Time constant for mass transfer

Compare the residence time for the L phase, Vl/L, with the time constant for mass transfer, l/KLa. Maintain a constant ratio of these two time constants but vary the individual parameters. How is the approach to steady state influenced by these changes ... 

Time Constants for Mass Transfer Rate Processes and Dimensionless Numbers... 

The concentration of monomer in the polymer particles depends on relative time constants for mass transfer and polymerisatiou Except for poorly emulsified highly water-insoluble monomers, the time constant for mass transfer is negligible with respect to the time constant for polymerisation. Hence the concentrations of the monomers in the different phases are given by the thermodynamic equilibrium ... 

Additionally, we assume that the time constants for heat transfer and mass transport are of the same order of magnitude, i.e.,... 

Other Models for Mass Transfer. In contrast to the film theory, other approaches assume that transfer of material does not occur by steady-state diffusion. Rather there are large fluid motions which constantiy bring fresh masses of bulk material into direct contact with the interface. According to the penetration theory (33), diffusion proceeds from the interface into the particular element of fluid in contact with the interface. This is an unsteady state, transient process where the rate decreases with time. After a while, the element is replaced by a fresh one brought to the interface by the relative movements of gas and Uquid, and the process is repeated. In order to evaluate a constant average contact time T for the individual fluid elements is assumed (33). This leads to relations such as... 

Time constants. Where there is a capacity and a throughput, the measurement device will exhibit a time constant. For example, any temperature measurement device has a thermal capacity (mass times heat capacity) and a heat flow term (heat transfer coefficient and area). Both the temperature measurement device and its associated thermowell will exhibit behavior typical of time constants. 

In the case of a temperature probe, the capacity is a heat capacity C == me, where m is the mass and c the material heat capacity, and the resistance is a thermal resistance R = l/(hA), where h is the heat transfer coefficient and A is the sensor surface area. Thus the time constant of a temperature probe is T = mc/ hA). Note that the time constant depends not only on the probe, but also on the environment in which the probe is located. According to the same principle, the time constant, for example, of the flow cell of a gas analyzer is r = Vwhere V is the volume of the cell and the sample flow rate. 

Here for simplicity we assume a constant mass-transfer coefficient times area of mass transfer Ka for all trays, i.e., Kgjamj = const = Ka. 

Note Since the model is linear for the special case considered, the same equation is also satisfied by the other three variables.) The following observations may be made from Eq. (98) that expresses the dimensionless dispersion coefficient A (i) The first term describes dispersion effects due to velocity gradients when adsorption equilibrium exists at the interface. We note that this expression was first derived by Golay (1958) for capillary chromatography with a retentive layer, (ii) The second term corresponds to dispersion effects due to finite rate of adsorption (since this term vanishes if we assume that adsorption and desorption are very fast so that equilibrium exists at the interface), (iii) The effective dispersion coefficient reduces to the Taylor limit when the adsorption rate constant or the adsorption capacity is zero, (iv) As is well known (Rhee et al., 1986), the effective solute velocity is reduced by a factor (1 + y). (v) For the case of irreversible adsorption (y — oo and Da —> oo), the dispersion coefficient is equal to 11 times the Taylor value. It is also equal to the reciprocal of the asymptotic Sherwood number for mass transfer in a circular... 

The liquid film has a varying thickness and is alternately exposed to the gas and to the liquid with different concentrations. However, the film damps the effect of varying concentration, and the concentration at the wall is almost constant. The time constant for diffusion in the liquid film is bj/2D = 0.1 sec. (Eq. 32), and the contact time for the gas bubble and the liquid slug is 0.02 sec. Thus the wall concentration will be almost constant, and the mass transfers directly from the gas bubble and through the liquid slug can be added using the same driving potential. 

It is assnmed that the gas is completely backmixed. Gas-side resistance for mass transfer is neglected. The reaction is performed under isothermal conditions. Initially, a slurry of Ca(OH)2 in water is prepared and the liqnid is saturated with Ca(OH)2. Then CO2 gas is sparged to the reactor. It is assnmed that the number of reacting Ca(OH)2 particles per nnit volnme of the reactor is constant (no breakage or agglomeration) until the particles are completely consnmed. The instantaneous rate of reaction is integrated with respect to time until all the Ca(OH)2 is consumed. Thus, the batch time is obtained ... 

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