Ken R. Morison

The mathematical modelling of transient systems using differential-algebraic equations

Abstract The mathematical difficulties associated with a class of mixed systems of differential and algebraic equations are presented and an algorithm for dealing with them is described. Two classes of chemical engineering models which give rise to such systems, are identified. Also some problems arising from rigorous dynamic distillation models are analysed.

A multi-component approach to salt and water diffusion in cheese

Abstract A theoretically based model was developed using the Maxwell–Stefan equation to predict the salt gain and moisture loss of cheese during brine salting. The model was used to predict changes in the salt and moisture profile, and dimensions of the cheese. The best solutions were obtained when the diffusivities were made functions of porosity and salt concentration. For Gouda cheese the predicted moisture and salt/moisture profiles were within 0.6% moisture and 0.3% salt/moisture of published experimental data. The model predicted an overall gain in salt of 1.55% by weight, an overall reduction in moisture from 43.4 to 41.0%, a mass loss of 1.5% and a volume reduction of 2.6% after 8 days of brining.

Limitations of the Weissler reaction as a model reaction for measuring the efficiency of hydrodynamic cavitation

The Weissler reaction in which iodide is oxidised to a tri-iodide complex (I(3)(-)) has been widely used for measurement of the intensity of ultrasonic and hydrodynamic cavitation. It was used in this work to compare ultrasonic cavitation at 24 kHz with hydrodynamic cavitation using two different devices, one a venturi and the other a sudden expansion, operated up to 8.7 bar. Hydrodynamic cavitation had a maximum efficiency of about 5 x 10(-11) moles of I(3)(-) per joule of energy compared with the maximum of almost 8 x 10(-11) mol J(-1) for ultrasonic cavitation. Hydrodynamic cavitation was found to be most effective at 10 degrees C compared with 20 degrees C and 30 degrees C and at higher upstream pressures. However, it was found that in hydrodynamic conditions, even without cavitation, I(3)(-) was consumed at a rapid rate leading to an equilibrium concentration. It was concluded that the Weissler reaction was not a good model reaction for the assessment of the effectiveness of hydrodynamic cavitation.

Viscosity of lactose and whey protein solutions

The viscosity of lactose and whey protein solutions was measured over the range of compositions and concentrations that might be encountered within whey ultrafiltration and reverse osmosis plants and over the temperature range 10°C to 50°C. The data obtained was compared with other literature values and correlations were obtained to enable the prediction of the viscosity of lactose and whey protein solutions. It was found that Einsteins equation can be used for protein concentrations up to 15% and an empirical relationship is proposed for higher concentrations. Temperature correction parameters have been obtained.

Blood drop size in passive dripping from weapons

Passive dripping, the slow dripping of blood under gravity, is responsible for some bloodstains found at crime scenes, particularly drip trails left by a person moving through the scene. Previous work by other authors has established relationships, under ideal conditions, between the size of the stain, the number of spines and satellite stains, the roughness of the surface, the size of the blood droplet and the height from which it falls. To apply these relationships to infer the height of fall requires independent knowledge of the size of the droplet. This work aims to measure the size of droplets falling from objects representative of hand-held weapons. Pig blood was used, with density, surface tension and viscosity controlled to fall within the normal range for human blood. Distilled water was also tested as a reference. Drips were formed from stainless steel objects with different roughnesses including cylinders of diameter between 10 and 100 mm, and flat plates. Small radius objects including a knife and a wrench were also tested. High speed images of the falling drops were captured. The primary blood drop size ranged from 4.15±0.11 mm up to 6.15±0.15 mm (depending on the object), with the smaller values from sharper objects. The primary drop size correlated only weakly with surface roughness, over the roughness range studied. The number of accompanying droplets increased with the object size, but no significant correlation with surface texture was observed. Dripping of blood produced slightly smaller drops, with more accompanying droplets, than dripping water.

Betaine structure and the presence of hydroxyl groups alters the effects on DNA melting temperatures

Betaine lowers the melting temperature of deoxyribonucleic acid (DNA) and decreases its dependence on base composition. The effects of synthetic betaine analogs on the melting of DNA samples with different GC content were measured. Since many polyhydroxy compounds also lower DNA melting temperatures, hydroxyl-substituted betaine analogs were included. Some synthetic sulfonate analogs of betaine lowered the DNA melting temperatures by twice as much at the same molar concentration. They were up to twice as effective at decreasing the base pair dependence. Some carboxylate homologs of betaine, substituted with hydroxyl groups, increased the melting temperature. This effect was greater with low GC content DNA. Sulfonate analogs of betaine with hydroxyl groups usually destabilize the DNA, while their carboxylate analogs stabilize the DNA. Distances between the charges of these synthetic zwitterionic solutes influence the effect on DNA, with the optimum separation being two or three methylene groups. A betaine with two hydroxyl groups on one N-alkyl group had a greater effect than an isomer with two hydroxyl groups on separate N-alkyl substituents. We suggest that the effect of these solutes depends on structuring the hydration water of DNA, as well as interactions with the DNA structure itself.

THE DEVELOPMENT AND INVESTIGATION OF A MODEL MILK MINERAL FOULING SOLUTION

Dissolved minerals in whey permeate cause fouling on heat transfer equipment, especially evaporators. To enable the study of mineral fouling, a model milk mineral fouling solution was developed to mimic whey permeate. It was found that whey permeate could be modelled by a solution made up of simulated milk ultrafiltrate with 5% lactose and about 0.08% protein from whey protein concentrate. The components and fouling conditions of the model solution were varied to gain an understanding of the mechanism and prevention of fouling of whey permeate. Fouling was reduced when the pH was higher, the preheating was greater, and the citrate concentration was lower. It was increased when the surface temperature was higher and the protein concentration was greater than zero. It was found that any component or treatment that stabilized calcium phosphate in solution caused greater fouling, while treatments that destabilized calcium phosphate caused precipitation in solution and hence a reduction of surface fouling.

Liquid Distribution from Cleaning-in-Place Sprayballs

There is little independently published data available which defines the processes and important parameters involved in cleaning-in-place with sprayballs. Initial tests showed that, in some circumstances, a sprayball was ineffective in cleaning soluble material from a surface. Quantitative experimental data was obtained for the wetting of a surface by a single water jet. The wetting rate ranged from 0.1 to 0.3 kg m -1 s -1 , which was consistent with the expected results, but lower than a previously suggested design value of 0.4 kg m -1 s -1 . The wetting rate decreased when the temperature of the water was increased, and increased with the addition of a small quantity of detergent to the water. No significant difference was observed between the wetting rates for acrylic and stainless steel, or when 1% sodium hydroxide solution was substituted for water. The results are discussed from a design perspective.

Viscosity and Non-Newtonian Behaviour of Concentrated Milk and Cream

The effect of the composition of milk solutions on their viscosities over the temperature range of 20–60°C was investigated using previously reported data and new experimental data. Low-fat milk of known composition was concentrated to obtain samples with 9 to 50% total solids content and the viscosity was measured. At concentrations up to 20% total solids, the liquid was Newtonian, but above 30% concentration skim milk concentrates exhibited pseudoplastic (shear thinning) behaviour, which is consistent with previous studies. The previous and new data were analysed to determine the fit to a recently proposed equation. The contributions of lactose, fat, casein, and whey protein were determined so that the viscosity of a liquid dairy product could be calculated from its composition over the entire experimental range.

Optimisation and graphical representation of multi-stage membrane plants

A procedure is given for the design and optimisation of continuous multi-stage membrane plants using the example of whey ultrafiltration. During the design stage, the number of stages, area per stage, diafiltration water ratios and possible pressures can be varied to minimise capital and operating costs. The concept of an optimal or ideal plant was developed to provide a basis for comparison for the designs. To interpret the results, and check the validity of the optimisation results, a variety of graphical representations were developed. Graphical profiles of purity versus total solids, and of protein concentration versus lactose concentration were effective when interpreting design results and a graph of component mass flux helped identify yield losses. These and other graphs provided insight into the designs and often enable sensible improvements to them.