Effect of composition numbering on the Fick matrix K˜. In the matrix representation the species n chosen for elimination is usually referred to as the solvent. The choice of “solvent” species is arbitrary, but it can have an effect on the coefficient and the structure of the resulting form as shown below. A system with a very large variation in binary diffusion values was studied by Wesselingh and Krishna (2000). The three components are hydrogen (1), nitrogen (2), and dichlorodifluoromethane (3). Estimate the binary pair values from Eq. (1.53) given in Chapter 1. Find the K matrix if species (3) is the solvent. Also show that the K matrix has different values if species (2) is the solvent. Although the three matrices look different, show that the eigenvalues….
Diffusion across a porous plug: the effect of a third component (adapted from BSL). When two gases A and B are forced to diffuse through a third gas C, there is a tendency of A and B to separate because of the difference in their diffusivities in gas C. This phenomenon could possibly be used for isotope separation. Consider a “diffusion tube” of diameter d and length L packed with some non-reacting material such as glass wool. One end of the tube, z = 0, the feed side, is maintained at mole fractions of xAf and xBf. The other end, the product end, z = L, is maintained at xAp and xBp. Your task is to model the degree of separation that can be achieved in this system….
Two solutions are separated by a porous sintered disk (1 mm thick) that permits diffusion across the disk. On one side we have a mixture of 1 M HCl and 1 M BaCl2 while on the other side we have pure water. It is required to find the flux across the system. Both salts are completely ionized and diffuse as H+, Cl−, and Ba2+ across the disk. Set up the model to compute the fluxes. From the fluxes, find the effective diffusivities of these ions across the disk. Use for the ionic diffusivity for Ba ions 0.85×10−9 m2/s. For the other ions, use the values in Table 22.1. Use the condition of no net current to solve for the potential. Answers: H, 6.14; Cl, 2.2268; and Ba, 0.271.
Design arrangements in electrophoresis: a case-study problem. Various methods have been developed in order to increase the throughput in electrophoresis. Most of these designs vary in the flow arrangement and the changes in the direction of the electric field. These include the Philpot design, Hanning design, annular design, and rotating annular column, among many others. Discuss these arrangements. A comparison of the performance analysis has been done by Yoshisato et al. (1986), who used the well-studied glycine– glutamic-acid solute pair as a model system. Study this and related papers and do a case study on performance analysis of various designs.
The proton-exchange membrane (PEM) fuel cell: a case-study problem. A hydrogen fuel cell using a PEM consists of a gas-diffusion backing layer with a Pt on C supported catalyst as anode and cathode. The two electrodes are separated by a membrane, which permits selective transport of H+ ions. The protons are released by reaction of hydrogen gas at the anode: H2 → 2H+ + 2e− These protons diffuse across the membrane and react at the cathode with the oxygen (air) gas: 1/2 O2 + 2H+ + 2e− → H2O The overall reaction is simply oxidation of hydrogen to produce water. This reaction is spontaneous with a negative free energy, G◦ = 24 000 kJ/mol at 298 K. An equivalent voltage is generated in the system under conditions of….