external film and macropore diffusion resistance which varies little with temperature. 

Assuming the validity of this approach, and in agreement with the SEC mechanism, similar elution volumes correspond to similar hydrodynamic volumes. 

Figure 2. Chemical heterogeneity of the second kind in which polymers of different composition may coelute because of similar hydrodynamic volumes. (Reproduced from reference 5. Copyright 1986 American Chemical Society.)...

The deactivation of the diromia-alumina catalyst for the oxidation of gas streams A and B was smdied in the "fluid-bed" reactors under similar hydrodynamic conditions. The gas flow was just suHldcnt to keep the bed agitated at the reaction temperature axtd thus the hydrodynamic regime ofihcsc reactors corresponded to conditions of incipient fluidization. The initial temperature <360 for the oxidation of stream A and 385... 

Differential toxicity of copper (II) oxide nanoparticles of similar hydrodynamic diameter on human differentiated intestinal Caco-2 cell monolayers is correlated in part to copper release and shape. Nanotoxicology 6(7) 789-803... 

For the mechanical behavior of two particle-fluid systems to be simitar, it is necessary to have geometric, hydrodynamic, and particle trajectory similarity. Hydrodynamic similarity is achieved by fixing the Reynolds number for the flow around the collector. By (4.26), similarity of the particle trajectories depends on the Stokes number. Trajectory similarity also requires that the particle come within one radius of the surface at the same relative location. This means that the interception parameter, R = dp/L, must also be preserved. 

It is clear that chemical evidence is, at present, available both for and against a branched framework in softwood glucomannans. It was mentioned (Part I, p. 286) that (4-0-methylglucurono)xylans and cellulose apparently occupy a similar hydrodynamic volume in solution. In view of this fact, it appears fairly safe to assume that the same should apply to the glucomannans, which are structurally much closer to cellulose than... 

The linearity of the plot in Fig. 7 suggests that e acquires a similar hydrodynamic volume (F) in each of these alcohols, but when an effective radius is calculated from V (assuming stick boundary conditions) from the slope, the result is clearly too small, / =1.1 A. In fact, this is a typical result for rotating molecules where extensive slip is actually occurring. Thus a linear relationship between and i is not sufficient evidence to ignore the molecular aspects of the liquid dynamics. 

Many small bubbles are required in a dispersion to give a large gas-liquid interfacial area and thus effective mass transfer. Small bubbles are more readily entrained into the circulating liquid stream and so give more gas backmixing than larger bubbles under similar hydrodynamic conditions. 

The advantage of using Equation 4.81 for the mass transfer coefficient lies in the assumption that under similar hydrodynamic conditions, the film thickness 6 is constant, so that kl is directly proportional to Da-... 

It should be noted that a eertain hierarchy exists in the similarities. Hydrodynamic similarity is difficult (but not impossible) to achieve if no geometric similarity exists. Thermal similarity is facilitated by hydro-dynamic similarity. Because of the temperature dependence of the reaction rate, chemical similarity can only be obtained if thermal similarity exists. Moreover, when working with nonisothermal reactions, chemical similarity influences thermal similarity. 

The initial distribution is for both extruders the same (Fig. 12.3a and c). In practice this is the most logical situation where equal shear fields assure equal striation thickness and therefore equal reaction times. For scaling up multicomponent reactions this implies (apart from thermal similarities) hydrodynamic similarity and equal residence times. 

Although the phenomenon of polarisation has been illusuated by considering cation transport through cation-selective membranes, the same description applies to anions. However, the mobility of anions with the same valence in the boundary layer is a little greater than that of cations. This implies that under similar hydrodynamic conditions (equal thickness of the boundary layer, same cell construction) for the anion and cation, the limiting current densitj will be attained faster at a cation-exchange membrane than at an anion-exchange membrane. 

The advantage of nsing Equation 6.13 for the mass transfer coefficient lies in the assumption that under similar hydrodynamic conditions, the film thickness 5 is constant, so that the flux across the film, on the one hand, is equal to the convective flux, with a mass transfer coefficient of k l, and, on the other hand, is equal to a diffusive flux around a linear concentration gradient given by... 

In general, the average gas-to-particle heat transfer coefficients for ISDs are much higher than those in classical dryers that operate under similar hydrodynamic regimes. For example, when the heat... 

A more important one is that, it had been repeatedly overlooked that SEC separates polymer chains by their hydrodynamic volumes, not by their molar masses. Namely, for non-linear polymer chains, each retentive fraction in principle contains polymer chains with a similar hydrodynamic volume but not necessarily with a similar molar mass. Presumably, it is due to difficulties and limitations in both the sample preparation and experimental methods so that less attention has been paid to this very important point so far. 

Quantitatively revealed how the Nh and Nt affect the deformation property of one hyperbranched chain, namely, the measured critical flow rate (gc,branch) of hyperbranched chains passing through a small cylindrical pore is affected by both Nb and Nt as c,branch Nt N with y= 1.0 0.1 and

pore size D increases. The deviation between our experimental results and previous theoretical predictions is attributed to some inappropriate assumptions used before. Using the difference between the critical flow rates of different chains, we are able to separate hyperbranched chains with a similar hydrodynamic size but different subchain lengths. 

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