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The purpose of this paper is to present the establishment of a computational fluid dynamics model for investigating different non-Newtonian rheological models of solder pastes by simulating solder paste viscosity measurement. A combined material model was established which can follow the measured, apparent viscosity values with lower error.

The model included a parallel plate arrangement of rheometers. The diameter of the plate was 50 mm, whereas the gap between the plates was 0.5 mm. Only one quarter of the plate was modelled to enable using fine enough mesh, while keeping the calculation time low. Non-Newtonian properties were set using user defined function in Ansys, based on the Cross and Carreau–Yasuda material models. The viscosity values predicted by the mathematical models were compared to measured viscosity values of different types of solder pastes.

It was found that the Cross model predicts the apparent viscosity with a relatively high error (even approximately 50 per cent) at lower shear rates, whereas the Carerau–Yasuda model has higher errors at higher shear rates. The application of the proposed, combined model can result in a much lower error in the apparent viscosity between the calculated and measured viscosity values.

The error of Cross and Carreau–Yasuda material models has not been investigated yet in details. The proposed, combined material model can be applied for subsequent simulations via the described UDF, e.g. in the numerical modelling of the stencil printing. This can result in a more accurate modelling of the stencil printing process, which is inevitable considering the printing of solder paste for today fine-pitch, small size components.

The purpose of this paper is to propose three modified subgrid-scale (SGS) eddy-viscosity models to improve their original eddy-viscosity models (the Smagorinsky model (SM), the mixed-scale model (MSM), and the wall-adapted local eddy-viscosity model (WALE)) in the simulation of turbulent flows in near-wall region.

The subgrid viscosity is related to the norm of strain rate tensor of the smallest resolved scales, instead of the norm of the resolved strain rate tensor of the large scales.

All the SGS viscosity of the modified eddy-viscosity models (small-large model, modified MSM, and modified WALE) is closer to y+3 behavior than those of the original eddy-viscosity models (SM, MSM, and WALE) near the wall.

The norm of strain rate tensor of the smallest scales used in eddy-viscosity models, instead of the norm of strain rate tensor, makes the eddy viscosity in near-wall region approach to zero in a physical sense.

The purpose of this paper is to present a novel model for predicting the effective viscosity of nanofluids. At present, no unified model exists for the same.

The present effective viscosity model draws upon the regression analysis of carefully selected published papers covering experimental, numerical and theoretical findings.

Unlike some other models, this one is reliable and has a good level of accuracy. This model has been assessed in a numerical investigation using a 3D horizontal pipe, and the results are presented.

This is a new model for predicting the effective viscosity of nanofluids. The proposed model has been tested in a 3D horizontal pipe, and the predicted results for viscosity and Nusselt number show good agreement with the available data.

Viscosity is an important basic physical property of liquid solders. However, because of the very complex nonlinear relationship between the viscosity of the liquid ternary Sn-based lead-free solder and its determinants, a theoretical model for the viscosity of the liquid Sn-based solder alloy has not been proposed. This paper aims to address the viscosity issues that must be considered when developing new lead-free solders.

A BP neural network model was established to predict the viscosity of the liquid alloy and the predicted values were compared with the corresponding experimental data in the literature data. At the same time, the BP neural network model is compared with the existing theoretical model. In addition, a mathematical model for estimating the melt viscosity of ternary tin-based lead-free solders was constructed using a polynomial fitting method.

A reasonable BP neural network model was established to predict the melt viscosity of ternary tin-based lead-free solders. The viscosity prediction of the BP neural network agrees well with the experimental results. Compared to the Seetharaman and the Moelwyn–Hughes models, the BP neural network model can predict the viscosity of liquid alloys without the need to calculate the relevant thermodynamic parameters. In addition, a simple equation for estimating the melt viscosity of a ternary tin-based lead-free solder has been proposed.

The study identified nine factors that affect the melt viscosity of ternary tin-based lead-free solders and used these factors as input parameters for BP neural network models. The BP neural network model is more convenient because it does not require the calculation of relevant thermodynamic parameters. In addition, a mathematical model for estimating the viscosity of a ternary Sn-based lead-free solder alloy has been proposed. The overall research shows that the BP neural network model can be well applied to the theoretical study of the viscosity of liquid solder alloys. Using a constructed BP neural network to predict the viscosity of a lead-free solder melt helps to study the liquid physical properties of lead-free solders that are widely used in electronic information.

The purpose of this paper is to investigate the effect of different viscosity models (Cross and Al-Ma’aiteh) and different printing speeds on the numerical results (e.g. pressure over stencil) of a numerical model regarding stencil printing.

A finite volume model was established for describing the printing process. Two types of viscosity models for non-Newtonian fluid properties were compared. The Cross model was fitted to the measurement results in the initial state of a lead-free solder paste, and the parameters of a Al-Ma’aiteh material model were fitted in the stabilised state of the same paste. Four different printing speeds were also investigated from 20 to 200 mm/s.

Noteworthy differences were found in the pressure between utilising the Cross model and the Al-Ma’aiteh viscosity model. The difference in pressure reached 33-34% for both printing speeds of 20 and 70 mm/s and reached 31% and 27% for the printing speed of 120 and 200 mm/s. The variation in the difference was explained by the increase in the rates of shear by increasing printing speeds.

Parameters of viscosity model should be determined for the stabilised state of the solder paste. Neglecting the thixotropic paste nature in the modelling of printing can cause a calculation error of even approximately 30%. By using the Al-Ma’aiteh viscosity model over the stabilised state of solder pastes can provide more accurate results in the modelling of printing, which is necessary for the effective optimisation of this process, and for eliminating soldering failures in highly integrated electronic devices.

The purpose of the paper is to develop a methodology to characterize the rheological behaviour of macroscopic non-Brownian suspensions, like solder paste, based on microstructural evolution.

A structure-based kinetics model, whose parameters are derived analytically based on assumptions valid for any macroscopic suspension, is developed to describe the rheological behaviour of a given fluid. The values of the parameters are then determined based on experiments conducted at a constant shear rate. The parameter values, obtained from the model, are then adjusted using an optimization algorithm using the mean deviation from experiments as the cost function to replicate the measured rheology. A commercially available solder paste is used as the test fluid for the proposed method.

The initial parameter values obtained through the analytical model indicates a structural breakdown that is much slower than observations. But optimizing the parameter values, especially the ones associated with the structural breakdown, replicates the thixotropic behaviour of the solder paste reasonably well, but it fails to capture the structure build-up during the three interval thixotropy test.

The structural kinetics model tends to under-predict the structure build-up rate.

This study details a more realistic prediction of the rheological behaviour of macroscopic suspensions like solder paste, thermal interface materials and other functional materials. The proposed model can be used to characterize different solder pastes and other functional fluids based on the structure build-up and breakdown rates. The model can also be used as the viscosity definitions in numerical simulations instead of simpler models like Carreau–Yasuda and cross-viscosity models.

The rheological description of the solder paste is critical in determining its validity for a given application. The methodology described in the paper provides a better description of thixotropy without relying on the existing rheological measurements or the behaviour predicted by a standard power-law model. The proposed model can also provide transient viscosity predictions when shear rates vary in time.

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.

This paper aims to evaluate the dynamic viscosity and thermal conductivity of halloysite nanotubes (HNTs) suspended in SAE 5W40 using machine learning methods (MLMs).

A two-step method with surfactant was selected to prepare nanolubricants in concentrations of 0.025, 0.05, 0.1 and 0.5 wt%. Thermal conductivity and dynamic viscosity of nanofluids were ascertained over the temperature range of 25–70 °C, with an increment step of 5 °C, using a KD2-Pro analyser device and a digital viscometer MRC VIS-8. Additionally, four different MLMs, including Gaussian process regression (GPR), artificial neural network (ANN), support vector machine (SVM) and decision tree (DT), were used for predicting dynamic viscosity and thermal conductivity by using nanoparticle concentration and temperature as input parameters.

According to the achieved results, the dynamic viscosity and thermal conductivity of nanolubricants mostly increased with the rise of nanoparticle concentration in the base oil. All the proposed models, especially GPR with root mean square error mean values of 0.0047 for dynamic viscosity and 0.0016 for thermal conductivity, basically showed superior ability and stability to estimate the viscosity and thermal conductivity of nanolubricants.

The results of this paper could contribute to optimising the cost and time required for modelling the thermophysical properties of lubricants.

To the best of the author’s knowledge, in this available literature, there is no paper dealing with experimental study and prediction of dynamic viscosity and thermal conductivity of HNTs-based nanolubricant using GPR, ANN, SVM and DT.

The purpose of this paper is to develop a novel unstructured simulation approach for injection molding processes described by the Hele‐Shaw model.

The scheme involves dual dynamic meshes with active and inactive cells determined from an initial background pointset. The quasi‐static pressure solution in each timestep for this evolving unstructured mesh system is approximated using a control volume finite element method formulation coupled to a corresponding modified volume of fluid method. The flow is considered to be isothermal and non‐Newtonian.

Supporting numerical tests and performance studies for polystyrene described by Carreau, Cross, Ellis and Power‐law fluid models are conducted. Results for the present method are shown to be comparable to those from other methods for both Newtonian fluid and polystyrene fluid injected in different mold geometries.

With respect to the methodology, the background pointset infers a mesh that is dynamically reconstructed here, and there are a number of efficiency issues and improvements that would be relevant to industrial applications. For instance, one can use the pointset to construct special bases and invoke a so‐called “meshless” scheme using the basis. This would require some interesting strategies to deal with the dynamic point enrichment of the moving front that could benefit from the present front treatment strategy. There are also issues related to mass conservation and fill‐time errors that might be addressed by introducing suitable projections. The general question of “rate of convergence” of these schemes requires analysis. Numerical results here suggest first‐order accuracy and are consistent with the approximations made, but theoretical results are not available yet for these methods.

This novel unstructured simulation approach involves dual meshes with active and inactive cells determined from an initial background pointset: local active dual patches are constructed “on‐the‐fly” for each “active point” to form a dynamic virtual mesh of active elements that evolves with the moving interface.

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.