Complete mixing in the liquid

In considering the case of maximum release, it is apparent that complete mixing in the liquid phase will lead to a greater release rate than that expected in cases where diffusion operates in two phases. Therefore, consider the case where both the solvent (Na) and the solute (volatile fission product) diffuse through a gas layer of constant thickness. It follows from the solution to Fick s law with appropriate boundary conditions that... 

Assuming that there is thermodynamic equilibrium at the solid/liquid interface, no diffusion of impurities in solid, and complete mixing in the liquid,... 

For steady-state conditions and the assumptions of plug flow in the gas phase and complete mixing in the liquid phase, one can write the mass balance for reactant at any point in the reactor as... 

The above treatment assumes that solute mixing in the liquid is the result of diffusion only. It can be modified to allow for partial or complete mixing in the liquid (see Chalmers In these circumstances long-range segregation will still occm. 

The Solute Distribution in a Bar Solidified under Conditions of Complete Mixing in the Liquid... 

Partial mutual solubility in the solid state. Fig. 2.9 shows different examples of binary systems for which there is still a complete miscibility in the liquid state, but only a limited mutual solubility in the solid state, depending on the temperature. The Ni-Au system, for instance, still has complete mutual solid solubility but only at high temperature, that is, by decreasing the temperature, de-mixing... 

Other uranium binary systems de-mixing in the liquid state are U-Pb and U-Bi and several uranium-lanthanides systems which are characterized by nearly complete immiscibility in the liquid and solid state. 

This analysis refers to a small area for vertical flow, and Emv is therefore the point or local Murphree efficiency. The relation between this point efficiency and the tray efficiency depends on the nature of the liquid mixing on the tray. If there is complete mixing of the liquid, x = xn for the liquid, and ye and y will also be constant over a horizontal plane. The tray efficiency EMv = Emv. With no mixing of the liquid, the liquid may be considered to be in plug flow. If ye = mx + b and Emv is taken as constant over tray, it may be shown" 91 that ... 

The two liquid phases are completely mixed in the agitated sections, but in the last section the two phases are allowed to separate so that the acid can be recycled and the hydrocarbon phase sent off to a distillation column for separation. 

At a specified point in the tank, 100 cm of hydrochloric acid 1.2N(Cg0 = 0.83 moles. m- after complete mixing in the tank in the absence of reaction) were injected by means of a cylinder obturated at its lower end by an elastic membrane which becomes inflated and bursts out when submitted to the pressure of the liquid pushed by a piston. The acid was thus injected without any preferential direction. This locally released acid B triggers reactions f2j and 3]. If the local micromixing state is perfect, the acid is totally and instantaneously neutralized, as it is in stoichiometric defect with respect to A. The first reaction being very fast as compared to the second one, the precipitate S does not appear. Conversely, if mixing of the acid is not instantaneously... 

Let us consider a system of c components and suppose first that these components are completely miscible in the liquid state, but completely immiscible in the solid state. On freezing, the solution yields various crystals each variety of which consists of a single constituent, since the formation of mixed crystals is excluded. The co-existence curve of the solution with crystals of component 1 is given by (18.21) ... 

If the liquid is completely mixed in the horizontal direction (a reasonable approximation for small diameter columns) then the tray efficiency and the point efficiency are one and the same (all points being equal as it were) and = E y... 

C. Equilibrium between Solid and Liquid Phases only. I. The Components are Completely Miscible in the Liquid State. a) The pure components only occur as solid phases. Polymorphism of components. Determination of the equilibrium curve. Example, b) Compounds are formed with a congruent meltings point. The indifferent point. Determination of the composition of a compound by thermal analysis. Examples, (c) Compounds are formed with an %ncongruent melting-point. Determination of the composition of the coinpound by thermal analysis. Example. (d) Solid solutions or " mixed crystals are formed, i) The two components can form an unbroken series of solid solutions. Examples. Melting-point curve. Example. Fractional crystallisation of solid solutions, h) The two components do not form a continuous series of solid solutions. Examples. Changes in solid solutions with the temperature. II. The Components are not Completely Miscible in the Liquid State. Suspended transformation. 

The description of phase equilibria makes use of the partial molar free enthalpies, i, called also chemical potentials. For one-component phase equilibria the same formalism is used, just that the enthalpies, G, can be used directly. The first case treated is the freezing point lowering of component 1 (solvent) due to the presence of a component 2 (solute). It is assumed that there is complete solubility in the liquid phase (solution, s) and no solubility in the crystalline phase (c). The chemical potentials of the solvent in solution, crystals, and in the pure liquid (o) are shown in Fig. 2.26. At equilibrium, ft of component 1 must be equal in both phases as shown by Eq. (1). A similar set of equations can be written for component 2. By subtracting j,i° from both sides of Eq. (1), the more easily discussed mixing (left-hand side, LHS) and crystallization (right-hand side, RHS) are equated as Eq. (2). 

Components A and B in Figure 17.12, on the other hand, behave differently. Liquid A and liquid B still mix to form a homogeneous solution, but when solid A and solid B are mixed together, they dissolve into one another to a limited extent. Salt will dissolve into water, but not without limit - it will dissolve only until the water becomes saturated. Similarly, solid B will dissolve into solid A, but not without limit. It dissolves into A until A is saturated with B, and at the same time A dissolves into B until B is saturated with A. The saturation limits of each component in the other is shown by a line called the solvus. The existence of a solvus shows that A and B exhibit limited miscibility in the solid state. They exhibit complete miscibility in the liquid state. Miscibility does not really mean mixability, although they sound similar. MixabiUty, if it is a word, just means things can be mixed together - mutual dissolution is not implied. Miscibility means the ability to dissolve into something else. 

Since complete liquid mixing occurred in the columns of Sellers and Augood, and since their data fit those of t ie pilot plant column, the case for complete mixing in the pilot plant column is reinforced. In these instances, the efficiencies measured would correspond to values of. Figures illustrates this argument. 

The perfect mixing assumption in a void is well understood for gas phase turbulent flow. In the liquid phase, however, a small number of diffusivities may retard complete mixing in the void and a higher Re of... 

The total volume gas and liquid is 7.38 m —only slightly more than in the stirred case, whereas (Gi)out is even lower. This is easily explained on the basis of the model, which assumes plug flow for the gas in the nonstirred case, against complete mixing in the stirred case. Some design aspects of a continuous stirred tank for the liquid-phase oxidation of toluene into phenol have been discussed by van Dierendonck et al. [ 1974]. ... 

Assuming (1) complete mixing in the gas and liquid phase, (2) constant gas flow rate, (3) absorption with slow reaction and (4) neglecting convective transport of A (ul (c/ lo " c/ l) 0) the following relation between the conversion of A and B can be derived... 

Mixtures of at least two components with a defined mix ratio, which are completely immiscible in the solid state and completely miscible in the liquid state, are called eutectic . The eutectic mix ratio is defined by the minimum melting point of all possible mixtures (combinations) of the components. It means in practice that at temperatures exceeding the eutectic one at least a part of the mixture is liquid. In the solid state the eutectic is a mixture of finely divided tiny crystals of in most cases two different compositions. 

Case (4) Liquid on the plate is completely mixed in the direction of flow and is at steady state. Therefore, the local vapor-liquid mass-transfer efficiency controls the stage efliciency use equation (8.3.14). We will treat this case first however, before we do, we look at local mass transfer. 

Fig. 4.11 Concentration-distance profiles for a bar solidified under conditions of complete solute mixing in the liquid.

Fig. 4.13 Solute (lisu ibutions in a solid bar frozen from liquid of initial concentration Co, for (a)equiUbrium freezing (h). white mixing in the liquid by diffusion only (c) complete solute mixing in the liquid (rf) partial solute mixing in the...

In Chapter 4 it was stated that the solute profile in a bar solidified direetionally with complete solute mixing in the liquid was given by... 

These contaminants may be rigid or deformable solids, when they can be separated by a filter, or perhaps by a sedimentation process. Distinct liquid droplet contaminants can also be removed in this way, using filter-like separators or sedimentation. As indicated in Section lA, where these contaminants are completely mixed in the carrying fluid (gas dispersed in a gas, liquid dissolved in another liquid), then filtration or sedimentation are not suitable for their separation, and phase change processes such as adsorption (e.g. with activated carbon, or perhaps molecular sieves) must be used. The middle ground is occupied by some solid/liq-uid or liquid/liquid solutions whose value is such as to justify purifying by means of a membrane separation process. 

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