Diffusion coefficients bulk density

Therefore, in tire limiting case—tire surface concentration of tire reacting species is zero as all tire arriving ions immediately react—tire current density becomes voltage independent and depends only on diffusion, specifically, on tire widtli of tire Nerstian diffusion layer S, and of course tire diffusion coefficient and tire bulk concentration of anions (c). The limiting current density (/ ) is tlien given by... 

Example 8 Estimation of Rate Coejficient Estimate the rate coefficient for flow of a 0.01-M water solution of NaCl through a bed of cation exchange particles in hydrogen form with e = 0.4. The superficial velocity is 0.2 cm/s and the temperature is 25 C. The particles are 600 im in diameter, and the diffusion coefficient of sodium ion is 1.2 X 10 cmVs in solution and 9.4 X 10 cmVs inside the particles (of. Table 16-8). The bulk density is 0.7 g dry resin/cnd of bed, and the capacity of the resin is 4.9 mequiv/g dry resin. The mass action eqiiihbrium constant is 1.5. 

The order of the mobilities of alachlor, butylate, and metolachlor in columns of various soils was metolachlor > alachlor > butylate. This correlates directly with the water solubilities and inversely to the adsorption coefficients and octanol/water partition coefficients of these compounds. Diffusion of these compounds in soil thin-layers was as follows butylate > alachlor > metolachlor, which correlates directly with the vapor pressures of these compounds. Significant soil properties affecting diffusion appeared to be bulk density and temperature. Soil moisture is also probably important, but its effect on the diffusion of these compounds was not determined. 

Results in Table I illustrate some of the strengths and weaknesses of the ST2, MCY and CF models. All models, except the MCY model, accurately predict the internal energy, -U. Constant volume heat capacity, Cv, is accurately predicted by each model for which data is available. The ST2 and MCY models overpredict the dipole moment, u, while the CF model prediction is identical with the value for bulk water. The ratio PV/NkT at a liquid density of unity is tremendously in error for the MCY model, while both the ST2 and CF models predictions are reasonable. This large error using the MCY model suggests that it will not, in general, simulate thermodynamic properties of water accurately (29). Values of the self-diffusion coefficient, D, for each of the water models except the CF model agree fairly well with the value for bulk water. 

It should be emphasized that n.. and JPS, and therefore c and T, refer to the condition at the pore tip. The dissolution valence and the temperature can be assumed to be independent of pore depth. This is not the case for the HF concentration c. Because convection is negligible in macropores, the mass transport in the pore occurs only by diffusion. A linear decrease in HF concentration with depth and a parabolic growth law for the pores according to Pick s first law is therefore expected, as shown in Fig. 9.18 a. The concentration at the pore tip can be calculated from the concentration in the bulk of the electrolyte c, the pore length l, the diffusion coefficient DHf (Section 1.4) and the flow of HF molecules FHf. which is proportional to the current density at the pore tip ... 

These studies showed that sulfonate groups surrounding the hydronium ion at low X sterically hinder the hydration of fhe hydronium ion. The interfacial structure of sulfonafe pendanfs in fhe membrane was studied by analyzing structural and dynamical parameters such as density of the hydrated polymer radial distribution functions of wafer, ionomers, and protons water coordination numbers of side chains and diffusion coefficients of water and protons. The diffusion coefficienf of wafer agreed well with experimental data for hydronium ions, fhe diffusion coefficienf was found to be 6-10 times smaller than the value for bulk wafer. 

This equation relates the temporal concentration of a diffusing chemical to its location in space. In real soil and aquifer materials, the diffusion coefficient can be affected by the temperature and properties of the solid matrix, such as mineral composition (which affects sorption, a process that can be difficult to separate from diffusion), bulk density, and critically, water content. 

Example 6.2. Calculate the diffusion limiting current density for the deposition of a metal ion at a cathode in a quiescent (unstirred) solution assuming a diffusion layer thickness 8 of 0.05 cm. The concentration of ions in the bulk (cj,) is 10 moEL (10 moEcm ), the same as in Example 6.1. The diffusion coefficient D of in the unstirred solution is 2 X lO cm /s. Using Eq. (6.83), we calculate that the limiting diffusion current density for this case is... 

Hashimoto et al. (1977) studied the removal of DBS from an aqueous solution in a carbon fixed-bed adsorber at 30 °C. The dimensions of the bed were D = 20 mm and Z = 25.1 cm. Carbon particles of 0.0322-cm radius were used, with 0.82 g/cm3 particle density, and 0.39 g/cm3 bulk density. The concentration of the influent stream was 99.2 rng/L and the superficial velocity was 0.0239 cm/s. The fixed bed was operated under upflow condition. Furthermore, the isotherm of the DBS-carbon system at 30 °C was found to be of Freundlich type with Fr = 0.113 and = 178 (mg/g)(L/mg)0113. Finally, the average solid-phase diffusion coefficient was found to be 2.1 X 10 10 cm2/s. The approximate value of 10 9 m2/s could be used for DBS liquid-phase diffusion coefficient. 

Nafion (17) is a perfluorinated polymer related to teflon (polytetrafluoroethylene). An electrode is conveniently coated by allowing an ethanolic solution of the polymer to evaporate. The film produced is stable, rather more so in fact than other polymer films, e.g. polyvinylpyridine (see Section 57.3.2.2). At the microscopic level the polymer separates into two phases, the bulk polymer and the lower density ionic cluster phase. Diffusion of ions can occur quite freely for example, the diffusion coefficient of Na+ in Nafion (MW 1200) is only slightly less than in water.44... 

In Equation (9.6), x is the direction of flux, nt [mol m-3 s 1 ] is the total molar density, X [1] is the mole fraction, Nd [mol m-2 s 1] is the mole flux due to molecular diffusion, D k [m2 s 1] is the effective Knudsen diffusion coefficient, D [m2 s 1] is the effective bimolecular diffusion coefficient (D = Aye/r), e is the porosity of the electrode, r is the tortuosity of the electrode, and J is the total number of gas species. Here, a subscript denotes the index value to a specific specie. The first term on the right of Equation (9.6) accounts for Knudsen diffusion, and the following term accounts for multicomponent bulk molecular diffusion. Further, to account for the porous media, along with induced convection, the Dusty Gas Model is required (Mason and Malinauskas, 1983 Warren, 1969). This model modifies Equation (9.6) as ... 

The simulations of volatilization were conducted using the complete model described by Jury et al. (33) where each chemical is present in the soil at a uniform concentration of 1 kg/ha to a depth, L, in the soil and is allowed to volatilize through a stagnant air boundary layer for a specified time period in the presence or absence of water evaporation. The standard conditions or common properties assumed in the simulations are the same as those indicated in Jury et al. (35, 36), i.e., air diffusion coefficient, 0.43 m /d water diffusion coefficient, 4.3 X 10-3 m /d atmospheric relative humidity, 50% temperature, 25°C soil porosity, 50% bulk density, 1.35 g/cm3 soil water content, 0.30 organic carbon fraction, 0.0125 amount of pesticide in soil, 1 kg/ha depth in soil, 1 or 10 cm water evaporation rate, 0, 0.25, or 0.50 cm/d. 

Here, iiim is the limiting current density, bCf is the salt concentration of the diluate in the bulk solution, Az is the thickness of the laminar boundary layer, Tm and T5 are the transport numbers in the membrane and the solution, Ds is the salt diffusion coefficient in the solution, F is the Faraday constant, z is the charge number, and the subscript i refers to cation and anion. 

The characteristics of the experimental aquifer were independently determined from appropriate flowthrough column experiments or obtained directly from the literature. The dry bulk density of the sand ph= 1.61 kg/1, and the aquifer porosity 0=0.415 were evaluated by gravimetric procedures. The dimensionless retardation factor, R= 1.31, of the aqueous-phase TCE was determined from a column flowthrough experiment. The tortuosity coefficient for the aquifer sand was considered to be x =1.43 [75]. The molecular diffusion coefficient for the aqueous-phase TCE is D=0.0303 cm2/h [76]. The pool radius is r=3.8 cm. Bromide ion in the form of the moderately soluble potassium bromide salt was the tracer of choice [77 ] for the tracer experiment conducted in order to determine the longitudinal and transverse aquifer dispersivities a =0.259 cm and a-,— 0.019 cm, respectively. The experimental pool contained approximately 12 ml of certified ACS grade (Fisher Scientific) TCE with solubility of Cs=1100 mg/1 [78]. 

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