Volume mixing

Ko//M //s. When dispersion is requited ia exceedingly viscous materials, the large surface area and small mixing volume of roU mills allow maximum shear to be maintained as the thin layer of material passiag through the nip is continuously cooled. The roUs rotate at different speeds and temperatures to generate the shear force with preferential adhesion to the warmer roU. 

Tne derivation of eq 10 was undertaken with the assumption that the sample effluent was monodisperse in molecular weight at any V. In reality this is never the case. First, if the frequency of branching varies with molecular weight, species of different molecular weight (but equivalent hydrodynamic volume) may elute at the same V (1 ). Second, molecular weight polydispersity at V results from assorted hardware mixing volumes and band-spreading of the SEC columns 0,11). 

In this model of non-ideal reactor mixing, a fraction, fi, of the volumetric feed rate, F, completely by-passes the mixing in the reactor. In addition, a fraction, f2, of the reactor volume, V, exists as dead space. F3 is the volumetric rate of exchange between the perfectly mixed volume Vi and the dead zone volume V2 of the reactor. 

Fig. 2.6.11 Flow dispersion profiles obtained with (a) a capillary, (b) with a model microfluidic chip device containing a channel enlargement, directly connected to a capillary and (c) with the same microfluidic chip connected to a capillary via a small mixing volume. A sketch of the model microfluidic device is placed at the right side of each image, drawn to...

Fig. 5.17 shows the curves for the potentiometric titration of Ca2f in the range 5 10 3-5 10 2 M with a titrant carrier stream of 5 10 4 M EDTA using a calcium ion-selective electrode each titration is initiated by an abrupt increase in the potential, followed by an S-shaped decrease in which the inflection point marks the end of titration. According to eqn. 5.12, where the titration product is AB , the mixing volume V, the original concentration of A in the sample Cl and the titrant concentration CB, can be calculated. In the experiments in Fig. 5.17 the sample volume was 200/d and/ = 0.84 ml min-1 by... 

Osmond, J. K., Kaufman, M. I., Cowart, J. B., Mixing volume calculations, sources and aging trends of Floridan aquifer water by uranium isotopic methods, Geochim. et Cosmochim. Acta, 38, 1083-1100 (1974). 

The reactor was preceded by a preheater which had a sufficiently small mixing volume so that it did not contribute significantly to the dispersion of the feedstream pulses. 

For gradient applications at low flow rates (<0.2mL/min), piston size and mixing volumes of the LC pumps can be the limiting factors. Use specialized pumps for microbore and capillary columns (see the pump section of Chapter 3). 

One might intuitively expect that infinite recycle rates associated with a system as described by eqn. (61) would produce a completely well-mixed volume with concentration independent of location. This is indeed so and under these conditions, the performance tends to that of an equal sized CSTR. At the other extreme, when R is zero, PFR performance pertains. Fractional conversions at intermediate values of R may be determined from Fig. 14. The specific form of recycle model considered is thus seen to be continuously flexible in describing flow mixing between the PFR and CSTR extremes just as was the tanks-in-series model. The mean and variance of this model are given by eqns. (62) and (63) and these may be used for moments matching purposes of the type illustrated in Example 6. 

The electrolyte composition and pH should not be too detrimental. Aspects such as pressure, temperature, and injection technique may have an influence. Concerning the interface, the sheath flow should be optimized with respect to composition, pH, and flow rate. Furthermore, the positions of the fused-silica capillary as well as the API probe need to be carefully optimized. The mixing volume at the tip of the capillary must be kept at a minimum to avoid postcolumn band broadening caused by diffusion. 

Box 23.1 Linear One-Box Model for Well-Mixed Volumes of Ponds, Lakes, and Oceans... 

The mobility of lattice oxide ion was evaluated by the complete mixing volume of lattice oxide ion according to the method proposed by Keulks and co-workers (30). By assuming the 180 concentration of lattice oxide ions in a dilution volume of catalyst is equal to that in oxidized products in the reaction at a given time, the complete mixing volume can be calculated from the results of l8C>2 tracer experiments by the following ... 

In this equation (1), A is the total amount of molecular oxygen consumed in the reaction until a given time and V is the complete mixing volume. Equation (1) is rewritten as... 

Thus, when the residence time ta , is sufficiently large relative to the appropriate time scale of the reaction, t1/2, the time-invariant condition of the well-mixed volume considered approaches chemical equilibrium. 

Mix 0.15 mL of 0.5 mg/mL solution of antigen with 0.15 appropriate adjuvant and mix (volumes based on group of three mice). 

The mixing volume of the capillary-in-capillary mixer is adjustable and can be controlled automatically, i.e. it is not necessary to have a set of various capillaries and to exchange them to match the single conditions of each new experiment [133],... 

Inner and outer diameters of large capillary 182 pm, 356 pm Mixing volume and dead (mixing) time 2 nl, 8 ms... 

The main effect of the presence of gases and vapors in the reactor head is the relevance of an additional variable, the pressure. In a simple mathematical model, each phase may be described as a well-mixed volume (even if no mechanical stirrer is present in the gaseous phase), and it is also possible to consider thermal and mechanical equilibrium between the phases, i.e., to set equal values of temperature and pressure in the two phases. 

FIGURE 3-5. Example of mixing volume due to cavities, (a) Creation of cavity due to mismatched fitting. The gap results from inserting, into a deep port, a tube that was originally made up in a shallow port. The scale drawing shows a 1/16 in. OD x 0.0010 in. ID tube and a 0.090 in. gap, creating a 4.5-jaL cavity, (b) Creation of cavity due to trapped particle and tube end which is not cut square. This represents a 1/16-in. tube, a bore of 0.010 in. ID, a port bore of 0.013 in., and a cavity volume of about 0.6 /xL. (Reproduced with permission of Rheodyne.)... 

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