A good example of the successful application of membrane technology is the processing of cheese whey. Table 1 gives some background to the problem. The production of cheese whey is growing at 4% per year and it is estimated that only about 50% of the whey is utilized in any form either for animal feed or in human foods. The proximate composition shown in Table 1 emphasizes some of the problems in treating whey. It has a low solids content, and a very unfavorable protein to lactose ratio of 11:89, which makes it difficult to utilize as animal feed or in human food products. This explains why reverse osmosis (RO) and ultrafiltration (UF) have attracted the attention of cheese producers, since it now affords the possibility of simultaneously purifying, fractionating and concentrating (at low energy cost) the whey and thus enhancing its utilization and reducing its pollution problems.

It has been shown that the Fourier transform method can be used to evaluate the one-centre matrix elements of the modified Coulomb operator (r₁₂+a)⁻¹ wherer₁₂ is the interelectronic distance. Four typical integrals of the Coulomb and exchange variety have been explicitly evaluated and their numerical values presented for select values of the parameter a.

The preceding chapter deals with the permeability of one-dimensional barriers to particles of specified energy W. Under normal conditions a chemical reaction involves a large number of systems covering a range of energies, and in this context a more realistic model consists of a stream of particles in thermal equilibrium impinging on a barrier. The simplest form of energy distribution in such a stream is given by (3.1) $$ \frac{{dN}}{N} = \frac{1}{{kT}}{e^{ - W/kT}}dW $$ in which dN/N is the fraction of particles having energies between W and W + dW.

Summary

2-Amino-5(o-hydroxyphenyl)-1,3,4-thiadiazole (AHPT) complexes of the type M(AHPT-H), (M = Cu^ll, Ni^lI, Co^lI, Zn^ll and Fell) have been prepared and characterized by analytical, magnetic, spectral (electronic and i.r.), powder x-ray diffraction and t.g. techniques. Magnetic and electronic data indicate that the Fe^II, Co^II, Cu^II complexes are octahedral and that the Ni^lI complex is a mixture of square planar and octahedral geometries.