Maximum Packing Fraction Research Articles

Rheology of flexible fiber-reinforced cement pastes: Maximum packing fraction determination and structural build-up analysis

The maximum packing fraction (φfm) of flexible fibers is an essential parameter for understanding the rheological behavior of flexible fiber-reinforced cement paste (FFRCP). However, direct measurement of φfm of flexible fibers is still lacking. In this study, a shear rheology-based method for direct measurement of φfm was proposed and the assumption of fiber conformation under shear was verified by micro-CT. Based on this, a yield stress model for FFRCP was constructed to explain the entanglement and friction effects in the fiber network. Finally, static yield stress tests and small amplitude oscillatory shear (SAOS) tests were carried out to explore the structural build-up of FFRCP. It was found that the proposed method enables direct determination of φfm through only a few viscosity-fiber content data for a given FFRCP. Furthermore, the proposed model can describe the static yield stress of FFRCP well. Finally, the relative structural build-up rate of FFRCP follows a similar trend as the relative yield stress, with a critical relative fiber volume fraction (0.299) as the boundary. Subsequently, the relative structural build-up gradually deviates from the relative yield stress due to the limiting effect of the fibers.

Packing properties assessment of cement and alternative powders: Artefacts and protocols

This paper introduces three major recommendations for the assessment of the maximum packing fraction of mineral powders through compressive rheology. First, our results show that a minimum compressive stress is required for the measured solid volume fraction to tend towards a constant jamming fraction. Second, we show that the modification of the particles surface properties, especially their friction coefficient, by polymer adsorption, allows for this jamming fraction to get closer to the particle maximum packing fraction. Finally, we show that a minimal value of the initial solid volume fraction of a sample is necessary to prevent particle size separation during testing. We moreover show that the measured jamming fraction depends on the initial solid volume fraction of cement-based samples. We suggest that such a peculiar behavior finds its origin in the dependency of early hydrates volume or morphology on the initial supersaturation.

Role of the constriction angle on the clogging by bridging of suspensions of particles

Confined flows of particles can lead to clogging, and therefore failure, of various fluidic systems across many applications. As a result, design guidelines need to be developed to ensure that clogging is prevented or at least delayed. In this Letter, we investigate the influence of the angle of reduction in the cross section of the channel on the bridging of semidilute and dense non-Brownian suspensions of spherical particles. We observe a decrease of the clogging probability with the reduction of the constriction angle. This effect is more pronounced for dense suspensions close to the maximum packing fraction where particles are in contact in contrast to semidilute suspensions. We rationalize this difference in terms of arch selection. We describe the role of the constriction angle and the flow profile, providing insights into the distinct behavior of semidilute and dense suspensions. Published by the American Physical Society 2024

Crystal Resorption as a Driver for Mush Maturation: an Experimental Investigation

Abstract The thermal state of a magma reservoir controls its physical and rheological properties: at storage temperatures close to the liquidus, magmas are dominated by melt and therefore mobile, while at lower temperatures, magmas are stored as a rheologically locked crystal network with interstitial melt (crystal mush). Throughout the lifetime of a magmatic system, temperature fluctuations drive transitions between mush-dominated and melt-dominated conditions. For example, magma underplating or magma recharge into a crystal mush supplies heat, leading to mush disaggregation and an increase in melt fraction via crystal resorption, before subsequent cooling reinstates a crystal mush via crystal accumulation and recrystallisation. Here, we examine the textural effects of such temperature-driven mush reprocessing cycles on the crystal cargo. We conducted high-P-T resorption experiments during which we nucleated, grew, resorbed, and recrystallised plagioclase crystals in a rhyolitic melt, imposing temperature fluctuations typical for plumbing systems in intermediate arc volcanoes (20–40 °C). The experiments reproduce common resorption textures and show that plagioclase dissolution irreversibly reduces 3D crystal aspect ratios, leading to more equant shapes. Comparison of our experimental results with morphologies of resorbed and unresorbed plagioclase crystals from Mount St. Helens (MSH) (USA) reveals a consistent trend in natural rocks: unresorbed plagioclase crystals (found in MSH dacite, basalt and quenched magmatic inclusions [QMIs]) have tabular shapes, while plagioclase crystals with one or more resorption horizons (found in MSH dacite, QMIs, and mush inclusions) show more equant shapes. Plagioclase crystals showing pervasive resorption (found in the dacite and mush inclusions) have even lower aspect ratios. We therefore suggest that crystal mush maturation results in progressively more equant crystal shapes: the shapes of plagioclase crystals in a magma reservoir will become less tabular every time they are remobilised and resorbed. This has implications for magma rheology and, ultimately, eruptibility, as crystal shape controls the maximum packing fraction and permeability of a crystal mush. We hypothesise that a mature mush with more equant crystals due to multiple resorption–recrystallisation events will be more readily remobilised than an immature mush comprising unresorbed, tabular crystals. This implies that volcanic behaviour and pre-eruptive magmatic timescales may vary systematically during thermal maturation of a crustal magmatic system, with large eruptions due to rapid wholesale remobilisation of mushy reservoirs being more likely in thermally mature systems.

Repacking in Compacting Mushes at Intermediate Melt Fractions: Constraints From Numerical Modeling and Phase Separation Experiments on Granular Media

AbstractBefore large volumes of crystal poor rhyolites are mobilized as melt, they are extracted through the reduction of pore space within their corresponding crystal matrix (compaction). Petrological and mechanical models suggest that a significant fraction of this process occurs at intermediate melt fractions (ca. 0.3–0.6). The timescales associated with such extraction processes have important ramifications for volcanic hazards. However, it remains unclear how melt is redistributed at the grain‐scale and whether using continuum scale models for compaction is suitable to estimate extraction timescales at these melt fractions. To explore these issues, we develop and apply a two‐phase continuum model of compaction to two suites of analog phase separation experiments—one conducted at low and the other at high temperatures, T, and pressures, P. We characterize the ability of the crystal matrix to resist porosity change using parameterizations of granular phenomena and find that repacking explains both data sets well. A transition between compaction by repacking to melt‐enhanced grain boundary diffusion‐controlled creep near the maximum packing fraction of the mush may explain the difference in compaction rates inferred from high T + P experiments and measured in previous deformation experiments. When upscaling results to magmatic systems at intermediate melt fractions, repacking may provide an efficient mechanism to redistribute melt. Finally, outside nearly instantaneous force chain disruption events occasionally recorded in the low T + P experiments, melt loss is continuous, and two‐phase dynamics can be solved at the continuum scale with an effective matrix viscosity.

Improvement of permeability by enhancing packing fraction through tri-modal powder mixing of amorphous FeSiCrB

The improvement of packing fraction and magnetic permeability of amorphous FeSiCrB (FSCB) powder via the addition of Carbonyl Iron Powder (CIP) and nano Fe (NF) to insulated FeSiCrB (FSCB) amorphous powder was investigated. In the case of the bi-modal powder mixing, the packing fraction and permeability increased with the addition of CIP compared to FSCB, with the best packing fraction of 75.30 % and permeability of 25.86 at 20 wt% CIP. NF was added to maximize the packing fraction at 20 wt% CIP, and the maximum packing fraction of 76.69 % and permeability of 27.33 were found at 3 wt% NF. As the packing fraction increased with the addition of CIP and NF, the maximum permeability was obtained at the maximum packing fraction, which was consistent with Ollendorff's equation.

Effect of maximum packing fraction of powders on the rheology of metakaolin-based geopolymer pastes

In this work, we study the effect of maximum packing fraction of powders on the rheology of geopolymer pastes. A large range of metakaolin powders is generated either by blending or grinding powders. Blends of metakaolin with quartz and limestone are also studied. We show that the compressive packing model is able to predict correctly over a wide range of values the maximum packing fraction of these powders. We show that an increase of the maximum packing of powders leads to a decrease of the viscosity of geopolymer suspension at a constant solid volume fraction. We finally show that the viscosity of studied geopolymer suspensions can be well predicted by the Krieger Dougherty relation. We suggest that the highest potential degree of freedom allowing for the control of the viscosity of geopolymer pastes without modifying the composition of the suspension lies in the maximum packing fraction of the solid powders.

Viscosity of Suspensions of Strongly Bonded Spherical Particles of Nickel-Manganese-Cobalt Mixed Oxides (NMC) in Molten Poly(Ethylene Carbonate) for Batteries.

Ionically conductive polymers highly filled with active materials, such as metal oxides are increasingly studied for their potential use in all solid-state batteries. They offer the desirable processing ease of polymers for mass production despite interfacial issues that remain to be solved. In this study, it is shown that spherical particles of transition metal oxides can be introduced in co-polymers of alkene carbonate and ethylene oxide at loading close to the maximum packing fraction, without imparting the processability in the melt of the material. In particular, the viscosity does not show any yield stress and the increase of viscosity shows that the intrinsic viscosity of the filler does not match with the usual 2.5 value in the limit of the Einstein's equation. Conversely, rheological data show that the value is rather close to unity consistently with theoretical arguments that predicted that this scaling factor should be unity when particle rotation is precluded. In the present case, this behavior is attributed to strong bonding between polymer and filler that is proved by electronic microscopy and by dynamical mechanical spectroscopy showing a relaxation due to bound polymer.

Interparticle friction in sheared dense suspensions: Comparison of the viscous and frictional rheology descriptions

In the literature, two different frameworks exist for describing the rheology of solid/liquid suspensions: (1) the “viscous” framework in terms of the relative suspension viscosity, ηr, as a function of the reduced solid volume fraction, ϕ/ϕm, with ϕm the maximum flowable packing fraction, and (2) the “frictional” framework in terms of a macroscopic friction coefficient, μ, as a function of the viscous number, Iv, defined as the ratio of the viscous shear to the wall-normal particle stress. Our goal is to compare the two different frameworks, focusing on the effect of friction between particles. We have conducted a particle-resolved direct numerical simulation study of a dense non-Brownian suspension of neutrally buoyant spheres in slow plane Couette flow. We varied the bulk solid volume fraction from ϕb=0.1 to 0.6 and considered three different Coulomb friction coefficients: μc=0, 0.2, and 0.39. We find that ηr scales well with ϕ/ϕm, with ϕm obtained from fitting the Maron–Pierce correlation. We also find that μ scales well with Iv. Furthermore, we find a monotonic relation between ϕ/ϕm and Iv, which depends only weakly on μc. Since ηr=μ/Iv, we thus find that the two frameworks are largely equivalent and that both account implicitly for Coulomb friction. However, we find that the normal particle stress differences, N1 and N2, when normalized with the total shear stress and plotted against either ϕ/ϕm or Iv, remain explicitly dependent on μc in a manner that is not yet fully understood.

Effect of shear ratio on rheological properties of suspension in two-step flocculation process for fine iron tailings

In the two-step flocculation process, shear has a significant impact on the rheological properties of the flocculating slurry. In this study, the orthogonal experiments of two-step flocculation process for fine iron tailings were designed. Based on the change of shear ratio, different shear rates and shear time were designed, the yield stress, plastic viscosity and maximum packing fraction of the flocculated suspension in each group were measured and calculated with a rheometer. The result of range and variance analysis shows the shear rate in the primary broken phase was the biggest factor affecting the yield stress and plastic viscosity of the flocculated slurry in two-step flocculation process. When the shear rate increased from 100 s-1 to 400 s-1, the yield stress and the plastic viscosity of the flocculated slurry increased by 7.14% and 21.30%, respectively. When the shear rate changed from 400 s-1 to 800 s-1, they decreased by 23.27% and 33.17%, respectively. Since the shear ratio in a two-step flocculation process is also related to both shear action and floc structure parameter, the shear ratio was introduced into the first-order reversible kinetic rate equation. Through establishing the relationship between the shear ratio and the floc structural parameter of flocculating suspension, a theoretical model of the shear-dependent maximum packing fraction was established. The measured values and theoretical calculated values of the maximum packing fraction in two-step flocculation experiments were in good agreement and the error was within 5%. Last but not least, the internal mechanism of the theoretical model was discussed from the microscopic point of view.

Paediatric solid oral dosage forms for combination products: Improving in vitro swallowability of minitablets using binary mixtures with pellets

There is a growing interest in enhancing the acceptability of paediatric pharmaceutical formulations. Solid oral dosage forms (SODF), especially multiparticulates, are being considered as an alternative to liquid formulations, but they may compromise palatability when large volumes are required for dosing. We hypothesised that a binary mixture of multiparticulates for paediatric use, designed to increase the formulation maximum packing fraction, could reduce the viscosity of the mixture in soft food and facilitate swallowing.Using the Paediatric Soft Robotic Tongue (PSRT) – an in vitro device inspired by the anatomy and physiology of 2-year-old children – we investigated the oral phase of swallowing for multi-particulate formulations, i.e., pellets (350 and 700 µm particles), minitablets (MTs, 1.8 mm), and their binary mixtures (BM), by evaluating oral swallowing time, the percentage of particles swallowed, and post-swallow residues. We also conducted a systematic analysis of the effect of the administration method, bolus volume, carrier type, particle size, and particle volume fraction on pellets swallowability.The results demonstrated that the introduction of pellets affected the flowing ability of the carriers, increasing shear viscosity. The size of the pellets did not appear to influence particle swallowability but raising the particle volume fraction (v.f.) above 10% resulted in a decrease in the percentage of particles swallowed. At v.f. 0.4, pellets were easier to swallow (+ 13.1%) than MTs, being the administration method used highly dependent on the characteristics of the multi-particulate formulation under consideration. Finally, mixing MTs with only 24% of pellets improved particle swallowability, achieving swallowing levels similar to those of pellets alone. Thus, combining SODF, i.e., MTs and pellets, improves MT swallowability, and offers new possibilities for adjusting product palatability, being particularly attractive for combination products.

A refined Morphological Representative Pattern approach to the behavior of polydisperse highly-filled inclusion–matrix composites

This study presents a new micromechanical model that is simple, explicit, and directly applicable for broad engineering applications to predict the effective elastic moduli of very high-contrast component property composites containing high concentrations of particles. The approach is based on the Morphological Representative Pattern scheme, where the first pattern comprises a spherical fictitious inclusion embedded in an infinite effective homogeneous medium with physical properties of the matrix, while the others correspond to the classical three-phase generalized self-consistent problem. Instead of using the mean distance between particles, as addressed in existing literature, the volume fraction of patterns is calculated based on the maximum packing fraction estimated from the packing model. This approach shows perfect coherence with experimental data for benchmark examples of effective properties of suspensions of monodisperse particles in an elastic matrix and porous materials. Furthermore, a refined version of the model is proposed, which includes a free parameter representing the shape of the fictitious inclusion to evaluate the polydisperse effect on the overall properties of these materials.

Elucidating the particle concentration-dependent flow behavior of aqueous TiO2 suspensions based on polymer dispersant structures and interparticle surface distances

Flowing behavior of concentrated aqueous TiO2 suspensions was evaluated in relation to the structure of polymeric dispersants, their adlayer thickness on particle surface, and particle concentrations. Comb-type polymeric dispersants comprising polyethylene glycol-based side chains with different combinations of unit number and side chain length were investigated. Based on particle concentration–apparent viscosity curves of the suspensions with TiO2 nanoparticles saturated with dispersants, maximum packing fraction and polymer adlayer thickness were estimated through the Krieger–Dougherty model. When the steric repulsive force of polymer dispersant dominated van der Waals attractive forces, the flow curves of the suspension exhibited hysteresis characteristics as the average particle surface distance approached the adlayer thickness of polymer dispersants. Additionally, by introducing the concept of relative surface distance, which is the average particle surface distance divided by the adlayer thickness, the particle concentration dependency of the suspension viscosities with different dispersants followed a unified trend.

Effect of polydispersity in concentrated magnetorheological fluids

Magnetorheological fluids (MRF) are smart materials of increasing interest due to their great versatility in mechanical and mechatronic systems. As main rheological features, MRFs must present low viscosity in the absence of magnetic field (0.1–1.0 Pa.s) and high yield stress (50–100 kPa) when magnetized, in order to optimize the magnetorheological effect. Such properties, in turn, are directly influenced by the composition, volume fraction, size, and size distribution (polydispersity) of the particles, the latter being an important piece in the improvement of these main properties. In this context, the present work aims to analyze, through experiments and simulations, the influence of polydispersity on the maximum packing fraction, on the yield stress under field (on-state) and on the plastic viscosity in the absence of field (off-state) of concentrated MRF (φ = 48.5 vol.%). Three blends of carbonyl iron powder (CIP) in polyalphaolefin oil were prepared. These blends have the same mode, but different polydispersity indexes (α), ranging from 0.46 to 1.44. Separate simulations show that the random close packing fraction increases from about 68% to 80% as the polydispersity indexes increase over this range. The on-state yield stress, in turn, is raised from 30 ± 0.5 kPa to 42 ± 2 kPa (B ≈ 0.57 T) and the off-state plastic viscosity, is reduced from 4.8 Pa.s to 0.5 Pa.s. Widening the size distributions, as is well known in the literature, increases packing efficiency and reduces the viscosity of concentrated dispersions, but beyond that, it proved to be a viable way to increase the magnetorheological effect of concentrated MRF. The Brouwers model, which considers the void fraction in suspensions of particles with lognormal distribution, was proposed as a possible hypothesis to explain the increase in yield stress under magnetic field.

Film formation properties of asphalt emulsion under ambient temperature drying

ABSTRACT The film formation properties of asphalt emulsion under ambient temperature drying are important to the mechanical properties of cold asphalt emulsion mixture. Nevertheless, the importance of these properties is not fully understood yet. The dynamic modulus and bonding ability of emulsion residue were studied to characterise the film formation properties of asphalt emulsion. The maximum packing fraction of asphalt droplets (ϕ m) formed during drying was proposed to quantitatively characterise the film structure of emulsion residue. The relationship between the film properties and ϕ m of asphalt emulsion was studied to reveal the mechanism for the different film formation properties of asphalt emulsions. Results showed that the residue properties of different asphalt emulsions could be significantly different due to the various film structure of emulsion residue formed under ambient temperature drying. The dynamic modulus and bonding ability of emulsion residue can linearly increase with the ϕ m of asphalt emulsion. Besides, the ϕ m of asphalt emulsion is decreased with the increasing asphalt droplet size. Therefore, to ensure higher dynamic modulus and bonding ability of emulsion residue, asphalt emulsion with small droplets size is recommended.

Numerical Study on Effect of Contact and Interfacial Resistance on Thermal Conductivity of Dispersed Composites.

A series of finite element analyses were conducted to clarify the effect of contact and interfacial resistance between constituents on effective thermal conductivities of dispersed composites. Equally dispersed fillers in FCC (face-centered cubic) and BCC (body-centered cubic) material systems were extracted from cyclic microstructures as unit cell models. In addition to spherical fillers, a polyhedron called the Wigner-Seitz cell that can realize a fully packed microstructure was chosen as the shape of the filler to investigate the effect of contact between the high volumetric fraction of fillers. The effective thermal conductivities of the resulting composites were calculated based on the FEA results and compared to the theoretical results for various volume fractions of the fillers including the maximum packing fraction. The following conclusions were obtained from the present study: 1. The effect of the contact depending on the shape and configuration of the fillers has more of a significant influence on the effective thermal conductivity than the influence of the increase in the volume fraction of the fillers. 2. When the contact occurred, the effective thermal conductivity became more than double that without contact. 3. Interfacial thermal resistance must be less than the order of 10-4 m2 K/W to obtain improvement in the effective thermal conductivity by compounding the fillers.

Realizability of iso-g2 processes via effective pair interactions.

An outstanding problem in statistical mechanics is the determination of whether prescribed functional forms of the pair correlation function g2(r) [or equivalently, structure factor S(k)] at some number density ρ can be achieved by many-body systems in d-dimensional Euclidean space. The Zhang-Torquato conjecture states that any realizable set of pair statistics, whether from a nonequilibrium or equilibrium system, can be achieved by equilibrium systems involving up to two-body interactions. To further test this conjecture, we study the realizability problem of the nonequilibrium iso-g2 process, i.e., the determination of density-dependent effective potentials that yield equilibrium states in which g2 remains invariant for a positive range of densities. Using a precise inverse algorithm that determines effective potentials that match hypothesized functional forms of g2(r) for all r and S(k) for all k, we show that the unit-step function g2, which is the zero-density limit of the hard-sphere potential, is remarkably realizable up to the packing fraction ϕ = 0.49 for d = 1. For d = 2 and 3, it is realizable up to the maximum "terminal" packing fraction ϕc = 1/2d, at which the systems are hyperuniform, implying that the explicitly known necessary conditions for realizability are sufficient up through ϕc. For ϕ near but below ϕc, the large-r behaviors of the effective potentials are given exactly by the functional forms exp[ - κ(ϕ)r] for d = 1, r-1/2exp[ - κ(ϕ)r] for d = 2, and r-1exp[ - κ(ϕ)r] (Yukawa form) for d = 3, where κ-1(ϕ) is a screening length, and for ϕ = ϕc, the potentials at large r are given by the pure Coulomb forms in the respective dimensions as predicted by Torquato and Stillinger [Phys. Rev. E 68, 041113 (2003)]. We also find that the effective potential for the pair statistics of the 3D "ghost" random sequential addition at the maximum packing fraction ϕc = 1/8 is much shorter ranged than that for the 3D unit-step function g2 at ϕc; thus, it does not constrain the realizability of the unit-step function g2. Our inverse methodology yields effective potentials for realizable targets, and, as expected, it does not reach convergence for a target that is known to be non-realizable, despite the fact that it satisfies all known explicit necessary conditions. Our findings demonstrate that exploring the iso-g2 process via our inverse methodology is an effective and robust means to tackle the realizability problem and is expected to facilitate the design of novel nanoparticle systems with density-dependent effective potentials, including exotic hyperuniform states of matter.

Constraints on Magma Properties at Fragmentation During the 2011 Sub‐Plinian Eruptions of Kirishima Shinmoe‐dake Volcano, Japan

AbstractWe investigated essential factors controlling magma fragmentation during the 2011 sub‐Plinian eruptions of Kirishima Shinmoe‐dake volcano, Japan, based on observational data and the analysis of the conduit flow system. Key observational data of the Shinmoe‐dake eruptions are geophysically estimated magma discharge rate and petrologically measured crystallinity and porosity at the time of fragmentation. Using formulations of fragmentation criterion and conduit flow model, we derived analytical expressions describing the relationship among magmatic and geological parameters at the time of strain rate‐induced or stress fragmentation. The combination of the observational data and the analytical expressions revealed the relationship among weakly constrained parameters at the fragmentation, such as pressure, gas permeability in the magma, conduit radius, and maximum packing fraction of crystals, β*. From this relationship, we found that a smaller β*, less than approximately 0.5, is necessary for the fragmentation to occur for a wide range of the conduit radii under realistic pressure and gas permeability values. This reflects that in the case of the sub‐Plinian eruption with a moderate magma discharge rate, a drastic increase in magma viscosity induced by the smaller β* plays a crucial role in the occurrence of fragmentation. The strong dependence of the fragmentation process on β* indicates that the suspension rheology of crystal‐bearing magma is an essential factor controlling the magma ascent process during the moderate explosive eruption.

Formation of Mixed-Powder composites with improved magnetic properties by adding carbonyl iron powders to FeSiCrB amorphous powder

We investigated the changes in the magnetic properties of FeSiCrB amorphous powder because of the addition carbonyl iron powder (CIP) with different contents. With addition of CIP, the magnetization saturation value of the FeSiCrB amorphous powder effectively increased, and thus, an excellent DC-bias characteristic was expected. As the CIP content was increased to 20 wt%, the maximum packing fraction was obtained, and with further CIP addition, the packing fraction decreased. According to the Ollendorff formula, a higher packing fraction results in a higher permeability is obtained, and the composite with a CIP content of 20 wt% showed about 50 % higher permeability than that of the single-FeSiCrB amorphous powder composite. However, the core loss of the composite with a CIP content of 30 wt% was 69.77 kW/m3, which was the best value. Thus, it was confirmed that the magnetic properties could be selectively changed by adding CIP as a fine powder.

Rheological characteristics of concentrated Indian coal ash slurries and flow through pipelines

The present study investigates concentrated coal ash slurries' rheological and pipe flow characteristics. Our results reveal coal ash slurries' shear thinning flow behavior regardless of solid volume fraction (ϕ) = 0.17–0.6. Rheo-microscopy study explains the thixotropy, yielding where slurry microstructure varies with time and applied shear. Experimental viscosity data fit with Dabak and Yucel model with a maximum coal ash packing fraction (ϕm) = 0.63. The yield stress (τy) determined using the creep test, stress sweep, Herschel-Bulkley model, and oscillatory sweep tests indicate the exponential relationship of τy with ϕ = 0.43–0.6. The head loss (hL) during pipeline transportation of slurries increases with coal ash concentration (ϕ = 0.272–0.349) and slurry velocity (vm = 0.5–3 m/s). hL estimated from the rheological data is comparable with the experimental pipe-loop data with pipe length, L = 12 m, and pipe diameters, D = 25 and 50 mm at higher vm (∼2–3 m/s).