A well-known, but quite inefficient, representation of dead time in a continuous process is that of a series of staged vessels with equal time constants. Buckley (1) compares such a series approximation for dead time, TD, with other methods of dead time representation. The transfer function for this approximation (equivalent to k wellmixed stages in series) is given as The transfer function given by Equation ( 1) , applied to the problem of residence-time distributions of particles residing in a system of k serially-staged well-mixed vessels, indicates that as the number of tanks in series increases, a uniformity of residence time within the total system occurs.As k -+ 00 the residence-time distribution of plug-flow (pure dead time) is predicted.Robinson and Roberts ( 2 ) attacked the problem of predicting crystal size distribution in a staged crystallizer by calculating the residence-time distribution of particles in the system, assuming they grew at the same linear rate in each of the vessels. It was further necessary to assume that all particles entered (were formed) at zero size in the first stage. These authors did not dwell on the narrowing of crystal size distribution expected in such a system. Randolph and Larson (3) considered the same problem of crystal size distribution in staged systems, but allowed for particle formation (nucleation) in each of the stages. The resultant population distribution leaving the kth stage was calculated to be (2) L rT rV where x = -= -LQ is a dimensionless particle size.Again, it was necessary to assume that the product of linear growth rate and mean retention time was equal in each stage. Cumulative weight distribution was obtained from population distribution as Alan D. Randolph ib at the University of Arizona, Tucson, Arizona. Chand Deepak is with the American 0 1 1 Co., Whiting, Indiana.The occurrence of nucleation in each stage results in a wider distribution of residence times, and hence wider crystal size distribution, but the above cited reference did not comment on this aspect.In the general problem of predicting crystal size distribution from a serially-staged crystallization process, one must take into account nucleation-growth rate kinetics as well as a mass balance, which latter constrains the growth rates obtainable. A sufficient set of equations to describe crystal size distribution produced from a general staged crystallization process with segregated particle withdrawal is as follows. The solution of these equations for a particular system would yield complete information about the system, including concentrations, production rates, and crystal size distribution in each stage. Such calculations can only be meaningful when a large amount of information concerning kinetics of nucleation and growth, as well as particle draw-down rates, Q(L), is available on a particular system.It is the purpose of this paper to generalize on the form, but not the magnitude, of crystal size distribution obtainable from such serially staged processes. Particle drawdown rates, Q ...

This investigation was carried out to study effect of packaging and storage period on the specific gravity at 25°C (Sp. Gr) , refractive index(R.I.),color intensity; acid value, peroxide value(P .V), thiobarbituric acid (TBA) ,iodine value (IV) ,fatty acid composition , and keeping quality of Sunflower oil. The obtained results revealed that the storage of sunflower oil at ambient temperature for nine months did not seem to have any appreciable effect on the specific gravity, while the refractive index was decreased gradually .In contrast the color intensity increased as the storage period increased. The rate of change(either increase or decrease) was depended on the storage period as well as type of container. The obtained results showed that the acid value, peroxide value and TBA increased gradually in all oil samples during storage. The highest increase in acid value was recorded in the colorless glass containers while the lowest increase was observed in plastic and brown glass containers. Also, the results showed that the I.V. decreased gradually in all oil samples. The extent of decrease was affected by storage period and type of container. The results revealed that the saponification value (S.V.) increased gradually in all oil samples as storage period increased. The highest increase in S.V. was recorded in oil samples stored in colorless glass containers,. In contrast, the lowest increase in the S.V. due to prolonged storage was observed in oil samples stored in brown glass containers. The unsaponifiable matter percentage decreased gradually in all oil samples during storage. The results obtained reveald that the values of fatty acids C18:2, C18:3, TPUFA, TUFA and ratio of TUFA: TSFA, C18:2: C18:1 as well as iodine value were decreased with increasing the storage period., while the values of fatty acids C18:2, C18:3, TPUFA, TUFA and ratio of TUFA: TSFA, C18:2: C18:1 as well as iodine value were decreased with increasing the storage period. The rate of change in the values of fatty acids was depended on the storage period and types container. The oil samples packed in colorless glass containers showed the highest value of changes in comparison with other oil samples packed in plastic and brown glass containers. It could be mention that the decrease in C18:2 and C18:3 was accompanied by the decreased in the I.V.

Two brands of ghee, three brands of butter oil and two brands of hydrogenated oils were examined for compositional properties and keeping quality. Analysis indicated that the samples were within the usual requirements, except one ghee sample which had a very high initial rate of free fatty acids (FFA).During storage the FFA and peroxide values (PV) increased. The increase in FFA was more obvious at 20°C than at 35"C, but in general the increase was not large. The PV showed a faster increase at 35°C than at 20°C. The increase at 20°C was mostly below 20 mEq peroxide/kg, which had no practical effect on flavour changes. This suggested that oxidative rancidity could be a major problem if the fat is stored at temperatures above 20°C. Among the fat samples examined, ghee samples (Egyptian products) showed the least storage stability, while butter oil Frico brand (Netherlands product) showed the highest storage stability.

A typical ghee flavour was obtained by heating vegetable fats with fermented milk or fermented whey at 125°C for 2 min. The resulting product had an acceptability preference and better storage stability than the untreated vegetable fat. It is suggested that whey proteins and fermentation products are the major contributors to development of ghee flavour in vegetable fats. The increase in storage stability could be due to the formation of reactive sulphydryl groups from whey proteins during the heating process.