Unmixing

It has been found that x is directly proportional to where M is the molecular weight. It should be noted that we are here extrapolating from solution to a concentrated dough system. However, the general behavior is thought to be analogous. 

An equation to describe the tensile strength of polymers was introduced by Flory (1945)  

Oq = limiting tensile strength (the value reached at very high M ) 

= number-average molecular weight of the polymer Mj = a threshold molecular weight 

This equation has been found to hold well for polymers with a narrow range of MWs. However, for polymers with a high degree of polydis-persity, the relationship breaks down. Bersted and Anderson (1990) have proposed a modified Flory equation that predicts the tensile strength of polydispersed polymers quite well  

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The binary polymer blend exliibits a second-order unmixing transition. Close to the critical temperature the... 

We conclude that in the presence of electromagnetic fields the components remain unmixed, correct to the order 0(1 /c). 

In the case of unmixed vapors between the plates, the equations, being implicit in Ey, have also been solved numerically (112). The results depend on the arrangement of the downcomers and are not too different numerically from equation 93. In reaHty, however, the Hquid is neither completely backmixed nor can the tray be considered as a plug-flow device. 

Fig. 3. Comparison of flux for an aromatic polyamide (FT30-BW) membrane for (---) mixed and (-----) unmixed solutions of CaSO, where the initial...

Subsection B This subsection contains rules pertaining to the methods of fabrication of pressure vessels. Part UW is applicable to welded vessels. Service restric tions are defined. Lethal service is for lethal substances, which are defined as poisonous gases or liquids of such a nature that a very small amount of the gas or the vapor of the liquid mixed or unmixed with air is dangerous to life when inhaled. It is stated that it is the user s responsibility to advise the designer or manufacturer if the service is lethal. All vessels in lethal service shall have all butt-welded joints fully radiographed, and when practical, joints shall be butt-welded. All vessels fabricated of carbon or low-aUoy steel shall be postweld-heat-treated. 

Gas unmixed liquid flows in the same direction on successive plates. 

Equation (22-106) gives a permeate concentration as a function of the feed concentration at a stage cut, 0 = 0, To calculate permeate composition as a function of 0, the equation may be used iteratively if the permeate is unmixed, such as would apply in a test cell. The calculation for real devices must take into account the fact that the driving force is variable due to changes on both sides of the membrane, as partial pressure is a point function, nowhere constant. Using the same caveat, permeation rates may be calciilated component by component using Eq. (22-98) and permeance values. For any real device, both concentration and permeation require iterative calculations dependent on module geometiy. 

Figure 3-17. LMTD correcHon foctors 1-pass, cross-flow bol+i fluids unmixed. (From Gas Processors Suppliers Association, Engineering Data Book, 9th Edition.)...

Entmilzung, /. splenectomy, entmischen, v.t. i. separate into component parts, disintegrate, decompose, dissociate, segregate, unmix demulsify. 

Jamieson and McNeill [142] studied the degradation of poIy(vinyI acetate) and poly(vinyI chloride) and compared it with the degradation of PVC/PVAc blend. For the unmixed situation, hydrogen chloride evolution from PVC started at a lower temperature and a faster rate than acetic acid from PVAc. For the blend, acetic acid production began concurrently with dehydrochlorination. But the dehydrochlorination rate maximum occurred earlier than in the previous case indicating that both polymers were destabilized. This is a direct proof of the intermolecular nature of the destabilizing effect of acetate groups on chlorine atoms in PVC. The effects observed by Jamieson and McNeill were explained in terms of acid catalysis. Hydrochloric acid produced in the PVC phase diffused into the PVAc phase to catalyze the loss of acetic acid and vice-versa. 

Specializing to symmetrical mixtures (Na = Nb = N) for simplicity, it is easy to also find the order parameter i ocx of the unmixing transition... 

Diffusion Flame. Wlien the fuel and oxidizer are initially unmixed and then mix in a thin region where the flame is located, the flame is called a diffusion flame (Figure 2). The word diffusion is used to describe the flame because the fuel and oxidizer are mixed on the molecular level by the random thermal motion of the molecules. An example of a diffusion flame is a candle flame or flares at an oil refinei y. 

From Figure 8-31 the effect of mixed and unmixed pools of liquid can be noted. For a completely mixed tray, there is no concentration gradient from inlet to outlet, and therefore the entire tray has a uniform composition. The degree of mixing across the tray as determined by the number of discrete mixing pools on the tray has an effect on the relationship between Eqg E y as a function of X. 

Determine LMTD if flows are counterflow and apply the correction factor of Bowman et al, established for this type of unmixed shell-side flow (Figure 10-129). ... 

MTD CORREaiON FACTORS 1 PASS-CROSS FLOW BOTH FLUIDS UNMIXED... 

Now suppose we have the gases Gb G2,. . G in the amounts specified at the beginning of this section, all at the same temperature T, separately confined in vessels of volumes Vi, V2,. . V , respectively. If we add together the free energies of the separate gases, the sum may be called the free energy of tlic unmixed gases. Thus ... 

Further, if Uo, U are the total intrinsic energies of the unmixed and mixed gases, respectively then ( 58) ... 

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