Method 284 dilute phase

Figure 8.3b shows that phase separation in polymer mixtures results in two solution phases which are both dilute with respect to solute. Even the relatively more concentrated phase is only 10-20% by volume in polymer, while the more dilute phase is nearly pure solvent. The important thing to remember from both the theoretical and experimental curves of Fig. 8.3 is that both of the phases which separate contain some polymer. If it is the polymer-rich or precipitated phase that is subjected to further work-up, the method is called fractional precipitation. If the polymer-poor phase is the focus of attention, the method... 

The new pressure loss equation presented here is based on determining two parameters the velocity difference between gas and conveyed material and the falling velocity of the material. The advantage of this method is that no additional pressure loss coefficient is needed. The two parameters are physically clear and they are quite easily modeled for different cases by theoretical considerations, which makes the method reliable and applicable to various ap>-plications. The new calculation method presented here can be applied to cases where solids are conveyed in an apparently uniform suspension in a so-called lean or dilute-phase flow. 

This phenomenon can be exploited for separation and concentration of solutes. If one solute has certain affinity for the micellar entity in solution then, by altering the conditions of the solution to ensure separation of the micellar solution into two phases, it is possible to separate and concentrate the solute in the surfactant-rich phase. This technique is known as cloud point extraction (CPE) or micelle-mediated extraction (ME). The ratio of the concentrations of the solute in the surfactant-rich phase to that in the dilute phase can exceed 500 with phase volume ratios exceeding 20, which indicates the high efficiency of this technique. Moreover, the surfactant-rich phase is compatible with the micellar and aqueous-organic mobile phases in liquid chromatography and thus facilitates the determination of chemical species by different analytical methods [104]. 

The phase equilibrium between a liquid and a gas can be computed by the Gibbs ensemble Monte Carlo method. We create two boxes, where the first box represents the dense phase and the second one represents the dilute phase. Each particle in the boxes experiences a Lennard-Jones potential from all the other particles. Three types of motion will be conducted at random the first one is particle translational movement in each box, the second one is moving a small volume from one box and adding to the other box, the third one is removing a particle from one box and inserting in the other box. After many such moves, the two boxes reach equilibrium with one another, with the same temperature and pressure, and we can compute their densities. 

As mentioned previously, Bibette [95] has developed a very elegant method for the purification of coarse, polydisperse emulsions to produce monodisperse systems. This technique is based on the attractive depletion interaction between dispersed phase droplets, caused by an excess of surfactant micelles in the continuous phase. A phase separation occurs under gravity, between a cream layer and a dilute phase since the extent of the separation increases with increasing droplet diameter, a separation based on size occurs. By repeating this process, emulsions of very narrow size distribution can be produced. 

Three types of theoretical approaches can be used for modeling the gas-particles flows in the pneumatic dryers, namely Two-Fluid Theory [1], Eulerian-Granular [2] and the Discrete Element Method [3]. Traditionally the Two-Fluid Theory was used to model dilute phase flow. In this theory, the solid phase is being considering as a pseudo-fluid. It is assumed that both phases are occupying every point of the computational domain with its own volume fraction. Thus, macroscopic balance equations of mass, momentum and energy for both the gas and the solid... 

A common feature of all models for the upper part of circulating fluidized beds is the description of the mass exchange between dense phase and dilute phase. Analogously to low-velocity fluidized beds, the product of the local specific mass-transfer area a and the mass-transfer coefficient k may be used for this purpose. Many different methods for determining values for these important variables have been reported, such as tracer gas backmixing experiments [112], non-steady-state tracer gas experiments [117], model reactions [115], and theoretical calculations [114],... 

The standard addition method was also applied to the extracted micellar layers containing iron(III). The results obtained with both procedures were found in good agreement, as well as which obtained from DC-plasma spectrometry after analysis of the aqueous dilute phases. 

The weight of catalyst in a vessel is determined by measuring the pressure differential between taps installed at the top and bottom. Density of the fluidized catalyst is determined in a similar manner from the differential pressure between taps located a measured distance apart in the dense phase. Location of the catalyst level can be determined from the combination of the density and the total weight of catalyst, or by the use of a series of pressure taps placed at intervals along the height of the vessel. A hot-wire probe has been used to locate the level in laboratory fluidized beds (250), but this technique has not been adopted for fluid cracking units. The method depends upon the fact that heat-transfer rate from the heated wire is much higher when immersed in the dense phase of fluidized solids than when in the dilute phase. 

Indirect ISE methods dilute the sample in a diluent of fixed high ionic strength so that for Na, the activity coefficient approaches a value of 1. Under these circumstances, the measurement of activity, a (where a = y x concentration, and y is the activity coefficient), is tantamount to measurement of concentration. Flame photometry measures emission of a specific ion after dilution in solutions of high reference ion concentration so that specific emission is also tantamount to the measurement of concentration of the specific ion in total plasma volume. It is the dilution of total plasma volume and the assumption that plasma water volume is constant that render both indirect ISE and flame photometry methods equally subject to the electrolyte exclusion effect. In certain settings, such as ketoacidosis with severe hyperlipidemia or multiple myeloma with severe hyperproteinemia, the negative exclusion effect may be so large that laboratory results lead clinicians to believe that electrolyte concentrations are normal or low when, in fact, the concentration in the water phase may be high or normal, respectively. 

Cyclic peptides have been prepared entirely in solution or by assembling the linear precursor following a solid-phase approach, cleaving the peptide from the resin, and cyclizing in solution. Despite efforts to develop practical and convenient methods, solution-phase methodologies suffer from several drawbacks, such as cyclodimerizations and cyclo-oligomerization side reactions, which may occur even at high dilutions. 

The prevalidation phase may be regarded as a method optimization phase where the calibration model is confirmed range, LLOQ, and ULOQ are defined and matrix interference is evaluated. The use of anchor points for the calibration curve may be feasible. As mentioned above, determination of the LLOQ may be difficult because of the presence of the endogenous analyte. Dilutional linearity may be evaluated as well. It is also considered useful to assess the biomarker in healthy and diseased individuals. For this purpose, at least 25 individuals should be tested [9] to account for intrasubject variability caused by circadian and seasonal fluctuations and intersubject variability. 

As stated earlier, dilute-phase conveying is the commonly employed method for transporting a wide variety of suspended solids using air flowing axially along a pipeline. The method is mainly characterized by the low solids to air... 

Concentration and separation of dyes in nonionic surfactant anploying a cloud point technique has been explored by Tatara et al. (2(X)4). The researchers used oxyethylated nonionic surfactants and investigated their potential to separate two direct dyes and one basic dye for recovery. It was found that the method had some potential however, separation occurred slowly by accumulation of the organic solute in the surfactant-rich phase. Both surfactant and dye as well as other reaction parameters had to be selected appropriately for reasonable results. Cloud point extraction was also explored by Purkait et al. (2(X)4) for the direct dye Congo Red. Nonionic surfactant was used and recovered from the dilute phase by solvent extraction with heptane. 

Vapour pressure depression and membrane osmometry are the most common methods to determine the polyer-solvent interaction parameter. The latter method will be described briefly. In a membrane osmometer a dilute polymer solution has been separated from pure solvent by means of a membrane. The membrane is penneable for solvent molecules but not for polymer molecules. Due to a chemical potential difference solvent molecules will diffuse from the diluted phase to the concentrated phase and this results in a pressure increase which is called the osmotic pressure ti (see also section VI - 2 for a more detaUed description of osmosis). The osmotic pressure is given by... 

Typical dilute phase systems are shown in Figures 8.5 and 8.6. Blowers are normally of the positive displacement type which may or may not have speed control in order to vary volume flow rate. Rotary airlocks enable solids to be fed at a controlled rate into the air stream against the air pressure. Screw feeders are frequently used to transfer solids. Cyclone separators (see Chapter 9) are used to recover the solids from the gas stream at the receiving end of the transport line. Filters of various types and with various methods of solids recovery are used to clean up the transport gas before discharge or recycle. 

Here Cdc and represent the drag coefficient and superficial shp velocity for particles inside the dense phase k, respectively. With these relations, one can determine all the superficial sHp velocities of each dense phase and the superficial fluid velocities of the dilute and dense phases by using binary search method. Then, each particle in the dense phase k experiences two drag components, one suffering from the fluid in the dense phase and the other from the dilute phase as a whole and equally distributed over each particle in the dense phase. So, the drag force acting on each particle in the dense phase is... 

However, when a number of these so-called pulai methods were applied by the author to fairly ordinary and typical dilute-phase systmns (e.g. transporting poly pellets and wheat), an unexpectedly wide range of scatter of results was obtained. Consequendy, it was considered necessary to carry out sensitivity analyses and also address particular areas of concern (e.g. detinitions, limitations, measurement techniques). The findmgs from this study have been published by Wypych [5], but have been extended to include more recent modeb, some examples being presented in Figs. 7 and 8. 

Spencer developed a method for evaluating the distribution from the experimental data obtained with his summative fractionation procedure. His method is bsised on the assumption that the separation according to molecular weight is ideally sharp, i.e. all molecules above a given size are present in the concentrated phase, whereas shorter chains are confined to the dilute phase. This assumption cannot be reconciled with the actual situation, as was pointed out by Billmeyer eind Stock-MAYER (69). 

---