Donald J. Cleland

Reducing gas exchange of fruits with surface coatings

Abstract Surface coatings can increase a fruits skin resistance to gas diffusion, modify its internal atmosphere composition and depress its respiration rate; effects on transpiration tend to be comparatively small. A steady state mathematical model which considered diffusion through cuticle and pores separately was used to investigate two possible mechanisms by which coatings achieve these effects: either by acting as a film wrap or by blocking pores. It was concluded that coatings mainly exert their effects on skin resistance to diffusion of the permanent gases by blocking a greater or lesser proportion of the pores on the fruit surface. Both covering of the cuticle and blocking pores were important for resistance to water vapour diffusion. Coupled with a proposed differential resistance of the skin to oxygen, carbon dioxide and water vapour, this accounts for the observed effects of coatings on internal atmosphere modification, respiration and transpiration rates. Coating treatments which achieved substantial reductions in transpiration rates were associated with the fruit becoming anaerobic. Inherent variability in skin resistance to gas diffusion and fruit respiration rate, and differing proportions of pores blocked by coating, appear to be responsible for the highly variable response of individual fruit to a given coating treatment. Surface coatings may therefore be better suited to treating fruits destined for processing, in which fruit to fruit variability may be less critical, than to fruits destined for the fresh market, in which uniformity of individual fruit quality is of paramount importance.

Modelling the performance of a transcritical CO2 heat pump for high temperature heating

Abstract A prototype transcritical CO2 heat pump was constructed for heating water to temperatures greater than 65°C while providing refrigeration at less than 2°C. The heating capacity was 115 kW at an evaporation temperature of +0.3°C and a hot water temperature of 77.5°C, with a heating coefficient of performance (COP) of 3.4. Performance data is presented for each of the compressor, the gas cooler, and the recuperator as well as for the overall heat pump system. Equipment performance data was incorporated into a computer model to enable parametric investigations of heat pump performance. Model predictions showed that the hot water temperature could be increased from 65 to 120°C with a relatively small reduction in heating capacity and heating COP of 33 and 21%, respectively. Model predictions also highlight the potential for significant capacity improvements by eliminating the recuperator in favour of a larger gas cooler.

Determination of lower oxygen limits for apple fruit

Abstract Knowledge of the lower oxygen limit ( LOL ) is critical for optimising the gaseous storage environment for fruits. The optimum storage atmosphere occurs just above the LOL at which aerobic respiration is at the lowest level which can be achieved without development of anaerobic metabolism. Measures of LOL based on a fruits internal atmosphere, rather than external or package atmospheres, estimate the true LOL as these account more directly for differences in respiration rate and skin permeance of individual fruit. Two measures of LOL were considered: the anaerobic compensation point ( ACP ) and the fermentation threshold ( FT ). The ACP was described in terms of plots of the internal partial pressure of CO 2 versus internal O 2 ( p O 2 i ) and external O 2 ( p O 2 e ) partial pressures. The FT was described in terms of plots of both the respiratory quotient ( RQ ) and ethanol concentration versus p O 2 i and p O 2 e , and occurred at higher p O 2 than the ACP . Mathematical solutions for estimating the ACP and the FT based on the RQ ( FT RQ ) are described. A statistical ‘bootstrap’ procedure is described for estimating the FT based on ethanol concentration ( FT EtOH ) and was also suitable for estimating all other LOLs and their confidence intervals. LOL s were estimated for ‘Coxs Orange Pippin’ apples ( Malus domestica , Borkh) at 24 °C using controlled atmospheres (CA). The steady-state internal partial pressures of O 2 , CO 2 and concentrations of acetaldehyde, ethyl acetate and ethanol were estimated non-invasively by sampling the headspace of 1000 mm 3 glass surface chambers sealed to the equatorial surface of the apples. LOLs estimated on a p O 2 i basis were on average 1.69 kPa, 1.94 kPa and 2.10 kPa p O 2 lower for ACP , FT RQ and FT EtOH respectively than those estimated relative to p O 2 e . The bootstrap 95% confidence limits for internal ACP ( ACP i ) were 0.70 to 0.78 kPa p O 2 i whilst for internal FT RQ ( FT RQ ) the interval was 1.04 to 1.20 kPa p O 2 i and for internal FT EtOH ( FT EtOH ) 0.68 to 0.87 kPa P O 2 i . Bootstrap estimates were similar, though typically higher, than mathematically fitted estimates. Determining LOL s on a steady-state internal atmosphere basis estimates the true LOL more accurately than those estimated from external or package atmospheres, and provides a more mechanistic basis for models used to predict fruit responses to CA. As the FT RQ represents the critical point at which fermentation occurs it was considered the safest estimate of the true LOL for optimising storage atmospheres.

Prediction of freezing and thawing times for multi-dimensional shapes by numerical methods

Abstract An assessment of the accuracy of numerical methods used in the prediction of freezing and thawing times was made using a comprehensive set of freezing and thawing data for both regular and irregular multidimensional shapes. For regular shapes, a finite difference method gave accurate predictions with reasonable computation costs. Predictions for two finite element method formulations were not always accurate. This was due to practical constraints on the computation costs which meant that time and spatial grids could not always be made sufficiently fine to ensure that the prediction method uncertainty was insignificant compared with the other sources of imprecision. Guidelines are suggested for the use of the finite element method as a freezing or thawing time predictor. These should ensure that the prediction method error is small while keeping the computation costs reasonable.

Prediction of thawing times for foods of simple shape

Abstract A set of 104 experimental measurements of thawing time were made over a wide range of conditions for slab, infinite cylinder and sphere shapes of a food analogue material. These results were used to assess existing thawing time prediction methods. Versions of both the finite difference and the finite element numerical methods that accounted for continuously temperature-variable thermal properties gave accurate predictions. No previously published simple prediction formula was found that was both sufficiently accurate and expressed in a form suitable for it to be adopted as a general thawing time prediction method. Four accurate, but simple, empirical formulae based on Planks equation were developed. These formulae predicted thawing times that were both highly correlated with those predicted by the numerical methods and agreed with the experimental data to within ±10% at the 95% level of confidence. The agreement was more limited by uncertainties in the experimental and thermal property data than by inaccuracy in the prediction formulae. Significantly more accurate simple formulae are unlikely to be developed unless more accurate experimental data are available.

Prediction of freezing and thawing times for multi-dimensional shapes by simple formulae part 2: irregular shapes

Calculated and experimental data for multi-dimensional irregular shapes wer used to assess various methodologies to include the effect of shape in empirical freezing and thawing time prediction methods. The principles underlying two existing geometric factors, EHTD and MCP, were found to be valid; so there seems to be no need for other approaches. Used in conjunction with accurate slab freezing and thawing time prediction methods, the proposed empirical formulae for EHTD and MCP gave accurate predictions for all of the two-dimensional shapes and most of the three-dimensional shapes tested, except those with oval cross-sections in the third dimension. This was attributed to the lack of data for this group of shapes.

Prediction of freezing and thawing times for foods of regular multi-dimensional shape by using an analytically derived geometric factor

Abstract Analytical solutions for transient heat conduction with phase change and general boundary conditions were used to calculate a geometric factor to take account of the effect of product geometry on freezing and thawing times for a number of regular two- and three-dimensional objects. These analytically derived formulae depend only on the Biot number and simple parameters that describe object shape. The accuracy of these formulae was demonstrated by comparisons with both large sets of experimental food freezing and thawing data and numerically calculated data. The performance of the new formulae was better than that of any previous ones and the formulae are simple to use.

Changes in respiration and ethylene production of apples in response to internal and external oxygen partial pressures

Variations in respiration rate and ethylene production of ‘Coxs Orange Pippin’ and ‘Granny Smith’ apples in response to reduced oxygen partial pressures were characterised by studying O2, CO2 and C2H4 partial pressure differences between the internal and external atmospheres (ΔpO2, ΔpCO2 and ΔpC2H4, Pa) of individual fruit maintained in different O2 atmospheres at 20 ± 1°C. ΔpO2 decreased at low O2 levels, reflecting the decreased rate of O2 uptake in low O2 partial pressures. Oxygen uptake relative to that in air (relrO2) approximately followed Michaelis-Menten kinetics, with a half-maximal rate at 3.3 kPa O2 for internal oxygen (piO2) and 10.4 kPa O2 for external oxygen (peO2). An equation was developed to describe aerobic and anaerobic components of CO2 production relative to that in air (relrCO2) as a function of peO2 or piO2. The relationship between rate of C2H4 production relative to that in air (relrC2H4) and piO2 was reasonably described by a Michaelis-Menten type hyperbolic curve, confirming the expectation that small changes in O2 partial pressure would have a much greater effect on relrC2H4 at low piO2 than they do at high piO2. In contrast, presence of the skin as a diffusion barrier resulted in development of an apparent ‘lag phase’ in the relationship between relrC2H4 and peO2 such that it became essentially sigmoidal. These differences are attributed to differences in O2 partial pressure between internal and external atmospheres.

Experimental data for freezing and thawing of multi-dimensional objects

Abstract Testing the accuracy of freezing and thawing time prediction methods requires accurate experimental data. To complement existing data, 175 experimental measurements, 68 for thawing of rectangular bricks and 107 for both freezing and thawing of 12 different multi-dimensional irregular shapes, were made using Tylose, a food analogue, over a wide range of conditions. Twelve additional experiments were conducted using an actual food material, minched lean beef. Details of all the experimental conditions are reported.

A simple method for prediction of chilling times: extension to three-dimensional irregular shapes

Abstract The extension of a previously published empirical chilling time prediction method to three-dimensional irregular shapes was investigated. The real geometric shapes were related to equivalent ellipsoids using simple geometric measurements. Chilling time estimates were made using two shape-dependent parameters in conjunction with the first term in the series-analytical solution for convective cooling of a sphere. Experiments for eight geometric shapes (21 runs) were used to validate the model for thermal centre temperature predictions. The accuracy of the model for predicting mass-average temperatures of irregular shapes was not tested. Accurate chilling time prediction by a method employing only simple algebraic expressions is now possible for objects of any shape.