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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.

Numerous researchers have probed the peristaltic flows because of their immense usage in industrial engineering, biomedical engineering and biological sciences. However, the investigation of peristaltic flow in two-phase fluid of a rotating frame in the presence of a magnetic field has not been yet discussed. Therefore, to fulfill this gap in the existing literature, this paper will explicate the peristaltic flow of two-phase fluid across a rotating channel with the effect of wall properties in the presence of a magnetic field. The purpose of this study is to investigate the two-phase velocity distribution and rotation parameter when magneto-hydrodynamics is applied.

The constituent equations are solved under the condition of low Reynolds number and long wavelength. The exact method is used to attain the subsequent equations and a comprehensive graphical study for fluid phase, particulate phase velocity and flow rates are furnished. The impacts of pertinent parameters, magnetic field and rotation are discussed in detail.

It is witnessed that the velocity profile of particulate phase gets higher values for the same parameters as compared to the fluid phase velocity. Moreover, the axial velocity increases with different values of particle volume fraction, but in case of magnetic field and rotation parameter, it shows the opposite behavior.

The outcomes of study have viable industrial implementations in systems comprising solid-liquid based flows of fluids involving peristaltic movement.

The investigation of peristaltic flow in two-phase fluid of a rotating frame in the presence of a magnetic field has not been yet discussed. Therefore, to fulfill this gap, the present study will explicate the peristaltic flow of two-phase fluid across a rotating channel with the effect of wall properties in the presence of magnetic field.

This work focuses on the laminar flow of a two‐phase particulate suspension induced by a suddenly accelerated infinite vertical permeable surface in the presence of fluid buoyancy, magnetic field, heat generation or absorption, and surface suction or blowing effects. The governing equations for this modified Stokes problem are developed based on the continuum representation of both the fluid and the particle cloud. Appropriate dimensionless variables are introduced. The resulting dimensionless equations are solved numerically by an accurate implicit finite‐difference method for two situations. The first case corresponds to an impulsive start of the surface from rest while the second case corresponds to a uniformly accelerated surface. The numerical results for these cases are illustrated graphically. Comparisons with previously published work are performed and the results are found to be in good agreement. Typical fluid‐ and particle‐phase velocity and temperature distributions as well as wall shear stress and heat transfer results are reported for various values of the particle loading, Hartmann number, wall mass transfer coefficient and the heat generation or absorption coefficient.

The purpose of this paper is to conduct a detailed investigation of the two-dimensional natural convection flow of a dusty fluid. Therefore, the incompressible boundary layer flow of a two-phase particulate suspension is investigated numerically over a semi-infinite vertical flat plate. Comprehensive flow formations of the gas and particle phases are given in the boundary layer region. Primitive variable formulation is employed to convert the nondimensional governing equations into the non-conserved form. Three important two-phase mechanisms are discussed, namely, water-metal mixture, oil-metal mixture and air-metal mixture.

The full coupled nonlinear system of equations is solved using implicit two point finite difference method along the whole length of the plate.

The authors have presented numerical solution of the dusty boundary layer problem. Solutions obtained are depicted through the characteristic quantities, such as, wall shear stress coefficient, wall heat transfer coefficient, velocity distribution and temperature distribution for both phases. Results are interpreted for wide range of Prandtl number Pr (0.005-1,000.0). It is observed that thin boundary layer structures can be formed when mass concentration parameter or Prandtl number (e.g. oil-metal particle mixture) are high.

The results of the study may be of some interest to the researchers of the field of chemical engineers.

This present aims to present the numerical study of the unsteady stretching/shrinking flow of a fluid-particle suspension in the presence of the constant suction and dust particle slip on the surface.

The governing partial differential equations for the two phases flows of the fluid and the dust particles are reduced to the pertinent ordinary differential equations using a similarity transformation. The numerical results are obtained using the bvp4c function in the Matlab software.

The results revealed that in the decelerating shrinking flow, the wall skin friction is higher in the dusty fluid when compared to the clean fluid. In addition, the effect of the fluid-particle interaction parameter to the fluid-phase can be seen more clearly in the shrinking flow. Other non-dimensional physical parameters such as the unsteadiness parameter, the mass suction parameter, the viscosity ratio parameter, the particle slip parameter and the particle loading parameter are also considered and presented in figures. Further, the second solution is discovered in this problem and the solution expanded with higher unsteadiness and suction values. Hence, the stability analysis is performed, and it is confirmed that the second solution is unstable.

In practice, the flow conditions are commonly varying with time; thus, the study of the unsteady flow is very crucial and useful. The problem of unsteady flow of a dusty fluid has a wide range of possible applications such as in the centrifugal separation of particles, sedimentation and underground disposable of radioactive waste materials.

Even though the problem of dusty fluid has been broadly investigated, limited discoveries can be found over an unsteady shrinking flow. Indeed, this paper managed to obtain the second (dual) solutions, and stability analysis is performed. Furthermore, the authors also considered the artificial particle-phase viscosity, which is an important term to study the particle-particle and particle-wall interactions. With the addition of this term, the effects of the particle slip and suction parameters can be investigated. Very few studies in the dusty fluid embedded this parameter in their problems.

This paper aims to study the influence of microparticles on the surface cavitation behavior of 2Cr3WMoV steel; microparticle suspensions of different concentration, particle size, material and shape were prepared based on ultrasonic vibration cavitation experimental device.

2Cr3WMoV steel was taken as the research object for ultrasonic cavitation experiment. The morphology, quantity and distribution of cavitation pits were observed and analyzed by metallographic microscope and scanning electron microscope.

The study findings showed that the surface cavitation process produced pinhole cavitation pits on the surface of 2Cr3WMoV steel. High temperature in the process led to oxidation and carbon precipitation on the material surface, resulting in the “rainbow ring” cavitation morphology. Both the concentration and size of microparticles affected the number of pits on the material surface. When the concentration of microparticles was 1 g/L, the number of pits reached the maximum, and when the size of microparticles was 20 µm, the number of pits reached the minimum. The microparticles of Fe3O4, Al2O3, SiC and SiO2 all increased the number of pits on the surface of 2Cr3WMoV steel. In addition, the distribution of pits of spherical microparticles was more concentrated than that of irregularly shaped microparticles in turbidity.

Most of the current studies have not systematically focused on the effect of each factor of microparticles on the cavitation behavior when they act separately, and the results of the studies are more scattered and varied. At the same time, it has not been found to carry out the study of microparticle cavitation with 2Cr3WMoV steel as the research material, and there is a lack of relevant cavitation morphology and experimental data.

The purpose of this paper is to expand the theoretical meaning and application of the separate components of the interaction coefficient as obtained from the generalized viscosity model.

Both theoretical and experimental analysis have been utilized to better understand the meaning of the separate components of the interaction coefficient obtained from the generalized viscosity model. Analysis of the experimental data of Schaller and Humphrey has been used to successfully isolate the separate components of the interaction coefficient.

The relative unhindered volume is the volume outside the sphere of influence of a particle that is responsible for the viscosity characteristics of a coating. This is the volume available for particles to move in the suspension and still contribute to the viscosity. The smaller the relative unhindered volume the higher the viscosity. As the interaction coefficient, σ, increases the particles increase their interaction with each other and the relative unhindered volume decreases. Using the data of Schaller and Humphrey, it was found that the interaction coefficient agreed best with the theoretical expectation relative to particle size when the ionic strength was low. At high levels of ionic strength, the solvent‐particle component of the interaction coefficient was dominant and the influence of particle size on the interaction coefficient was minimal.

Only one set of experimental data was successfully utilized for illustrative purposes in this study but the resulting analysis has implicated a broad range of practical applications. In addition, the general theoretical concepts elucidated relative to the interaction coefficient should still be applicable independent of the experimental results.

The analysis presented in this paper provides several practical guidelines to separate and control the charge component of pigments in a suspension from their size component using the interaction coefficient as described in this study. Consequently, the results of this study should provide several new practical approaches to use when attempting to control the viscosity of suspensions for a broad range of practical applications and for a broad range of suspension types including coatings.

This is the first time that the theoretical statistical character of the interaction coefficient as indicated in the generalized viscosity model has been specifically elucidated. In addition, the relatively simple experimental separation of the interaction coefficient into its size and electrical components has been shown to be widely applicable in this paper.

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.

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.

This article describes the development of a novel optical sensor, based on chromatic modulation, for characterising the particulate emissions from diesel engines, in situ and in real‐time.