Variation in diffusion rate

Either calibration graphs prepared from standards or the method of standard addition (p. 30) can be used. For the former, the standards should be as similar as possible in overall chemical composition to that of the samples so as to minimize errors caused by the reduction of other species or by variation in diffusion rates. Often, the limiting factor for quantitative work is the level of impurities present in the reagents used. 

In the diffusive-flow test, also called the forward flow test, the filter membrane or candle in its tightly closed case is set under continuous test gas pressure. The amount of air that diffuses through the filter membrane per time unit is measured downstream, on the sterile side of the filter. The pressure drop over the membrane should be constant during the test to prevent variations in diffusion rate. Collection and measurement of the air on the sterile side often require actions that may lead to contamination of the setup, and thus these actions should be performed aseptically. Furthermore, for small filter surface areas the volume of air that diffuses through the filter is small and therefore no accurate measurements are possible for these small filters. 

In regard to the solubility of the monomer in its polymer, the diffusion of vinyl chloride into PVC varies with the physical state of the resin. Earlier work frequently dealt with studies involving PVC films more recently, powdered resins were studied. In the latter case, variations in diffusion rates were found to depend on the method of polymerization (emulsion vs, suspension method) as well as on the physicochemical parameters [53]. The equilibrium solubility of vinyl chloride monomer in poly(vinyl chloride) was found to be a function of polymer type, polymer history, time, temperature, and the VCM partial pressure [7]. Above atmospheric pressure, with the ratio of the partial pressure of VCM to the initial partial pressure of the monomer greater than approximately 0.5, the solubility of vinyl chloride is 0.300 gm per gram of poly(vinyl chloride). At lower pressures, the solubility shows a distinct decrease with temperature. Kuchanov and Bort [36] state that the solubility of VCM in PVC varies between 22.1% and 23.7% between 30° and 60°C. 

Explain what is meant by diffusion in materials. Account for the variation of diffusion rates with (a) temperature, (b) concentration gradient and (c) grain size. 

More recent work has shown that the observed variation in propagation rate constants with composition is not sufficient to define the polymerization rates.5" 161,1152 There remains some dependence of the termination rate constant on the composition of the propagating chain. Thus, the chemical control (Section 7.4.1) and the various diffusion control models (Section 7.4.2) have seen new life and have been adapted by substituting the terminal model propagation rate constants (ApXv) with implicit penultimate model propagation rate constants (kpKY -Section 7.3.1.2.2). 

Schiesser and Lapidus (S3), in later studies, measured the liquid residencetime distribution for a column of 4-in. diameter and 4-ft height packed with spherical particles of varying porosity and nominal diameters of in. and in. The liquid medium was water, and as tracers sodium chloride or methyl orange were employed. The specific purposes of this study were to determine radial variations in liquid flow rate and to demonstrate how pore diffusivity and pore structure may be estimated and characterized on the basis of tracer experiments. Significant radial variations in flow rate were observed methods are discussed for separating the hydrodynamic and diffusional contributions to the residence-time curves. 

Heat transfer is an extremely important factor in CVD reactor operation, particularly for LPCVD reactors. These reactors are operated in a regime in which the deposition is primarily controlled by surface reaction processes. Because of the exponential dependence of reaction rates on temperature, even a few degrees of variation in surface temperature can produce unacceptable variations in deposition rates. On the other hand, with atmospheric CVD processes, which are often limited by mass transfer, small susceptor temperature variations have little effect on the growth rate because of the slow variation of the diffusion with temperature. Heat transfer is also a factor in controlling the gas-phase temperature to avoid homogeneous nucleation through premature reactions. At the high temperatures (700-1400 K) of most... 

Rates of reaction between acids and hydroxyl ions are found to follow a similar pattern to rates of reaction between bases and hydrogen ions, in that they are diffusion-controlled on condition that the bond being formed is stronger than the bond being broken, and there are no complicating factors. Variations in the rate coefficients can be explained in terms of steric effects, ionic charge effects, solvent structure effects and intramolecular hydrogen-bond effects. A short list of rate coefficients for... 

It is possible to determine whether the rate-limiting step is the diffusion of Oj to the surface (Eq. 1) or the reaction of Oj and Cu at the surface (Eq, 2) by measuring the variation in reaction rate with temperature. The rate of diffusion varies linearly with temperature, or 3% with a 10 C increase near ambient [6]. Chemical reaction rates typically grow exponentially with temperature and can double with each 10 C increase. The solubility of Oj in water also varies with temperature. 

We may first divide tubular reactors into those designed for homogeneous reactions, and therefore basically just an empty tube, and those designed for a heterogeneously catalyzed reaction, and hence to be packed with a catalyst. Both types can of course be operated adiabatically, and it was the simplest model of these that we discussed in the last chapter. If the temperature of the reactor is to be controlled this is through the wall, and the associated problems of heat transfer now arise. These include transfer at the wall and subsequent radial diffusion across the flowing reactants. In the empty tubular reactor there may be considerable variations in flow rate across the tube. For example, in the slow laminar flow the fluid... 

Variations in flow rate (Q) can affect sample dispersion in flow injection systems, as it influences both the parabolic distribution of linear flow velocities (Fig. 3.1) and the time available for sample diffusion. Therefore, two different trends have been reported in relation to the X vs Q function (see also Fig. 5.15). For lower flow rates, X decreases with decreasing flow rate [80], whereas an inverse effect is observed for higher flow rates [41,87], Consequently, there is a single point in the X vs Q function, Q (Fig. 5.14), where Ax/ AQ is zero. The Q value is independent of Vs, L and tubing internal diameter, and is dependent only on the diffusion coefficient of the substance (Dm — Eq. 3.4) and this opens up the possibility of a novel way to estimate diffusion coefficients [86]. The two different trends relating to the influence of Q on sample dispersion under laminar flow conditions were recently confirmed [88]. 

In this article a simplified mass balance has been used to describe the net transport of sand over an accreting mud bottom. The combination of these two sedimentary processes controls the transition from sand to mud on the floor of the Sound. The distribution of sand may be described with three parameters an advection velocity of sand grains, an eddy-diffusion coefficient for mobile sand, and a rate of accumulation of marine mud. (Only the ratios of these quantities are needed if the distribution is in a steady state.) The motion of sand is thereby represented with both a deterministic part and a statistical part. The net, one-way advection of sand is the result of the superposition of an estuarine circulation on the tidal stream, and unpredictable variations in the rate of sand transport are represented as an eddy-diffusion process. Sand is immobilized when it is incorporated into the permanent deposit of marine mud. 

Variability in the properties of agents is not the only difficulty in predicting rates of diffusion. Biological tissues present diverse resistances to molecular diffusion. Resistance to diffusion also depends on architecture tissue composition, structure, and homogeneity are important variables. This chapter explores the variation in diffusion coefficient for molecules of different size and structure in physiological environments. The first section reviews some of the most important methods used to measure diffusion coefficients, while subsequent sections describe experimental measurements in media of increasing complexity water, membranes, cells, and tissues. 

Variation in the rate of anodic oxidation of normal saturated hydrocarbons with the number of carbon atoms parallels the variation in the rate of diffusion of the hydrocarbon through the electrolyte. This holds for different electrolytes (CsF/HF, H3PO4, HF, H2SO4) and electrodes (Pt-black, Raney-Pt). The rates are low for methane, highest for ethane and propane and then gradually decrease . ... 

Mycobacterial polysaccharides are able to accelerate the diffusion of long-chain acylated derivatives of coenzyme A away from fatty-acid synthase. A general mechanism has been proposed to account for variations in the rates and products of reactions catalysed by the fatty-acid synthase from M. smegmatis over a wide range of experimental conditions." Mycobacterial polysaccharides are considered to form ternary complexes with enzyme-bound coenzyme A, causing the rapid release of fatty-acid derivatives. 

Gases and vapors permeate FEP resin at a rate that is considerably lower than that of most plastics. Because FEP resins are melt processed, they are void-free and permeation occurs only by molecular diffusion. Variation in crystallinity and density is limited, except in unusual melt-processing conditions. 

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