Dimensionless solute concentration

Isocratic Elution In the simplest case, feed with concentration cf is apphed to the column for a time tp followed by the pure carrier fluid. Under trace conditions, for a hnear isotherm with external mass-transfer control, the linear driving force approximation or reaction kinetics (see Table 16-12), solution of Eq. (16-146) gives the following expression for the dimensionless solute concentration at the column outlet ... 

Solute concentration in liquid Dimensionless solute concentration Solute concentration in cake prior to washing... 

We have already noted that mass transfer in a liquid is almost always characterized by large values of the Peclet number (the Peclet number for mass transfer involves the product of the Schmidt number and Reynolds number instead of the Prandtl number and Reynolds number) and that the dimensionless form of the convection-diffusion equation governing transport of a single solute through a solvent is still (9-7), with 6 now being a dimensionless solute concentration. For transfer of a solute from a bubble or drop into a liquid that previously contained no solute, the concentration 6 at large distances from the bubble or drop will satisfy the condition... 

In Chap. 9, we considered the solution of this equation in the limit Re 1, where the velocity distribution could be approximated by means of solutions of the creeping-flow equations. When Pe 1, we found that the fluid was heated (or cooled) significantly in only a very thin thermal boundary layer of 0(Pe l/3) in thickness, immediately adjacent to the surface of a no-slip body, or () Pe l/2) in thickness if the surface were a slip surface with finite interfacial velocities. We may recall that the governing convection di ffusion equation for mass transfer of a single solute in a solvent takes the same form as (111) except that 6 now stands for a dimensionless solute concentration, and the Peclet number is now the product of Reynolds number and Schmidt number,... 

To ccmplete the design requires specification of the extractor size, which is determined from the required to reach a given amount of extraction. The information required are the dimensionless solute concentration of the bulk phase feed a, and the dimensionless solute concentration which must be reached, oj. 

Ratio of reaction-effected diffusion coefficient to the no reaction diffusion coefficient Dimensionless parameter Dimensionless parameter Dimensionless reagent concentration Dimensionless solute concentration Dimensionless time Normalized solute concentration Dimensionless reaction front position... 

For the purpose of calculations, the family of curves in Figure 6.7 can also be derived from sequences of coefficients that describe plots of dimensionless solute concentration ( ) v. wash ratio for a range of dispersion number (see Appendix B and Wakeman and Tarleton (2005a)). Their numerical integration allows F to be evaluated as required. As an alternative to using the dispersion model a wash curve can be specified after experimental work, for instance in terms of F vs. W or F vs. t . In this case a dispersion number does not need to be calculated and the fractional recovery is interpolated directly from the wash curve. 

Wash ratio at the known F can be read directly from the design chart (Figure 6.7). Alternatively, as shown below, the curvefit coefficients for the plots of dimensionless solute concentration ( ) vs. W, from which Figure 6.7 is derived, can be used. Referring to Appendix B, values of (p are evaluated at a chosen number of wash ratios for both D = 50 and D ... 

For the case of Bi 00, it is worthy to mention. Under such condition, the mass transfer from gas phase to the interface will be no resistance thus, the interfacial concentration will remain at constant and in equilibrium with the partial pressure of gas phase. For this case, the boundary conditions of the model equations in Sect. 8.8.1 for mass transfer should be changed to c = c at z = where c is the interfacial solute concentration in equilibrium with the partial pressure of gas phase. The simulated results of dimensionless solute concentration and convection velocity at Ra = 10 and Sc = 200 are shown, respectively, in Figs. 8.36... 

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