Liquid phase diffusion coefficients

It is important to recognize that the effects of temperature on the liquid-phase diffusion coefficients and viscosities can be veiy large and therefore must be carefully accounted for when using /cl or data. For liquids the mass-transfer coefficient /cl is correlated in terms of design variables by relations of the form... 

In addition, it was concluded that the liquid-phase diffusion coefficient is the major factor influencing the value of the mass-transfer coefficient per unit area. Inasmuch as agitators operate poorly in gas-liquid dispersions, it is impractical to induce turbulence by mechanical means that exceeds gravitational forces. They conclude, therefore, that heat- and mass-transfer coefficients per unit area in gas dispersions are almost completely unaffected by the mechanical power dissipated in the system. Consequently, the total mass-transfer rate in agitated gas-liquid contacting is changed almost entirely in accordance with the interfacial area—a function of the power input. 

Estimate the liquid phase diffusion coefficient for the following systems at 25 °C ... 

C, calculated from measured liquid-phase diffusion coefficients, measured range -10 to 20°C,... 

Adapted from Schwartz (1984a), and Shi and Seinfeld (1991). ka = particle radius, Dg = gas-phase diffusion coefficient, D, = liquid-phase diffusion coefficient, H = Henry s law constant, a = mass accommodation coefficient, u.w = mean thermal speed, and k = first-order aqueous-phase rate constant. 

C0 = the total counterion concentration in the liquid-phase D = the liquid-phase diffusion coefficient S = the film thickness r0 = the particle radius aA 3 = the separation factor. 

The liquid-phase diffusion coefficient can be estimated from the Nemst-Haskell eq. (1-24) (see Appendix I) ... 

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. 

Die next parameter we need is the diffusion coefficient Df of hydrogen peroxide in water. Here, we can assume the approximate value of 10 9 m2/s. However, this coefficient will be needed further in this example for the determination of the effective solid-phase diffusion coefficient, in a calculation that is extremely sensitive to the value of the liquid-phase diffusion coefficient. For this reason, coefficient should be evaluated with as much accuracy as possible. The diffusion coefficient of solutes in dilute aqueous solutions can be evaluated using the Hayduk and Laudie equation (see eq. (1.26) in Appendix I) ... 

The liquid-phase diffusion coefficient of sulfur dioxide can be found from Table 1.10, Appendix I, and is equal to 1.7 x 10 9 m2/s. 

Di = liquid-phase diffusion coefficient, m2/s p = liquid density, kg/m3 Z = length of surface, m ki = liquid-film-transfer coefficient, (kg-mol)/[(s-m2)(kg-mol)/m3]... 

Thermodynamic nonidealities are considered both in the transport equations (A10) and in the equilibrium relationships at the phase interface. Because electrolytes are present in the system, the liquid-phase diffusion coefficients should be corrected to account for the specific transport properties of electrolyte solutions. 

The liquid-phase diffusion coefficients are found with the Nemst-Hartley equation (193), which describes the transport properties in weak electrolyte systems. The gas-phase diffusion coefficients are estimated according to the... 

The gas-phase diffusion coefficients are calculated using the equation given in Ref. [40]. The liquid-phase diffusion coefficients of components at infinite dilution in... 

Predict liquid-phase diffusion coefficient DLJ of each component as solute through the other components as solvent. 

Dg, Dl = vapor and liquid phase diffusion coefficients, m /s liL = liquid holdup, mm / = fractional approach to flood Fya = active area F-factor, Uap (active area = bubbling area of tray)... 

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