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Investigated milk fat fraction differs in physical attributes, first of all in melting point and solid fat content and its influence on crystallization process of cocoa butter i.e. chocolate mass. It means that this fraction slows down crystallization rate, decreases melting point of mixture with cocoa butter and causes chocolate softness. It is very important for quality of chocolate especially chocolate with nuts or sunflower kernel. The aim of this paper was to investigate the influence of low‐melting (26°C) milk fat fraction on crystallization processes in chocolate mass and define the optimal concentration of this fraction with suitable precrystallization temperature time regime. Solid fat content of chocolate which designates the influence of precrystallization changes in chocolate mass with addition of milk fat fractions was investigated.

The precrystallization was performed in a laboratory crystallizer that is in a modified Brabender pharinograph, which measures the rheological characteristics as indirect parameter of crystallization properties of chocolate mass depending on milk fat fraction concentration and precrystallization temperature. The experiments were performed according to the factorial plan 3² (two factors on three levels) and the results are statistically treated.

The results showed that the optimal conditions for achieving the satisfactory tempering rate (optimal concentration of crystals in chocolate mass) are addition of 3 per cent low‐melting milk fat fraction and precrystallization temperature of 25°C.

The addition of high‐melting milk fat fraction slows down the chocolate mass crystallization more then low‐melting milk fat fraction. Investigated fraction influenced decreasing in solid fat content of chocolate regardless of precrystallization temperature.

In this paper we use a large linked employer-employee data set on German establishments between 1993 and 2012 to investigate how the gender composition of the top layer of management affects a variety of establishment and worker outcomes. We use two different measures to identify the gender composition of the top layer based on direct survey data: the fraction of women among top managers, and the fraction of women among working proprietors. We document the following facts: (a) There is a strong negative association between the fraction of women in the top layer of management and several establishment outcomes, among them business volume, investment, total wage bill per worker, total employment, and turnover; (b) Establishments with a high fraction of women in the top layer of management are more likely to implement female-friendly policies, such as providing childcare facilities or promoting and mentoring female junior staff; (c) The fraction of women in the top layer of management is also negatively associated with employment and wages, both male and female, full-time and part-time. However, all of these associations vanish when we include establishment fixed effects and establishment-specific time trends. This reveals a substantial sorting of female managers across establishments: small and less productive establishments that invest less, pay their employees lower wages, but are more female-friendly are more likely to be led by women.

The purpose of this study is to present a newly proposed and developed sorting algorithm-based merging weighted fraction Monte Carlo (SAMWFMC) method for solving the population balance equation for the weighted fraction coagulation process in aerosol dynamics with high computational accuracy and efficiency.

In the new SAMWFMC method, the jump Markov process is constructed as the weighted fraction Monte Carlo (WFMC) method (Jiang and Chan, 2021) with a fraction function. Both adjustable and constant fraction functions are used to validate the computational accuracy and efficiency. A new merging scheme is also proposed to ensure a constant-number and constant-volume scheme.

The new SAMWFMC method is fully validated by comparing with existing analytical solutions for six benchmark test cases. The numerical results obtained from the SAMWFMC method with both adjustable and constant fraction functions show excellent agreement with the analytical solutions and low stochastic errors. Compared with the WFMC method (Jiang and Chan, 2021), the SAMWFMC method can significantly reduce the stochastic error in the total particle number concentration without increasing the stochastic errors in high-order moments of the particle size distribution at only slightly higher computational cost.

The WFMC method (Jiang and Chan, 2021) has a stringent restriction on the fraction functions, making few fraction functions applicable to the WFMC method except for several specifically selected adjustable fraction functions, while the stochastic error in the total particle number concentration is considerably large. The newly developed SAMWFMC method shows significant improvement and advantage in dealing with weighted fraction coagulation process in aerosol dynamics and provides an excellent potential to deal with various fraction functions with higher computational accuracy and efficiency.

In part I of this study a new dry coating analysis was developed relating pigment cluster voids and pigment particle distribution to the pigment cluster dispersion coefficient, C_q, and the critical pigment volume concentration (CPVC). Part II of this study has addressed a wet coating analysis to relate pigment particle size distribution and viscosity in a coating formulation to the pigment cluster dispersion coefficient.

This study introduced the relationships for the wet coating by building on the dry coating evaluations introduced in part I of this study. Part II of this study showed that the CPVC for a solvent based coating can be significantly influenced by a change in the viscosity measured interaction coefficient, σ, as influenced by a change in an additive such as the surfactant concentration in the matrix or polymer phase of the coating. The CPVC was also shown to be strongly influenced by a separate analysis of the pigment particle size distribution to modify the coating viscosity.

It was pointed out recently that an increase in flow additive increased the CPVC but decreased viscosity. Consequently, it was shown theoretically in this study that viscosities compared at the same relative viscosity, η/η₀, and at the same filler composition, f_i, using the generalized viscosity model would require decrease in the interaction coefficient, σ, to increase the global volume fraction of filler or pigment, Φ_F. This implied that a measurement of the interaction coefficient, σ, should be a direct measure of the ability of the CPVC to be modified. A minimum viscosity from the generalised viscosity model also resulted at the maximum packing fraction, which in turn was found to increase the CPVC of the coating. Consequently, part II of this study has yielded a useful relationship between the cluster dispersion coefficient, C_q, and the interaction coefficient, σ, from the generalised viscosity model.

While the experimental measurement of the parameters to isolate the clustering concepts introduced in this study may be difficult, it is expected that better quantitative measurement of clustering concepts will eventually prove to be very beneficial to providing improved suspension applications including coatings. The close relationship introduced in this study between clustering concepts and viscosity should provide an improved ability to measure the parameters to isolate clustering in coatings and other suspension applications.

The theoretical relationship developed in this study between the pigment cluster dispersion coefficient, C_q, and CPVC and the theoretical and experimental relationship between CPVC and the viscosity interaction coefficient, σ, inferred a direct relationship between C_q and the viscosity interaction coefficient, σ. Consequently, it was shown that the theoretical pigment cluster model developed in this study could be directly related to the experimental matrix additive composition controlling viscosity in a coating formulation. The practical implication is that the measurement tools introduced in this study should significantly influence future suspension formulations to provide better measurement and control of clustering and viscosity in coatings and other suspension applications.

Part II of this study has shown how a useful relationship can be generated between the interaction coefficient, σ, from the generalised viscosity model and the pigment cluster dispersion coefficient, C_q, developed in part I of this study. In addition, this study also showed that effective control of the CPVC of a coating can be modified by judicious control of the interaction coefficient using pigment particle size distribution and/or viscosity control additives in a wet coating analysis.

Multiple attribute decision making (MADM) is a conceptual agenda used for evaluation and selection of optimal nanofluid to assure best performance of heat exchanger. Most of the studies focus on nanofluids focus on individual ability at one time. Relatively, not even a single study is available for selection of nanofluid for heat exchanger using concurrent design and MADM approach. The purpose of this paper is to propose a concurrent design methodology using MADM approach to assist improved design of heat exchanger concurrently for all the x-abilities in an integrated manner.

A combined methodology of applying MADM approach using concurrent design for x-abilities is called CE-MADM approach. Implementation of nanofluid to improve thermal performance of heat exchanger entails thorough evaluation of nanofluids in various x-abilities (performance, maintenance, thermophysical properties and modelisation) to make exhaustive management decision. Sensitivity analysis is also proposed to study the behaviour of height of variation of density, heat capacity, thermal expansion and thermal conductivity with varying particle volume fraction and variation of relative closeness of available alternates from ideally best possible solution.

MADM approach considering various x-abilities concurrently provide an approach for relative ranking of available nanofluids for optimum performance. Fishbone diagrams of all x-abilities are constructed to identify all the attributes and converge large number of attributes into single numerical index that are concurrently responsible for the cause thus saving time for easy evaluation, comparison and ranking by decision makers. Sensitivity analysis to demonstration height of variation of pertinent attributes with varying particle volume fraction. A MATLAB programming is established to execute calculations involved in the procedure.

This paper comprises a predictable and effective mathematical approach to improve design of heat exchanger with nanofluid bearing in mind all the required x-abilities concurrently. This combined approach of CE-MADM is never applied before in the field of nanofluid to predict best possible results in feasible conditions considering all the x-abilities. Sensitivity analysis is also presented from the assumed mathematical equations of thermophysical properties.

The importance of maximizing the particle packing fraction in a suspension by maximizing average particle size ratio of D₅/D₁ has been adequately shown to be important as previously reported in the literature. This study aims to extend that analysis to include the best formulation approach to maximize the packing fraction with a minimum number of monodisperse particle sizes.

An existing model previously developed by this author was modified theoretically to optimize the ratio used between consecutive monodisperse particle sizes. This process was found to apply to a broad range of particle configurations and applications. In addition, five different approaches for maximizing average particle size ratio D̅₅/D̅₁ were addressed for blending several different particle size distributions. Maximizing average particle size ratio D̅₅/D̅₁ has been found to result in an optimization of the packing fraction. Several new concepts were also introduced in the process of maximizing the packing fraction for these different approaches.

The critical part of the analysis to maximize the packing fraction with a minimum number of particles was the theoretical optimization of the ratio used between consecutive monodisperse particle sizes. This analysis was also found to be effectively independent of the maximum starting particle size. This study also clarified the recent incorrect claim in the literature that Furnas in 1931 was the first to generate the maximum theoretical packing fraction possible for n different particles that was actually originally developed in conjunction with the Sudduth generalized viscosity equation. In addition, the Furnas generated equation was also shown to give significantly different results from the Sudduth generated equation.

Experimental data involving monodisperse particles of different blends with a minimum number of particle sizes that are truly monodisperse are often extremely difficult to obtain. However, the theoretical general concepts can still be applicable.

The expanded model presented in this article provides practical guidelines for blending pigments using a minimum number of monodisperse particle sizes that can yield much higher ratios of the particle size averages D̅₅/D̅₁ and thus potentially achieve significantly improved properties such as viscosity.

The model presented in this article provides the first apparent guidelines to control the blending of pigments in coatings by the optimization of the ratio used between consecutive monodisperse particle sizes. This analysis was also found to be effectively independent of the maximum starting particle size.

The primary objective of this two part study was to show theoretically how pigment cluster voids and pigment distribution can influence the critical pigment volume concentration (CPVC) and consequently the properties of a dry coating. In Part I of this study a pigment clustering model with an analytical solution has been developed that was a modification of an earlier model by Fishman, Kurtze, and Bierwagen that could only be solved numerically.

The original derivation of the clustering concept developed by Fishman et al. resulted in a mathematical analysis which was only able to be solved numerically and was found to be very tedious to utilize directly. In this study, a new successful derivation utilizing some of the original concepts of Fishman et al. was generated and shown to result in a practical and much more useable analytical analysis of the clustering concept. This new model was then applied directly to quantify the influence of flow agents or surfactants in a coating formulation on the CPVC as described by Asbeck.

It was found that the largest deviation from 100 per cent pigment dispersion with no pigment clusters occurred just before and just after the ultimate CPVC (UCPVC). A theoretical relationship was also found between the pigment cluster dispersion coefficient, C_q, and CPVC. This result was consistent with the experimental relationship between CPVC and the per cent flow additive as found by Asbeck. The density ratio of overall coating to the pigment density was found to go through a maximum at a global volume fraction of pigment that was slightly greater than the UCPVC as expected for a mechanical property. It was also identified that mechanical failure of most coating formulations should be apparent at either the “Lower Zero Limit” or the “Upper Zero Limit” global volume fraction pigment as defined in this study.

While the experimental measurement of the parameters to isolate the clustering concepts introduced in this study may be difficult, it is expected that better quantitative measurement of clustering concepts will eventually prove to be very beneficial to providing improved suspension applications including coatings.

The theoretical relationship developed in this study between the pigment cluster dispersion coefficient, C_q, and CPVC and the experimental relationship between CPVC and the per cent flow additive found by Asbeck inferred a direct relationship between C_q and the per cent flow additive. Consequently, it was shown that the theoretical pigment cluster model developed in this study could be directly related to the experimental matrix additive composition in a coating formulation. The implication is that the measurement tool introduced in this study can provide better measurement and control of clustering in coatings and other suspension applications.

In this study, a new successful derivation utilizing some of the original concepts of Fishman et al. was generated and shown to result in a practical and much more useable analytical analysis of the clustering concept. This new model was then applied directly to quantify the influence of flow agents or surfactants in a coating formulation on the CPVC as described by Asbeck.

This paper aims to present experimental and numerical analyses of fused filament fabrication (FFF) printed parts and show how mechanical characteristics of printed ABS-MG94 (acrylonitrile butadiene styrene) are influenced by the void volume fraction, cooling rate and residual thermal stresses.

Printed specimens were experimentally tested to evaluate the mechanical properties for different printing speeds, and micrographs were taken. A thermo-mechanical finite element model, able to simulate the FFF process, was developed to calculate the temperature fields in time, cooling rate and residual thermal stresses. Finally, the experimental mechanical properties and the microstructure distribution could be explained by the temperature fields in time, cooling rate and residual thermal stresses.

Micrographs revealed the increase of void volume fraction with the printing speed. The variations on voids were associated to the temperature fields in time: when the temperatures remained high for longer periods, less voids were generated. The Young's Modulus of the deposited filament varied according to the cooling rate: it decreased when the cooling rate increased. The influence of the residual thermal stresses and void volume fraction on the printed parts failure was also investigated: in the worst scenarios evaluated, the void volume fraction reduced the strength in 9 per cent, while the residual thermal stresses reduced it in 3.8 per cent.

This work explains how the temperature fields can affect the void volume fraction, Young's Modulus and failure of printed parts. Experimental and numerical results are shown. The presented research can be used to choose printing parameters to achieve desired mechanical properties of FFF printed parts.

This study aims to introduce a new theoretical approach to blend spherical and non‐spherical particles in a coating to improve its viscosity characteristics.

Theoretical analysis has been used to modify an existing model developed by this author to apply to a broad range of particle configurations.

Non‐spherical particles like fibres or discs in a suspension or coating have been found to have three different viscosity response regions. Consequently, the viscosity of suspensions or coatings with these types of particles appears to have two apparent maximums as a function of concentration. Improved viscosity control of coatings have been found to be directly achievable by blending particles with different shapes based on the concentration relative to this first maximum. This optimisation process has been found to be better understood using a new variable which has been described as the “sphericity”, s. The “sphericity”, s, as described in this study has been defined as the relative ratio of the surface to volume fraction for a non‐spherical particle to that of a sphere of equivalent volume.

Experimental data involving monodisperse particles of different configurations is often extremely difficult to obtain. However, the theoretical general concepts can still be applicable.

The model presented in this paper provides practical guidelines to blending pigments with different particle shapes to control the viscosity of coatings and suspensions.

The model presented in this paper provides the first apparent guidelines to control the blending of pigments in coatings and composites with different particle shapes using the “sphericity” of the pigment particle.

The purpose of this study is to demonstrate the usage of three-dimensionally (3D) printed polylactic acid (PLA)-carbon black (CB) conductive polymer composite in the measurement of the void fraction and liquid level.

PLA-CB conductive polymer composite is 3D printed through fused deposition modelling (FDM) technique and used as a capacitive sensor for void fraction measurement and liquid level sensing. The sensitivity of 3D printed ring and concave type capacitive sensors are compared for void fraction measurement. The effect of electrode length, thickness and pipe dimension on the capacitance achievable for the particular void fraction is studied. Concept of fringing capacitance is used for the sensing of liquid level.

Compared to the concave design comprising four electrodes, the ring-type capacitive sensor produced better results in void fraction measurement. Increase in pipe diameter and electrode length results in the enhancement of capacitance arising from specific void fraction. For a 100 mm diameter pipe, the capacitance of the 150 mm-long concave electrode (0.4 mm thick) increased from 9.98 to 67.77 pF as the void fraction decreased from 100% to 0%. Development of the fringing capacitance in 3D printed PLA-CB composite helps in the measurement of liquid level. Both parallel finger topology and interdigital electrode configuration are able to sense the liquid level.

Ability of the 3D printed conductive PLA-CB composite to act as a capacitive sensor is experimentally analysed. Performance of different electrode configuration is tested for both void fraction measurement and liquid level sensing. Results of experimentation prove that FDM printed PLA-CB composite is suitable for the void fraction and liquid level measurement.