Search

D.A. RATKOWSKY, T. ROSS, T.A. WCMEEKIN AND J. OLLEY. 1991. The development of Arrhenius-type (‘Schoolfield’) and Belehradek-type (square root) models that describe microbial growth rates is briefly described. Both types of model have been advocated for use in predictive microbiology. On the basis of published data sets for the growth of bacteria, the consequences of mathematical transformation of data and the use of invalid stochastic assumptions upon model predictions are demonstrated. Mean square error is shown to be an inappropriate criterion by which to compare the performance of predictive models. The data show that bacterial growth responses such as generation time and lag time become more variable as their mean magnitude increases. The practical consequences of such variability for predictive microbiology are discussed.

A broad class of solid phase catalytic chemical reaction kinetics can be modelled by the Hougen—Watson approach based upon the Langmuir adsorption isotherm. An appropriate statistical procedure for determining the parameters of the resulting models is nonlinear least squares. However, nonlinear least squares estimators are only asymptotically efficient, the departure from the asymptotic properties for small sample sizes being strongly dependent upon the form of the model. It is shown that there is a general form of parameterization for the Hougen—Watson approach that corresponds to a “close-to-linear” model, that is, one whose statistical properties approach that of a linear model even for small samples. The general formulation has all its parameters in the denominator of the expression for the reaction rate.

Five equations, viz. the Bacon, Bragg, Ergun, Lorentz and Ruland equations, for describing the preferred orientation of graphite-like materials were studied in combination with eleven sets of data using modern techniques for examining the behaviour of nonlinear regression models. The Bragg equation, which is based upon the normal (Gaussian) probability distribution, had the best statistical properties, in that the estimators of the parameters of the equation were close to being unbiased, normally distributed, minimum variance estimators. The other four equations were generally more erratic in their statistical behaviour, their estimators being highly biased and skewed in their distribution for at least one data set. The Bragg equation was generally the best fitting model, with the Lorentz and Ruland equations being generally the worst fitting models. The Bragg equation can therefore be recommended for general use to describe the preferred orientation of graphitic materials.

Solid particles of uniform size and shape were used to study the effect of particle shape on hindered settling in creeping flow ( Re o s 0.2), where fluid flow patterns are independent of Reynolds number and the effect of shape is most prominent. The particles of different shape studied were spherical glass beads, cubical sodium chloride crystals and ABS plastic pellets, brick-like sugar crystals, and angular (imperfect octahedral) mineral silicate crystals. The liquids used were aqueous polyethylene glycol solutions and various blends of hydrocarbon oils. Two particle sizes on the average were investigated for each particle shape, and five settling column diameters were employed, so that the overall range of column-to-particle diameter ratio covered was 22 – 226. A Richardson—Zaki type equation of the form u = u i ϵ n was found to correlate the constant settling rate data for each particle size and shape over the voidage range ϵ = 0.65 – 0.9. However, the wall effect on hindered settling rate was found in most cases to be considerably smaller than that predicted by Richardson and Zaki. The term u i , obtained by linearly extrapolating the settling velocity u (below ϵ = 0.9) to ϵ = 1 on a log—log plot of u versus ϵ, was found to be measurably lower than the corresponding free settling velocity. The index n varied from an average value of 4.8 for the smooth spheres to 5.4 for the cubes to 5.8 for both the brick-like and the angular particles. These values graphically display a definite trend with settled bed voidage, ϵ b , which is shape-dependent and easily measured, and may therefore be a convenient parameter for taking account of shape variation generally. The method proposed by Beranek and Klumpar for correlating fluidization data on different shaped particles, which depends on ϵ b , was found to be moderately successful in correlating the present settling data for different shapes.

The effectiveness of a progamme to recover mercury from the effluent of a zinc refinery situated on the banks of the Derwent River, Tasmania, was monitored by using sand flathead ( Platycephalus bassensis ), an easily caught, non-migratory, demersal finfish as a biological indicator of the changing quantities of mercury available from sediments at the bottom of the river and estuary. The programme involved determining the mercury concentration of sand flathead caught at four localities during the 1973/74 season and annually since the 1976/77 season. Marked declines in the mercury concentrations of the flathead were recorded in all localities. In the 1982/83 season, three of the localities had mercury concentrations less than 0.5 μg g −1 wet weight, with the fourth locality, an enclosed bay downstream from the refinery, yielding concentrations slightly below 0.6 μg g −1 wet weight. Only 2.3% of the individual fish caught had mercury concentrations in excess of 1.0 μg g −1 wet weight. This study demonstrates that an environment polluted by industrial sources of heavy metals can be improved in a relatively brief period by cutting off the source of the pollution.

Data have been obtained for mass transfer from naphthalene to air and phenol to air for horizontal cylinders vibrated vertically over a wide range of Reynolds number. It is shown that these data and the data of all previous investigations, including liquid systems, lie on or near a single smooth curve provided that an appropriate system of coordinates is selected. Further, for high Reynolds number and high Schmidt number, the data approach the theoretical equation of Jameson derived using boundary-layer theory. The authors have found that the mass transfer coefficient for sublimation can be increased by a factor of approximately 30 over that which prevails for the stationary (nonvibrating) case.