Adsorption uniform

Langmuir adsorption isotherm A theoretical equation, derived from the kinetic theory of gases, which relates the amount of gas adsorbed at a plane solid surface to the pressure of gas in equilibrium with the surface. In the derivation it is assumed that the adsorption is restricted to a monolayer at the surface, which is considered to be energetically uniform. It is also assumed that there is no interaction between the adsorbed species. The equation shows that at a gas pressure, p, the fraction, 0, of the surface covered by the adsorbate is given by ... 

It should be emphasized that the value of tf resulting from use of (1.49) or (1.50) applies to a particular value of n,. Because of the joint effects of the energetic non-uniformity of the adsorbent surface and the interaction of adsorbate molecules in the adsorbed film itself, the heat of adsorption in general varies significantly with the amount adsorbed. It is therefore essential to repeat the calculation of (f for a succession of values of n, and thereby obtain the curve of against n,. 

AH practical adsorbents have surfaces that are heterogeneous, both energetically and geometrically (not all pores are of uniform and constant dimensions). The degree of heterogeneity differs substantially from one adsorbent type to another. These heterogeneities are responsible for many nonlinearities, both in single component isotherms and in multicomponent adsorption selectivities. 

Dilution. In many appHcations, dilution of the flocculant solution before it is mixed with the substrate stream can improve performance (12). The mechanism probably involves getting a more uniform distribution of the polymer molecules. Since the dosage needed to form floes is usually well below the adsorption maximum, a high local concentration is effectively removed from the system at that point, leaving no flocculant for the rest of the particles. A portion of the clarified overflow can be used for dilution so no extra water is added to the process. 

As manufactured, most resias have a Gaussian-Hke distributioa of particle size. Very few are as small as 0.3 mm or as large as 1.0 mm. Most are betweea 0.5—0.8 mm. A backwash before usiag aew resia is common practice to assure uniform flow during the adsorption and regeneration steps. The backwash eliminates air pockets that may have formed while filling the column and sorts the beads such that the smaller sizes are at the top of the bed and... 

There are two types of stmctures one provides an internal pore system comprising interconnected cage-like voids the second provides a system of uniform channels which, in some instances, are one-dimensional and in others intersect with similar channels to produce two- or three-dimensional channel systems. The preferred type has two- or three-dimensional channel systems to provide rapid intracrystalline diffusion in adsorption and catalytic apphcations. 

In this section, we consider the transient adsorption of a solute from a dilute solution in a constant-volume, well-mixed batch system or, equivalently, adsorption of a pure gas. The solutions provided can approximate the response of a stirred vessel containing suspended adsorbent particles, or that of a very short adsorption bed. Uniform, spherical particles of radius are assumed. These particles, initially of uniform adsorbate concentration, are assumed to be exposed to a step change in concentration of the external fluid. 

In the irreversible limit R < 0.1), the adsorption front within the particle approaches a shock transition separating an inner core into which the adsorbate has not yet penetrated from an outer layer in which the adsorbed phase concentration is uniform at the saturation value. The dynamics of this process is described approximately by the shrinldng-core model [Yagi and Kunii, Chem. Eng. (Japan), 19, 500 (1955)]. For an infinite fluid volume, the solution is ... 

Treatments of constant pattern behavior have been carried out for multicomponent adsorption [Vermeulen, Adv. in Chem. Eng., 2, 147 (1958) Vermeulen et., Ruthven, gen. refs. Rhee and Amundson, Chem. Eng. ScL, 29, 2049 (1974) Cooney and Lightfoot, Jnd. Eng. Chem. Fundam., 5, 25 (1966) Cooney and Strusi, Jnd. Eng. Chem. Fundam., 11, 123 (1972) Bradley and Sweed, AJChE Symp. Ser. No. 152, 71, 59 (1975)]. The behavior is such that coexisting compositions advance through the bed together at a uniform rate this is the coherence concept of Helfferich and coworkers [gen. refs.]. 

When a carrier is impregnated with a solution, where the catalyst deposits will depend on the rate of diffusion and the rate of adsorption on the carrier. Many studies have been made of Pt deposition from chloroplatinic acid (HgPtClg) with a variety of acids and salts as coim-pregnants. HCl results in uniform deposition of Pt. Citric or oxalic acid drive the Pt to the interior. HF coimpregnant produces an egg white profile. Photographs show such varied distributions in a single pellet. 

The role of oxygen and hydrogen solutions in the metal catalyst does not appear to be that of impeding the major reactions, but merely to provide a source of these reactants which is uniformly distributed diroughout the catalyst particles, without decreasing die number of surface sites available to methane adsorption. It is drerefore quite possible that a significatit fraction of the reaction takes place by the formation of products between species adsorbed on the surface, and dissolved atoms just below the surface, but in adjacent sites to the active surface sites. 

Silylation of apparatus makes it repellant to water and hydrophilic materials. It minimises loss of solute by adsorption onto the walls of the container. The glassware is placed in a desiccator containing dichloromethyl silane (ImL) in a small beaker and evacuated for 5min. The vacuum is turned off and air is introduced into the desiccator which allows the silylating agent to coat the glassware uniformly. The desiccator is then evacuated, closed and set aside for 2h. The glassware is removed from the desiccator and baked at 180° for 2h before use. 

Although insulators other than aluminum oxide have been tried, aluminum is still used almost universally because it is easy to evaporate and forms a limiting oxide layer of high uniformity. To be restricted, therefore, to adsorption of molecules on aluminum oxide might seem like a disadvantage of the technique, but aluminum oxide is very important in many technical fields. Many catalysts are supported on alumina in various forms, as are sensors, and in addition the properties of the oxide film on aluminum metal are of the greatest interest in adhesion and protection. 

The relationship between adsorption capacity and surface area under conditions of optimum pore sizes is concentration dependent. It is very important that any evaluation of adsorption capacity be performed under actual concentration conditions. The dimensions and shape of particles affect both the pressure drop through the adsorbent bed and the rate of diffusion into the particles. Pressure drop is lowest when the adsorbent particles are spherical and uniform in size. External mass transfer increases inversely with d (where, d is particle diameter), and the internal adsorption rate varies inversely with d Pressure drop varies with the Reynolds number, and is roughly proportional to the gas velocity through the bed, and inversely proportional to the particle diameter. Assuming all other parameters being constant, adsorbent beds comprised of small particles tend to provide higher adsorption efficiencies, but at the sacrifice of higher pressure drop. This means that sharper and smaller mass-transfer zones will be achieved. 

In the case of multiparticle blockage, as the suspension flows through the medium, the capillary walls of the pores are gradually covered by a uniform layer of particles. This particle layer continues to build up due to mechanical impaction, particle interception and physical adsorption of particles. As the process continues, the available flow area of the pores decreases. Denoting as the ratio of accumulated cake on the inside pore walls to the volume of filtrate recovered, and applying the Hagen-Poiseuille equation, the rate of filtration (per unit area of filter medium) at the start of the process is ... 

Ultrafiltration utilizes membrane filters with small pore sizes ranging from O.OlS t to in order to collect small particles, to separate small particle sizes, or to obtain particle-free solutions for a variety of applications. Membrane filters are characterized by a smallness and uniformity of pore size difficult to achieve with cellulosic filters. They are further characterized by thinness, strength, flexibility, low absorption and adsorption, and a flat surface texture. These properties are useful for a variety of analytical procedures. In the analytical laboratory, ultrafiltration is especially useful for gravimetric analysis, optical microscopy, and X-ray fluorescence studies. 

One important direetion of study has been to use empirieal adsorption data, together with the preassumed model for loeal adsorption, and attempt to extraet information about the form of x(e) [13,14]. The ehoiee of the model for loeal adsorption, whieh is an important input here, has been eustomarily treated quite easually, assuming that it has rather limited influenee on the form and properties of the evaluated EADFs. Usually, one of so many existing equations developed for adsorption on uniform surfaees is used as the loeal adsorption isotherm. The most often used forms of 0 p, T,e) are the Langmuir [6] and the Fowler-Guggenheim [15] equations for loealized adsorption. Ross and Olivier [4] extensively used the equation for mobile adsorption, whieh results from the two-dimensional version of the van der Waals theory of fluids. The most radieal solution has been... 

Both extreme models of surface heterogeneity presented above can be readily used in computer simulation studies. Application of the patch wise model is amazingly simple, if one recalls that adsorption on each patch occurs independently of adsorption on any other patch and that boundary effects are neglected in this model. For simplicity let us assume here the so-called two-dimensional model of adsorption, which is based on the assumption that the adsorbed layer forms an individual thermodynamic phase, being in thermal equilibrium with the bulk uniform gas. In such a case, adsorption on a uniform surface (a single patch) can be represented as... 

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