Dispersion of the solids phase

The modeling of solid-liquid mixing requires an additional equation to predict the dispersion of the solid phase in the vessel. As mentioned before, the net-work-of-zones approach was used in this work, which is based on unsteady mass balances on the solid phase carried out on a set of cells. In the literature, such mass balances are predominantly made on regular cells (finite volumes) in structured grids. The cells typically consist of quadrangles in 2-D and hexahedra in 3-D. In the present work, due to the use of unstructured... 

This method is also referred to as the miscible-displacement or continuous-flow method. In this method a thin disk of dispersed solid phase is deposited on a porous membrane and placed in a holder. A pump is used to maintain a constant flow velocity of solution through the thin disk and a fraction collector is used to collect effluent aliquots. A diagram of the basic experimental setup is shown in Fig. 2-6. A thin disk is used in an attempt to minimize diffusion resistances in the solid phase. Disk thickness, disk hydraulic conductivity, and membrane permeability determine the range of flow velocities that are achievable. Dispersion of the solid phase is necessary so that the transit time for a solute molecule is the same at all points in the disk. However, the presence of varying particle sizes and hence pore sizes may produce nonuniform solute transit times (Skopp and McCallister, 1986). This is more likely to occur with whole soils than with clay-sized particles of soil constituents. Typically, 1- or 2-g samples are used in kinetic studies on soils with the thin disk method, but disk thicknesses have not been measured. In their study of the kinetics of phosphate and silicate retention by goethite, Miller et al. (1989) estimated the thickness of the goethite disk to be 80 /xm. 

Single circulation of the starting reactants in the step of formation of the reaction mixture (method 2) leads to disintegration of neodymium chloride particles to the size characteristic of the suspension formed in 4—5 h of the synthesis by method 1 (Fig. 12.1). With the complexation performed for more than 5 h, the neodymium chloride particle size is about 4 pm irrespective of the synthesis method. Thus, short hydrodynamic action in the turbulent mode on a suspension containing the starting NdClj considerably intensifies the dispersion of the solid phase particles in complexation with the alcohol. 

In what way does the viscosity of dispersion depend on concentration of the solid phase ... 

Two-phased samples, where the components of interest are present in high concentration in the liquid, can often be dealt with by simple filtration as the amount of material adsorbed on the surface of the solid phase, relative to that in the liquid phase is likely to be insignificant. Alternatively if the material is dispersed as a solid throughout the solid phase, then the sample can be filtered and the solid extracted exclusively. 

Stirred tank reactors are employed when it is necessary to handle gas bubbles, solids, or a second liquid suspended in a continuous liquid phase. One often finds that the rates of such reactions are strongly dependent on the degree of dispersion of the second phase, which in turn depends on the level of agitation. 

A common way to evaluate the anisotropy of porous structures requires that the three principal MILs(0, derived from the 3D distribution of the directional MILs(0, square root of the absolute value of the three main eigenvalues (A, B, and C) is defined as the magnitude of the principal MIL(0, supplies information about the dispersion degree of the solid phase around the principal MIL(0, [Pg.251]

As in fluidized bed adsorption, proteins are bound to porous particles as well, these parameters will remain important and must be considered when describing protein adsorption to fluidized beds. As mentioned above, fluidizing the adsorbent allows free movement of the particles within the adsorbent bed, so dispersion in the solid phase is another component determining process performance. 

Eq. (15) and 1.1 10- 7 m2/s according to Eq. (14). This significant difference may be explained by the fact, the Kang et al. used particles of uniform size whereas van der Meer et al. measured dispersion between two fractions of different particle size in a segregated fluidized bed. As adsorption in a frontal mode is performed using classified or otherwise stabilized fluidized beds, the lower Daxp resulting from van der Meer s correlation may be a better description of the solid phase dispersion in a fluidized bed for protein adsorption. 

Most generally during elution, the liquid flow is reversed and the resin bed is therefore packed. In contrast to conventional complex initial feedstock treatments, fluidized-bed processes combine clarification, expressed product specific capture, and concentration into a single step. Residence time distribution analysis showed a small degree of axial dispersion and the generation of a few dozen theoretical plates that are enough for a good efficiency of the capture step. The efficiency of the separation is, however, dependent on the particle size of the solid phase material. 

The pore diffusivity used in this analysis was determined by the Renkin equation4, the axial dispersion coefficient calculated by assuming a constant Peclet number of 0.2, and the mass transfer coefficient from the bulk to the particle surface calculated by the correlation of Wakao and Kaguei. The product of the heat capacity and density of the solid phase was taken to be the same as that used by Raghavan and Ruthven17. The density of the fluid phase was assumed to be that of pure C02 and was calculated from data provided by the Dionix Corporation in their AI-450 SFC software. Constant pressure heat capacities for the mobile phase were also assumed to be that of pure C02 and were taken from Brunner3. 

One method for changing the axial dispersion of the solids or the solids concentration distribution in the three-phase fluidized-bed reactor is to place... 

Ham et al. (1990) used Eqs. (30) and (31) and estimated the values of the solid phase dispersion coefficient using the experimental results on transition in solid-liquid fluidized beds. However, the estimated values of deviate from the experimental values of obtained by Dorgelo et al. (1985). It may be noted that the RTD based experimental values includes gross nonidealities in addition to the turbulent dispersion. 

The assumption of equality of dispersion coefficients of both the phases implies that the root mean square velocity and length scale of turbulence of the gas phase is the same as that of the solid (dispersed) phase. We have taken the length scale of the solid phase to be equal to twice the particle diameter. It is not clear whether the same length scale can be assumed for the gas phase, as the gas phase eddies can be smaller than the particle diameter. Also, the root mean square velocities of both the phases may not be equal. Furthermore, because of the slip velocity, sufficient time may not be available for the local gas phase eddies to be in equilibrium with the dispersed phase eddies. 

Prechilling the emulsion just enough to form a low level of solid fat (0.5-2.5%) followed by homogenization prior to normal processing is said to result in a very fine dispersion of the aqueous phase that obviates the need for preservatives (232). A novel process for forming stable low-fat emulsions of uniform droplet size has... 

Multiple-unit powders for local application are preferably packaged in a dredger or a pressurized container (for skin, teeth, or vaginal douche use). These preparations consist of a dispersion of a solid phase (drug) in a liquid propellant (liquid phase). By action on the actuator, the suspension is released by gas pressure. The propellant in contact with ambient air is evaporated and the powder remains on the treated area. The particle size obtained depends on the powder particle size before the preparation of the suspension. 

Authors indicated that as the descriptors in Eq.(36) refer to particular properties of the solutes, the coefficients in the equation will correspond to specific properties of the solid phase as follows r - refers to the ability of the phase to interact with solute ir- and n-electron pairs s to the phase dipolarity/polarisability a to the phase hydrogen-bond basicity b to the phase acidity, and 1 to the phase lipophilicity. Analysis of these coefficients lead authors to the statement that solute dipolarity/polarisability, hydrogen-bond acidity, and general dispersion interactions influenced adsorption. The examined fullerene was weakly polarisable and had some hydrogen-bond basicity. 

Interest in gas absorption in oil/water dispersions has increased with the emergence of biotechnology, because organic liquids are utilized as carbon sources in different industrial fermentation processes (e.g. paraffins in the fermentation of yeast). A dispersion process in a gas/liquid/liquid (G/I/L) system is involved in the supply of oxygen to such a material system, if biomaterial as an extremely fine dispersion of a solid phase is disregarded. 

The problem appears somewhat more complicated in the case of nanocapsules, where one deals with at least three different structural elements a continuous liquid phase, the solid phase represented by the capsule walls and the encapsulated liquid domain All techniques mentioned so far only allow for the differentiation of the solid phase from the two liquid phases. An example for poly-w-butylcyanoacrylate nanocapsules in aqueous dispersion is shown in Figs. 15 and 16. 

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