Rate coefficient film diffusion

More generally, the water-film dissolution rate coefficient for any compound, i, can be estimated from the reaeration rate coefficient, again by correcting for the differences in molecular diffusivities ... 

The diffusion coefficient depends upon the characteristics of the absorption process. Reducing the thickness of the surface films increases the coefficient and correspondingly speeds up the absorption rate. Therefore, agitation of the Hquid increases diffusion through the Hquid film and a higher gas velocity past the Hquid surface could cause more rapid diffusion through the gas film. 

Fig. 2a-c. Kinetic zone diagram for the catalysis at redox modified electrodes a. The kinetic zones are characterized by capital letters R control by rate of mediation reaction, S control by rate of subtrate diffusion, E control by electron diffusion rate, combinations are mixed and borderline cases b. The kinetic parameters on the axes are given in the form of characteristic currents i, current due to exchange reaction, ig current due to electron diffusion, iji current due to substrate diffusion c. The signpost on the left indicates how a position in the diagram will move on changing experimental parameters c% bulk concentration of substrate c, Cq catalyst concentration in the film Dj, Dg diffusion coefficients of substrate and electrons k, rate constant of exchange reaction k distribution coefficient of substrate between film and solution d> film thickness (from ref. 

Rate of Formation of Primary Precursors. A steady state radical balance was used to calculate the concentration of the copolymer oligomer radicals in the aqueous phase. This balance equated the radical generation rate with the sum of the rates of radical termination and of radical entry into the particles and precursors. The calculation of the entry rate coefficients was based on the hypothesis that radical entry is governed by mass transfer through a surface film in parallel with bulk diffusion/electrostatic attraction/repulsion of an oligomer with a latex particle but in series with a limiting rate determining step (Richards, J. R. et al. J. AppI. Polv. Sci.. in press). Initiator efficiency was... 

Both reactions are slow compared to the film diffusion in the liquid phase13-15. Hence, the reactions can be assumed to take place predominantly in the bulk phase of the liquid. The rate of mass transfer can be calculated using Equation 7.2. The interfacial concentration can be calculated using Henry Law. Mass transfer coefficients, interfacial area and gas hold-up data are required. Gas hold-up is defined as ... 

What is the significance of the parameter fi = (k2C BLDAf5 / kL in the choice and the mechanism of operation of a reactor for carrying out a second-order reaction, rate constant k2, between a gas A and a second reactant B of concentration CBL in a liquid In this expression, DA is the diffusivity of A in the liquid and kL is the liquid-film mass transfer coefficient. What is the reaction factor and how is it related to /l ... 

Relative Kga valid for all systems controlled by mass transfer coefficient (Kg) and wetted area (a) per unit volume of column. Some variation should be expected when liquid reaction rate is controlling (not liquid diffusion rate). In these cases liquid hold-up becomes more important. In general a packing having high liquid hold-up which is clearly greater than that in the falling film has poor capacity. 

According to their analysis, if c is zero (practically much lower than 1), then the fluid-film diffusion controls the process rate, while if ( is infinite (practically much higher than 1), then the solid diffusion controls the process rate. Essentially, the mechanical parameter represents the ratio of the diffusion resistances (solid and fluid-film). This equation can be used irrespective of the constant pattern assumption and only if safe data exist for the solid diffusion and the fluid mass transfer coefficients. In multicomponent solutions, the use of models is extremely difficult as numerous data are required, one of them being the equilibrium isotherms, which is a time-consuming experimental work. The mathematical complexity and/or the need to know multiparameters from separate experiments in all the diffusion models makes them rather inconvenient for practical use (Juang et al, 2003). 

A buffer solution containing urea flows along one side of a flat membrane and the same buffer solution without urea flows along the other side of the membrane, at an equal flow rate. At different flow rates the overall mass transfer coefficients were obtained as shown in Table P8.1. When the liquid film mass transfer coefficients of both sides increase by one-third power ofthe averaged flow rate, estimate the diffusive membrane permeability. 

When a chemical reaction is fast enough to become complete within the diffusion film, the chemical rate and diffusion rates are coupled differently. Fig. 5.4 shows the basis for derivation of the rate expression for a reaction in a two-phase organic reactant/water system when the reaction is first order in solute with rate constant k, the diffusion coefficient of the organic species in water is D and the saturation solubility of the organic reactant in water is Csat. We consider the system at steady state and take a mass balance across a slab... 

TABLE 5.1 Rate Coefficients for Film Diffusion, Particle Diffusion, and Chemical Reaction Rate Processes of K+ Adsorption under Static Conditions ... 

The square of this number represents the ratio between the maximum reaction rate of ozone near the water interface (film thickness) and the maximum physical absorption rate (i.e., the absorption without reaction). In Eq. (9), kD and kL are parameters representing the chemical reaction and physical diffusion rate constants, that is, the rate constant of the ozone-compound reaction and water phase mass transfer coefficient, respectively. Their values are indicative of the importance of both the physical and chemical steps in terms of their rates. However, two additional parameters, as shown in Eq. (9), are also needed the concentration of the compound, CM, and the diffusivity of ozone in water, Z)0i. The ozone diffusivity in water can be calculated from empirical equations such as those of Wilke and Chang [55], Matrozov et al. [56], and Johnson and Davies [57] from these equations, at 20°C, D0 is found to be 1.62xl0 9, 1.25xl0-9, and 1.76xl0 9 m2 s 1, respectively. 

Pilot plant studies (flow rates, 1 cm/s) with the SB-1 anion exchange resin (column diameter, 0.3-0.7 cm) yielded distribution coefficients of the order D = 400 cmVg. The boron sorption process was shown to be film diffusion controlled. The equilibrium values of boron loading were reached in 6-8 hr [280]. Boron elution and resin regeneration were carried out with 0.1 M NaOH. The complete elution of boron required 10 column volumes at 10 BV and yielded concentrates of 100 mg/L. This facilitated the eventual reduction to solid concentrates of alkali metal borates [281]. 

In order for the rate coefficients kf and f ., defined by Eqs, (49) and (SO), to be predicted it is necessary to know how K j and K j are expressed in terms of the chemical and physical properties involved in the desorption and reabsoiption processes. First of all, let us consider the mass-transfer coefficient for a j-mer radical in the individual diffusion films. There is a large number of published stndies concerning the mass-transfer cocSicient in an external diffusion film around a spherical particle. One of these is the following semitheoretical equation proposed by Ranz and Marshall (1952)... 

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