Particles , solid phase

H2CO3 (carbonic acid) aqueous phase HC2H3O2 (acetic acid) aqueous, gas phases HCHOz (formic acid) aqueous, gas phases H2C2O4 (oxalic acid) aerosol particles solid phase RCCX3H (many carboxylic acids)... 

The specific surface area. 1 of a porous solid that is formed of the monodisperse particles (solid phase) of volume I, and surface area. , is equal to the multiplication of the surface area of one particle by the number of particles Am in unit of mass. Using Equation 9.50,... 

Two automated complete assay systems, utilizing acridinium esters and particle solid phases, have been recently described. A high-throughput bench-top system is able to process 180 samples per hour and the time to the first assay result is 15 min. Actual assay times are 7 min per sample (K34). The dimethyl acridinium ester label in this system has already been described (L2). The second system employs an acridinium sulfonamide (M12) and coated 4-in. polystyrene beads or latex microparticles as solid phases. Assays for P-HCG, CEA, and TSH have been reported (K5). 

In the present case, a colloidal phase starts forming 7 h after the initiation of the reaction, which consists of nanoparticles suspended in the solution matrix. As a result of the self-aggregation of colloidal particles, solid-phase nucleation centers form with dendritic structure. These colloidal particles have been found to self-aggregate and exhibit nucleation centers of dendritic character. Earlier formed nuclei are more in number than those formed later and participated extensively in nucleation process. 

The majority of current applications use stationary phases [32] made of porous silica, aluminum oxide, or polymer particles. Solid-phase particles need to have small particle size (3-5 p,m are commonly used) and a well-defined pore diameter. The most commonly used silica phases have good mechanical stabihty (i.e., can be used at least up to 400 bar pressure) but have low pH tolerance (so can be used only... 

Density functional theory from statistical mechanics is a means to describe the thermodynamics of the solid phase with information about the fluid [17-19]. In density functional theory, one makes an ansatz about the structure of the solid, usually describing the particle positions by Gaussian distributions around their lattice sites. The free... 

Reiss H and Hammerich ADS 1986 Hard spheres scaled particle theory and exact relations on the existence and structure of the fluid/solid phase transition J. Phys. Chem. 90 6252... 

Charged particles in polar solvents have soft-repulsive interactions (see section C2.6.4). Just as hard spheres, such particles also undergo an ordering transition. Important differences, however, are that tire transition takes place at (much) lower particle volume fractions, and at low ionic strengtli (low k) tire solid phase may be body centred cubic (bee), ratlier tlian tire more compact fee stmcture (see [69, 73, 84]). For tire interactions, a Yukawa potential (equation (C2.6.11)1 is often used. The phase diagram for the Yukawa potential was calculated using computer simulations by Robbins et al [851. 

Static This is a dense bed of solids in which each particle rests upon another at essentially the settled bulk density of the solids phase. Specifically, there is no relative motion among solids particles (Fig. 12-26). 

Dilute This is a fully expanded condition in which the solids particles are so widely separated that they exert essentially no influence upon each other. Specifically, the solids phase is so fuUy dispersed in the gas that the den sity of the suspension is essentially that of the gas phase alone (Fig. 12-29). Commonly, this situation exists when the gas velocity at all points in the system exceeds the terminal setthng velocity of the solids and the particles can be lifted and continuously conveyed by the gas however, this is not always true. Gravity settling chambers such as prilling towers and countercurrent-flow spray diy-ers are two exceptions in which gas velocity is insufficient to entrain the sohds completely. 

Combined Pore and Solid Diffusion In porous adsorbents and ion-exchange resins, intraparticle transport can occur with pore and solid diffusion in parallel. The dominant transport process is the faster one, and this depends on the relative diffusivities and concentrations in the pore fluid and in the adsorbed phase. Often, equilibrium between the pore fluid and the solid phase can be assumed to exist locally at each point within a particle. In this case, the mass-transfer flux is expressed by ... 

Determination of Controlling Rate Factor The most important physical variables determining the controlhng dispersion factor are particle size and structure, flow rate, fluid- and solid-phase diffu-sivities, partition ratio, and fluid viscosity. When multiple resistances and axial dispersion can potentially affect the rate, the spreading of a concentration wave in a fixed bed can be represented approximately... 

Crystal Formation There are obviously two steps involved in the preparation of ciystal matter from a solution. The ciystals must first Form and then grow. The formation of a new sohd phase either on an inert particle in the solution or in the solution itself is called nucle-ation. The increase in size of this nucleus with a layer-by-layer addition of solute is called growth. Both nucleation and ciystal growth have supersaturation as a common driving force. Unless a solution is supersaturated, ciystals can neither form nor grow. Supersaturation refers to the quantity of solute present in solution compared with the quantity which would be present if the solution were kept for a veiy long period of time with solid phase in contac t with the solution. The latter value is the equilibrium solubility at the temperature and pressure under consideration. The supersaturation coefficient can be expressed... 

In many important cases of reactions involving gas, hquid, and solid phases, the solid phase is a porous catalyst. It may be in a fixed bed or it may be suspended in the fluid mixture. In general, the reaction occurs either in the liquid phase or at the liquid/solid interface. In fixed-bed reactors the particles have diameters of about 3 mm (0.12 in) and occupy about 50 percent of the vessel volume. Diameters of suspended particles are hmited to O.I to 0.2 mm (0.004 to 0.008 in) minimum by requirements of filterability and occupy I to 10 percent of the volume in stirred vessels. 

The secondary source of fine particles in the atmosphere is gas-to-particle conversion processes, considered to be the more important source of particles contributing to atmospheric haze. In gas-to-particle conversion, gaseous molecules become transformed to liquid or solid particles. This phase transformation can occur by three processes absortion, nucleation, and condensation. Absorption is the process by which a gas goes into solution in a liquid phase. Absorption of a specific gas is dependent on the solubility of the gas in a particular liquid, e.g., SO2 in liquid H2O droplets. Nucleation and condensation are terms associated with aerosol dynamics. 

In practice, however, the liquid velocity relative to fixed particles, Uf, is not very useful. Instead, the velocity of settling relative to the walls of an apparatus, Uf - u, is of practical importance. The volume of the solid phase moving downward should be equal to that of liquid moving upward. This means that volume rates of these phases must be equal. Consider a column of slurry having a unit cross section and imagine the liquid and solid phases to have a well defined interface. The column of solid phase will have a base 1 - e, and the liquid column phase will have a base e. Hence, the volumetric rate of the solid column will be (1 - e)u, and that of the liquid column will be (Uf - u)e. Because these flowrates are equal to each other, we obtain... 

Parameter P is equal to the ratio of the liquid volume entrained and the sum of the volumes of this liquid and particles. Values of P are determined experimentally from measured settling velocities. In general, the smaller the effective particle size, the more liquid is entrained by the same mass of solids phase. For example, particles of carborundum with d = 12.2 //.m have P = 0.268 d = 9.6 ftm, p — 0.288 and d = 4.6 fim, p = 0.35. 

Modeling of the force was actually based on the force balance of a single solid particle extending the result to cover a larger set of solid particles, we obtained Eq. (14.105). This method of modeling is adequate for a homogeneous flow where the particles move separately, not as a new kind of solid-phase structure. Weber has written the friction force in the form... 

Let us enter the world of liquid crystals built by the purely entropic forces present in hard body systems. The phase diagram of hard spherocylinders (HSC) shows a rich variety of liquid crystalline phases [71,72]. It includes the isotropic, nematic, smectic A, plastic, and solid phases [73]. In a plastic crystal the particle centers lie on lattice sites, but the orientations of the... 

Flocculation and sedimentation arc two processes used to separate waste streams that contain both a liquid and a solid phase. Both are well-developed, highly competitive processes, which arc oflcii used in the complete treatment of waste streams. They may also be used instead of, or in addition to, filtration. Some applications include the removal of suspended solid particles and soluble heavy metals from aqueous streams. Many industries use both processes in the rcmowal of pollutants from their wastewaters. These processes work best when the waste stream contains a low concentration of the contaminating solids. Although they are applicable to a wide variety of aqueous waste streams, these processes arc not generally used to treat nonaqueous or semisolid waste streams such as sludges and slurries. 

An estimation of the multiphase viscosity is a preliminary necessity for convenient particle processing. For particle-doped liquids the classical Einstein equation [20] relates the relative viscosity to the concentration of the solid phase ... 

Equation (2) is valid only for very dilute suspensions of nondeformable, smooth, uniform spheres. It assumes a Newtonian liquid phase and neglects interaction between particles, a plausible condition when the volume of the solid phase is small compared with the liquid phase. 

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