Solution perfect mixed

If perfect mixing occurs in each stage and the solute is not adsorbed preferentially at the surface of the sohd, then the concentration of the solution in the underflow is the same as that in the overflow and... 

Solution Both phases are assumed to be perfectly mixed so that (flg)o j is just ag. Equation (11.13) provides the material balance for component A in the liquid phase ... 

The principle of the perfectly-mixed stirred tank has been discussed previously in Sec. 1.2.2, and this provides essential building block for modelling applications. In this section, the concept is applied to tank type reactor systems and stagewise mass transfer applications, such that the resulting model equations often appear in the form of linked sets of first-order difference differential equations. Solution by digital simulation works well for small problems, in which the number of equations are relatively small and where the problem is not compounded by stiffness or by the need for iterative procedures. For these reasons, the dynamic modelling of the continuous distillation columns in this section is intended only as a demonstration of method, rather than as a realistic attempt at solution. For the solution of complex distillation problems, the reader is referred to commercial dynamic simulation packages. 

Note that when k] = k.2 = k3 = 0, Cao = 1> Cbo = 0- the program solves the case of a step input of tracer solution, which can be used to generate the typical F-diagram for a single perfectly mixed tank. Compare this result with the analytical solution. 

In the following example, a solid consisting of a soluble constituent A and an insoluble constituent B is considered. Leaching is carried out with a pure solvent S and a solution is produced containing a mass a of A, per unit mass of S and the total mass of A in solution is P. It will be assumed that the quantity of solvent removed in the underflow from each of the thickeners is the same, and that this is independent of the concentration of the solution in that thickener. It will be assumed that unit mass of the insoluble material B removes a mass s of solvent S in association with it. Perfect mixing in each thickener will be assumed and any adsorption of solute on the surface of the insoluble solid will be neglected. In a given thickener, therefore, the ratio of solute to solvent will be the same in the underflow as in the overflow. 

This temperature may be expected to be the lowest that can be reached through a solution procedure where perfect mixing of all three cations together has been achieved. Indeed, this is the synthesis temperature used by Horowitz et al. in their precipitation method using hyponitrites (16). 

A perfectly mixed vessel therefore can be considered as a batch vessel during the time required for the bubbles to sweep the vessel contents exactly once (i.c., up to /, = l/ 2 ). The definition of the singlebubble collection efficiency ( ) requires that the observed removal efficiency ( ) should equal after one bubble sweep. This assumes that all the oil drops that collide with a bubble stick to it. The solution of the First-order rate equation for a batch vessel for /j l/ 2 and ( = R yields ... 

Harris and Dranoff [115] appear to have been the first to use the LSPP model to study the performance of a photochemical reactor for scale-up purposes. Experimentally, two sizes of perfectly mixed photochemical reactor were used for the decomposition of hexachloroplatinic acid in dilute aqueous solution, and the result of the theoretical analysis was acceptable in comparison with the experimental data. 

Note that the concept of transport tayer can be extended to other transport modes such as convection. Indeed, in the presence of convection, this concept is associated with the simpie idea that the solution can be divided into two parts, a thin layer close to the electrode surface with only diffusion, on the one hand, and the bulk solution where the stirring ensures a perfect mixing, and therefore uniform concentration, on the other [52]. 

Assuming perfect mixing in each compartment of the membrane pack and reservoir of the ED unit shown in Figure 9, the solute concentration in any of them is uniform and equal to that of the outlet stream. Therefore, by assuming pseudo-steady state conditions in any compartment, the differential solute and water mass balances in the diluted (D) and concentrated (C) reservoirs can be written as follows ... 

To analyze data using these two methods one must make two assumptions (1) that a sorptive entering the chamber can either be sorbed or remain in solution, and (2) the sample is perfectly mixed i.e., the concentration in the mixing chamber equals the effluent concentrations. With these assumptions, one can then develop an equation for mass balance which can be used to analyze time-dependent data using a continuous flow method (Skopp and McAllister, 1986) ... 

In the next two chapters of this book we turn to the chemical reactor that is probably the most challenging the tubular or plug flow reactor. The inherent distributed nature of the unit (variables change with axial and radial position) gives rise to complex behavior, which is often counterintuitive and difficult to explain. The increase in the number of independent variables makes the development and solution of mathematical models more complex compared to the perfectly mixed CSTR and batch reactor. 

Bader et al. (1988) used common salt as a solid tracer, which was injected into a flowing catalyst bed. Solids samples, withdrawn downstream of tracer injection, were leached with water and the salt concentration determined by electrical conductivity of the solution. Their results indicated substantial solids backmixing. Li et al. (1991) observed solids mixing in a fast fluidized bed combustor by using raw coal as a tracer, which was injected into the ash bed. Their results also showed that near-perfect mixing prevailed. Similar experiments was also conducted by Chesonis et al. (1991) in a cold model. 

The reactor may be considered perfectly mixed, so that the contents are uniform and the concentration of A in the product stream equals that inside the tank. The tank is initially filled with a solution that contains 2.00 mol A/L, and the inlet and outlet flows then begin. 

Ninety kilograms of sodium nitrate is dissolved in UO kg of water. When the dissolution is complete (at time t = 0), pure water is fed to the tank at a constant rale m(kg/rnin), and solution is withdrawn from the tank at the same rate. The tank may be considered perfectly mixed. 

A 2000-liter tank initially contains 400 liters of pure water. Beginning at t = 0. an aqueous solution containing 1.00 g/L of potassium chloride flows into the tank at a rate of 8.00 L/s and an outlet stream simultaneously starts flowing at a rate of 4.00 L/s. The contents of the lank are perfectly mixed, and the density of the feed stream and of the tank solution. p(g/L), may be considered constant. Let V(r) L) denote the volume of the tank contents and C(/)(g/L) the concentration of potassium chloride in the tank contents and outlet stream. 

Since complete mixing is assumed in a cell, the mole fraction of a solute in an out-going stream from the nth cell is If the bed is viewed as a series of n perfect mixing cells each having surface area Ap/n and constant mass transfer coefficient ky, then for the steady-state mass transfer the material balance gives... 

---