Lateral mixing of solids

Lateral Mixing of Solids in Gas Solid Fluidized Beds... 

The lateral mixing of particles in gas solid fluidized beds is induced by bubble movement through the bed, bubble bursting at the bed surfaee, and gross particle circulation inside the bed. Through the random walk theory, Kunii and Levenspiel (1969) have derived an equation for the lateral dispersion eoeflieient, for lateral mixing of solids in gas olid fluidized beds ... 

The lateral particle dispersion coefficient was also studied by Shi and Fan (1984) and Subbarao et al. (1985). A one-dimensional diffusion model was used by Shi and Fan (1984) to characterize lateral mixing of solids. Through dimensional analysis and nonlinear regression analysis of the literature data, they arrived at an equation for the lateral dispersion coefficient for general application. 

Shi YF, Fan LT. Lateral mixing of solids in batch gas-solids fluidized beds. Ind Eng Chem Process Des Dev 23 337-341, 1984. 

The bubbles exert a very strong influence on the flow pattern in the bed and provide the mechanisim for the high degree of mixing of solids which occurs. The properties and behaviour of the bubbles are describe later in this Section. 

The theoretical derivation of these results is based on component particles which vary in size, shape, and density. This condition is not encountered in the practical mixing of solids and, as described later, any of these factors may prevent the formation of a random mixture. The value of the number of particles per sample derived in any example must therefore be raised if the limits given are to be maintained. 

Shallow bed model. Fan and coworkers (87,88) have treated the case of shallow reactors (bed height low relative to diameter or length for rectangular vessels). While mixing is rapid in the vertical direction, it tends to be limited in the lateral direction so that the residence time distribution for solids can differ considerably from the perfect mixing assumption adopted in most of the models covered in Sections 7.1 and 7.2. Lateral mixing of both solids and gas is described in terms of lateral dispersion coefficients. Unsteady state terms are retained in order to provide dynamic solutions. In other respects the models are "conventional in their treatment of two phases (bubbles and dense phase). It is shown that lateral... 

We will see later that this same equation applies to the mixing of liquids or solids when ideal solutions form. 

Diffusion flames can best be described as the combustion state controlled by mixing phenomena—that is, the diffusion of fuel into oxidizer, or vice versa—until some flammable mixture ratio is reached. According to the flow state of the individual diffusing species, the situation may be either laminar or turbulent. It will be shown later that gaseous diffusion flames exist, that liquid burning proceeds by a diffusion mechanism, and that the combustion of solids and some solid propellants falls in this category as well. 

Different household liquids can be tested such as ammonia, vinegar, tap water, lemon juice, and Sprite. Items such as orange juice that possess a characteristic color should be diluted and then tested. Diluted solutions of solids like dishwasher soap, cream of tartar, and baking soda can also be made. The indicator can be frozen or mixed with alcohol to preserve for later use. 

For the values selected above B is 1.4 to 2.1 m. This estimate agrees with current commercial practice of spacing feed points at intervals of 1 to 3 m. For our test case, this corresponds to one coal feed point for every 1.8 to 4 MW, or approximately 25 to 55 feed points. The requirement for a large number of feedpoints is one of the shortcomings of AFBC s. Methods of overcoming the problem of multiple feed points include the use of a spreader-stoker to distribute the coal evenly over the surface of the bed or the promotion of lateral mixing by recirculating bed solids. 

Properties of a° (pH) curves are basic elements in the Interpretation of more complicated systems involving oxides. One of these is the adsorption of hydrolyzable ions (Cd, Al, etc.) or anions that themselves can be titrated (HPO, etc.). In sec. 3.14 some of the relevant applications will be discussed. Another application is that of mixed oxides. The systems include mechanically mixed pure oxides and mixed crystals (such as spinels and ferrites). A number of authors have studied such mixed oxides, thereby reporting the variation of the pH° as a function of the mole fraction of the solid. Sometimes linearity was found, sometimes not. No genered rules can be given. The surface composition is not necessarily identical to that of the bulk, molecules of one oxide may leach and adsorb onto the other and lateral interactions of surface groups of the two constituents affect their pK s and pK s. Mixed oxides are important for a number of technical applications (heterogeneous catalysts with special properties, components of batteries) and also occur in clay minerals, the topic of the following subsection. 

The volume changes on mixing non-aqueous liquids, the densities of mixed liquids, of solutions of non-polar solutes in non-polar solvents, and the changes of total volume on the solution of solid salts in water, noticed at an early period and much investigated, can only be mentioned here some aspects of these will be dealt with later. Hyde found the densities of solutions of jp-nitrotoluene in carbon disulphide smaller than the density of either component, but the anomaly disappears if the p-nitrotoluene is supposed to be in the liquid state. Biron found that the volume change on mixing two liquids was Av=kx( —x where x , (1— ) are the mol fractions, and he investigated the effect of pressure on the value of Av. The apparent specific volume of alcohol in aqueous mixtures was determined by Brown, lo... 

In the actual bed, solid exchange between the ascending and descending zone is significant, and the circulation is seen as a series combination of localized recirculation. If this scheme of solid mixing is more realistic, the temperature profile may be suitably expressed in terms of an effective thermal diffusivity, which will be used later for discussion of instability in the dilute phase. 

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