Static Yield Research Articles

The “two-step” yielding process of the natural mud under steady and oscillatory shear stress

The rheological properties of natural mud are closely related to nautical depth estimation, wave propagation, and morphology evolution of muddy coast. In this study, the rheological properties of the natural mud collected from Luxi Island and Zhoushan Island in China were investigated. Shear stresses in steady state or oscillatory state were imposed on mud samples directly to obtain the yielding process under tidal currents or waves. The results showed that both apparent viscosity and complex viscosity experienced two sharp declines with increasing shear stress, indicating a two-step yielding nature of natural mud. Two yield stresses, namely, static yield stress and fluidic yield stress correspond to the yielding processes of elasticity and viscosity breakdown, respectively. The static yield stress in the oscillatory shear stress tests was lower than that in the steady shear stress tests, and the fluidic yield stress of natural mud in oscillatory shear stress tests was higher than that in the steady shear stress tests. The above phenomenon was explained by the viscoelastic-oscillation theory. Furthermore, the experimental results indicated that the initial storage modulus had a closer connection to both yield stresses in comparison with mud density. This study not only provided a guideline for having a better understanding of the two-step yielding process of natural mud, but will also provide scientific support for the assessment of fluid-mud formation, sediment transport and morphology evolution, the interaction between waves or tidal currents and muddy seabed, and protection of seafloor infrastructures.

Optimizing of chemical admixtures for 3D printable cementitious materials by central composite design

Printability of 3D printable cementitious materials is related to material rheological properties, and is affected and controlled by modern concrete chemical admixtures. In this work, the influence of several chemical admixtures including superplasticizer, retarder, and accelerator on the rheological characteristics of printable materials was investigated using central composite design (CCD). Twenty test points with varying dosages of chemical admixtures were performed to evaluate the primary effects of chemical admixtures and their combined interactive effects on the rheological properties. The results indicate that with the increase of retarder or superplasticizer dosage, all rheological parameters decrease while accelerator possesses an opposite impact. The rheological properties are negatively proportional to the combined interactive effect of retarder and accelerator. The combined interactive effect of retarder and superplasticizer positively affects dynamic yield stress, plastic viscosity, and thixotropy, while it negatively impacts static yield stress. The combined interactive effect of accelerator and retarder positively affects the yield stress, whereas it negatively influences the plastic viscosity and thixotropy. The results indicate that the CCD is an efficient method to find the desirable formulation within a given boundary.

Steady-State and Dynamic Rheological Properties of a Mineral Oil-Based Ferrofluid

In this study, nanoparticles were suspended in L-AN32 total loss system oil. The thixotropic yield behavior and viscoelastic behavior of ferrofluid were analyzed by steady-state and dynamic methods and explained according to the microscopic mechanism of magneto-rheology. The Herschel–Bulkley (H–B) model was used to fit the ferrofluid flow curves, and the observed static yield stress was greater than the dynamic yield stress. Both the static and dynamic yield stress values increased as the magnetic field increased, and the corresponding shear thinning viscosity curve increased more significantly as the magnetic field strength increased. The amplitude scanning results show that the linear viscoelastic region (LVE) is reached when the shear stress is 10%. The frequency scanning results showed that the storage modulus increased with the increase of the frequency at first. The storage modulus increased steadily at a higher frequency range, while the loss modulus increased slowly at the initial stage and rapidly at the later stage. In the amplitude sweep and frequency sweep experiments, the energy storage modulus and loss modulus are enhanced with the decrease of temperature. These findings are helpful to better understand the microscopic mechanism of magneto-rheology of ferrofluids, and also provide guidance for many practical applications.

Different methods for determining the yield stress of ferrofluids

The yield stress of ferrofluids has been a hot topic in their rheological studies, and it is still controversial which method could obtain the more accurate yield stress value. In this work, we used varieties of methods to obtain the yield stress of the ferrofluid, including steady shear and oscillatory shear. We obtained the static yield stress and dynamic yield stress of the ferrofluid by Herschel–Bulkley fitting of the flow curves measured by the controlled shear rate mode and the controlled shear stress mode, and found that at any magnetic field strength, the static yield stress was always significantly greater than the dynamic yield stress. We then performed oscillatory shear of the ferrofluid and determined the yield stress using three methods, where the yield stress value corresponding to the intersection of the storage modulus G′ and the loss modulus G″ is similar to the static yield stress value fitted by H-B at low magnetic field strength. The power law function and shear stress as a function of shear strain consistently gave the maximum value of the yield stress. Ultimately, we believe that which method is ultimately chosen depends on the practical application conditions of interest.

Rheological properties, shape stability and compressive strength of 3D printed colored cement composites modified by needle-like pigment

The shape stability and colorability of 3D printed colored cement composites (3DPCCCs) are restricting its development in the architectural decoration area. In this study, the needle-like yellow pigment (YP) and sheet-like blue pigment (BP) were investigated as the coloring components in the 3D printed white Portland cement-based materials to examine their impact on rheological properties, shape stability, colorability and compressive strength. Experimental results showed that the addition of YP improved the static yield stress and thixotropy of 3DPCCCs, corresponding to a significant reduction in structure deformation. Compared with the reference sample, the compressive strength of 3DPCCCs with 2% YP was improved by 12.3% to 47.4 MPa and structure deformation was reduced by about 50%. Although addition of BP improved the extrudability of 3DPCCCs, both shape stability and compressive strength were significantly reduced. Finally, in a scaled-up 3D printed pentagram component (length across to opposite point 270 mm) with 2% YP, the paste exhibited excellent extrudability and buildability, and 16 layers stacking was obtained without noticeable deformation. • Needle-like and sheet-like pigments are introduced in WPC based materials to prepare 3D printed colored components. • YP is beneficial to improve the rheological properties and shape stability of 3DPCCCs. • The compressive strength of 3DPCCCs with 2% YP increases to 47.4 MPa.

Rheological characteristics of Ultra-High performance concrete (UHPC) incorporating bentonite

This study aims to optimize the rheological properties of Ultra-high performance concrete (UHPC) based on the rheology pre-control strategy. To be specific, bentonite is employed as a rheology controller, and the UHPC skeleton is developed by the Modified Andreasen and Andersen (MAA) model. Then, the rheological properties, mechanical properties, and microstructure of the developed UHPC are evaluated carefully. The obtained results reveal that the addition of bentonite can effectively regulate the rheological properties of UHPC. More exactly, When the bentonite content rises from 0 wt% to 15.0 wt%, the flowability of the UHPC slurry decreases by 55.71%, while the static yield stress, dynamic yield stress, plastic viscosity and thixotropy increase by about 17.05 times more, about 5.57 times more, about 1.16 times more and about 0.04 times more, respectively. Due to the improvement of the rheological properties of the developed UHPC matrix, the orientation and distribution of the utilized steel fibres can be significantly improved, which could bring a maximum increase of about 60% for the UHPC flexural strength. Additionally, based on the microstructure analysis results, there is optimal bentonite content, which is beneficial for obtaining a much denser structure of UHPC composite.

A multi-method investigation into rheological properties, hydration, and early-age strength of cement composites with admixtures recovered from inorganic and bio-based waste streams

• Influence of supplementary admixtures on fresh properties, hydration and strength are compared. • Silica fume substantially increases yield stress, while glass powder reduces yield stress. • Final setting time is reduced in biochar-cement, while fly ash and glass powder delays the setting. • Biochar has the highest accelerating effect on hydration kinetics due to higher surface area for nucleation. • Silica fume and biochar offer 14% higher strength than control at 28-day mark. The selection of mineral admixtures to develop low-carbon cement composites must be diversified to balance the increasing demand and low supply of certain widely used admixtures. The research aims to advance scientific knowledge into the comparative influence of several admixtures recovered from different waste streams including silica fume (SF), fly ash (FA), pulverized glass powder (PGP), biochar (BC), and high-performance ash (HPA) on static yield stress, dynamic yield stress, plastic viscosity, setting, micro-structural build-up, degree of hydration and compressive strength of cementitious paste. Experimental findings show that adding 10 wt% silica fume results in a 300% increase in yield stress (under static and dynamic shear rate) and plastic viscosity than control, attributed to its fine particle size and higher gelling rate during early hydration. HPA leads to an 83% increase in static yield stress compared to control at 70 mins, but the application of a high shear rate leads to a marginal increase (18%) in yield stress than control. PGP leads to improvement in workability by reducing the dynamic and static yield stress by 50 – 55% than the control without significant change in plastic viscosity. Comparing the influence of BC, FA, and PGP, which have comparable particle size distribution in this research, the addition of biochar accelerates micro-structural build-up and final setting, evident from higher ultrasonic pulse velocity and faster hydration kinetics by 1.20 h. Cement pastes with FA, PGP and HPA demonstrate significantly lower compressive strength at 3-day and 7-day age than control but offer similar 28-day strength. The addition of SF and BC do not compromise 3-day and 7-day strength while offering 16% enhancement in 28-day strength than control attributed to a higher degree of hydration due to pozzolanic and filler effects respectively. The findings suggest that PGP, BC, and HPA could be potential alternatives to more widely used FA and SF as supplementary mineral admixtures in cement-based construction materials.

Determination of Static and Dynamic Yield Stress of Chengdu Clay Slurry

The yield stress of mud is one key to analyze the initiation and deposition of debris flow. Taking Chengdu clay as the experimental material, slurries with different solid volume concentrations were prepared. Using the blade rotor system of mcr301 rheometer and the continuous shear experimental method, the dynamic change process of shear stress of slurries with different solid volume concentrations was obtained with the shear rate increasing and decreasing continuously. According to the experimental results, the static and dynamic yield stress of Chengdu clay slurry is determined, and the influence of solid volume concentration on the yield stress is analyzed. The following conclusions are obtained: Chengdu clay slurry is a non-Newtonian fluid with yield stress. In the process of accelerated shear, for Chengdu clay slurry with solid volume concentration exceeding 35%, the shear rate is in the range of 0.01–1 s−1, and the shear stress increases rapidly to the maximum. When the shear rate exceeds 1 s−1, the shear stress decreases rapidly and finally tends to be stable. The shear rate appears stress overshoot near 1s−1. However, in the process of increasing shear rate, for Chengdu clay slurry with solid volume concentration of no more than 35%, the shear stress increases rapidly in the range of shear rate of 0.01–0.1 s−1, and the shear rate exceeds 0.1 s−1. The shear rate has little effect on the shear stress, and the stress overshoot disappears. In the process of deceleration shear, for all solid volume concentrations in the semi logarithmic coordinate system, the mud shear stress decreases steadily with the decrease of shear rate. The static and dynamic yield stress of slurry increases exponentially with particle concentration.

Dimensional effects on the electronic conductivity and rheological behaviors of LiFePO4 catholytes for rechargeable lithium slurry flow battery

Rechargeable lithium slurry flow battery represents a promising energy storage technology that combines high energy, affordable price, long life, easy maintenance and improved safety. Catholyte is a key component of lithium slurry flow battery, and its charge transport properties and rheological behaviors show a major influence on the electrochemical storage performances of lithium slurry battery. Herein, catholytes based on LiFePO4 cathode particles with different low-dimensional nanostructures (i.e., 0D nanoparticles, 1D nanorods and 2D nanosheets) were prepared to study the dimensional impacts on the electronic conductivity and rheological behaviors of the catholytes. Highest electronic conductivities of the three catholytes were measured at a LiFePO4 mass content of 20 wt.% regardless of particle dimension. The catholytes prepared by 2D nanosheets showed the maximum static viscosity and yield stress because of their smaller sizes. Furthermore, it also demonstrated much improved electrochemical storage performance in a lithium slurry flow battery, by reversibly outputting a discharge specific capacity of >150 mAh g−1 in an intermittent test and stably operating for over 70 h in a continuous flow model. This work sheds lights on reasonable design of catholytes towards practical realization of high-performance lithium slurry flow batteries.

Synergistic effect of shrinkage mitigating materials on rheological properties of flowable and thixotropic cement paste

This study investigates the effect of individual and combined additions of CaO-based expansive agent (EA), shrinkage reducing admixture (SRA), and super absorbent polymer (SAP) on key characteristics of flowable cement paste mixtures proportioned with a water-to-cement ratio of 0.40. Of special interest is the effectiveness of these admixtures to mitigate shrinkage of cementitious materials for 3D printing. Static and dynamic yield stress, plastic and apparent viscosities, and thixotropy were evaluated at 20-min intervals up to 90 min. Compressive strength development and autogenous shrinkage were also determined. A factorial design approach was developed to evaluate the synergetic effects of the shrinkage mitigating materials (SMM) on performance. Test results showed that the use of any given SMM increases the static and dynamic yield stress, plastic viscosity, and thixotropy. The individual use of SRA and the combination of EA-SRA presented the highest effect on reducing 20-min plastic viscosity and dynamic yield stress, respectively. The combinations of EA-SAP almost tripled the 90-min static yield stress. The individual or combined use of the SMM, especially EA and SAP, significantly reduced autogenous shrinkage. Such systems, however, reduced the 28-d compressive strength by 14%–65%. The lowest value was obtained with the paste made with EA-SRA. A multi-objective optimization based on the measured properties was performed. The results revealed that the use of 10% EA either with 0.125% SAP or 1% SRA can result in producing flowable and thixotropic cement paste with high pumpability and buildability for 3D printing applications, no autogenous shrinkage, and high strength.

In-Production Rheometry of Semi-Solid Metal Slurries

Semi-solid aluminium alloy processing (SSM) has advanced into a more mature process with many applications. The current paper aims to investigate the in-process behaviour of a production slurry using an engineering approach to estimate the properties. A method to assess the rheological properties of a semi-solid metal slurry was tested and found capable of producing meaningful measurements. The foundations of this were to use a Rushton turbine setup for the assessment through a model to optimize the factors included in the slurry rheology. In the analysis of the static and dynamic part of the viscosity, it was concluded that the slurry turns increasingly into a solid with increasing solid fractions where the static shear strength dominates the rheology more and more compared to the dynamic components. The static yield strength was also found significantly more dominant with increasing solid fraction, suggesting that the industrial-scale analysis using models based on Ostwald–de Waale and Carreau modelling is far from sufficient for a process, such as the RheoMetal process, with a very rapid slurry generation.

Influencing factors analysis and optimized prediction model for rheology and flowability of nano-SiO2 and PVA fiber reinforced alkali-activated composites

Alkali-activated composites (AAC) has real potential as a repair material of defective concrete structures by virtue of fast setting, high strength, and recyclability. Understanding the workability of AAC is the key to realize this environmental technology as a new repair material. In this work, the effects of water-reducing admixture, nano-SiO2 (NS), and polyvinyl alcohol (PVA) fiber contents on the rheology and the flowability of AAC were investigated through the impeller-rheometer and L-box tests respectively. Based on the results of rheology and flowability, the least squares support vector regression (LS-SVR) method was used for the multi-output prediction of the rheological parameters of AAC. The test results indicate that the fresh mixtures can be regarded as a Bingham fluid, and the proper NS and water-reducing admixture contents can promote the rheology and the flowability of the mixtures, while excessive PVA fiber and NS have negative influence on the workability. The predicted results exhibit that the predicted rheological parameters of mixtures are concordant with the experimental values (the correlation coefficients of static yield stress, dynamic yield stress and plastic viscosity are 0.990, 0.963 and 0.976, respectively). Consequently, the LS-SVR method can be applied for the inverse analysis of the rheological parameters of AAC.

STATIC YIELD STRESS MEASUREMENTS OF FINE AGGREGATES

Fine grained concrete with a maximum grain size of D = 2 mm can be designed as high-performance concrete with outstanding properties. Typical applications are 3Dprinting, grouts, textile-reinforced concrete and thin high-performance structures. Studies reported in the literature that with decreasing grain size the impact of the granulometric properties of the aggregates is increasing. These properties are not only influencing the water demand but also the rheological behavior, such as the static yield stress. In order to investigate and quantify the effects of granulometry on static yield stress measurements six different sands of threedeposits within the range of d/D = 0/2 mm and industrial made glass spheres were tested. The granulometric properties of the materials have been investigated using digital image analyzing. The measurement device was a rotational viscosimeter (Viskomat NT) equipped with a Vane-paddle. Factors as the sample preparation (compaction) and applied shear rateunder a constant shear rate protocol (CSR) were analyzed. An optimum measurement procedure for the grain mixtures was found in using 0.2 rpm and a layerwise static compaction. The analysis showed the importance of the grain size distribution of comparable grain mixtures regarding the static yield torque.

Transient dynamics of soft particle glasses in startup shear flow. Part II: Memory and aging

We explore the rheology during a startup flow of well-characterized polyelectrolyte microgel suspensions, which form soft glasses above the jamming concentration. We present and discuss results measured using different mechanical histories focusing on the variations of the static yield stress and yield strain. The behavior of the shear stress growth function is affected by long-lived residual stresses and strains that imprint a slowly decaying mechanical memory inside the materials. The startup flow response is not reversible upon flow reversal and the amplitude of the static yield stress increases with the time elapsed after rejuvenation. We propose an experimental protocol that minimizes the directional memory and we analyze the effect of aging. The static yield strain γp and the reduced static yield stress σp/σy, where σy is the dynamic yield stress measured from steady flow measurements, are in good agreement with our previous simulations [Khabaz et al., “Transient dynamics of soft particle glasses in startup shear flow. Part I: Microstructure and time scales,” J. Rheol. 65, 241 (2021)]. Our results demonstrate the need to consider memory and aging effects in transient measurements on soft particle glasses.

STATIC YIELD STRESS MEASUREMENTS OF FINE AGGREGATES

Fine grained concrete with a maximum grain size of D = 2 mm can be designed as high-performance concrete with outstanding properties. Typical applications are 3Dprinting, grouts, textile-reinforced concrete and thin high-performance structures. Studies reported in the literature that with decreasing grain size the impact of the granulometric properties of the aggregates is increasing. These properties are not only influencing the water demand but also the rheological behavior, such as the static yield stress. In order to investigate and quantify the effects of granulometry on static yield stress measurements six different sands of threedeposits within the range of d/D = 0/2 mm and industrial made glass spheres were tested. The granulometric properties of the materials have been investigated using digital image analyzing. The measurement device was a rotational viscosimeter (Viskomat NT) equipped with a Vane-paddle. Factors as the sample preparation (compaction) and applied shear rateunder a constant shear rate protocol (CSR) were analyzed. An optimum measurement procedure for the grain mixtures was found in using 0.2 rpm and a layerwise static compaction. The analysis showed the importance of the grain size distribution of comparable grain mixtures regarding the static yield torque.

Rheology and shape stability control of 3D printed calcium sulphoaluminate cement composites containing paper milling sludge

The shape instability and uncontrollable rheological properties of 3D printed calcium sulfoaluminate cement composites (CSACCs) limit its application in the field of architecture. In this study, paper milling sludge (PMS) was adopted to control the rheological properties using the oscillation and rotation shear protocols, aiming to control the printed structures accurately and achieve the resource utilization. Experimental results show that the incorporation of PMS in the 3D printed CSACCs can effectively improve the viscoelasticity, static yield stress and thixotropy. It should be noted that the thixotropy is the key influencing factor to affect the 3D printed structures. Similarly, according to the rotation variation of Lissaju-Bowditch (L-B) curves, it is confirmed that the thixotropic reconstruction of paste during the cycle can significantly affect the shape stability. Additionally, when the contents of PMS and pre-treated PMS (PPMS) reach 15%, the 3D printed CSACCs present better extrudability and shape stability, and the structure deformation decreases to 9.5% and 7.1%, respectively. In conclusion, the use of PMS and PPMS provides great potential for 3D printed CSACCs with improved rheology and shape stability. • The utilization of PMS develops 3D printed cement composites with controllable rheology. • Viscoelasticity test is used to evaluate the buildability of 3D printed paste. • Lissaju-Bowditch curve is used to evaluate the thixotropy of 3D printed paste.

Fine aggregate sizes effects on the creep behavior of asphalt mortar

Asphalt mortar consists of fine aggregates dispersed in an asphalt mastic (a matrix of asphalt binder and filler) and can have a significant influence on the high-temperature performance of asphalt mixtures. However, the fine aggregate sizes (FAS) governing the creep performance of asphalt mortar is not well understood. The effect of different FAS on the creep properties of asphalt mortar was investigated through experimental and numerical methods. A static compressive yield test and a dynamic triaxial creep test were performed on various asphalt mortar samples to determine their creep response under different conditions of temperature and stress level. It was found that the maximum strain in the asphalt mortar gradually reduces with an increase in FAS under the conditions of constant temperature – constant stress level, different temperature – constant stress level, and constant temperature – different stress level. Further, the modified Burgers model was proposed as a viscoelastic prediction model of asphalt mortar. A viscoelastic fitting analysis was carried out to validate the proposed model and the results indicated its adequacy for predicting the asphalt mortar’s creep response. At the end of the study, a grey relation entropy (GRE) analysis was done to quantify the degree of influence of the various FAS on the viscoelastic behavior of asphalt mortar. From the GRE analysis, FAS between 0.15 mm and 0.3 mm was found to be the most crucial. Below 0.15 mm FAS, asphalt mortar is mostly viscous. It begins to show elastic properties when the maximum FAS is between 0.15 mm and 0.3 mm, while above 0.3 mm and towards 2.36 mm the asphalt mortar increasingly becomes more elastic. The findings from this study can be useful to pavement engineers and other pertinent stakeholders seeking to optimize the aggregate gradation design of asphalt mixtures through the fine aggregate portion in order to enhance rutting resistance performance.

Effect of ultrasonic treatment on yield stress of highly concentrated cellulose nano-crystalline (CNC) aqueous suspensions

The yield stress of highly concentrated cellulose nano-crystalline (CNC) suspensions is an important rheological property for different applications. The ultrasonic treatment is a common technique for dispersing CNCs in aqueous media. Although the effect of ultrasonic processing on rheology of CNC suspensions has been previously investigated, a systematic approach studying the sonication effect on yield stress is missing in the literature. In this study, we investigated the effect of sonication energy within the energy level of 0–5000 J/gCNC on static, dynamic and true yield points of a highly concentrated (8 wt%) aqueous CNC suspension, through a rheo-optics analysis. To better understand the yielding behaviour, the sonication effect on physicochemical properties of the CNCs was also investigated. The results revealed that yield stress decreases with sonication energy through a four-step mechanism governed by the microstructural transformations of the CNC agglomerates.

Rheological properties of concentrated allophane, halloysite, and kaolinite suspensions

This study investigated the rheological properties of concentrated suspensions of allophane, halloysite, and kaolinite, which are representative of a series of weathering products of volcanic glass and feldspar minerals in volcanic rocks and deposits, to elucidate the mechanism of landslide generation involving these materials. All suspensions generally showed shear thinning during flow curve measurements, as represented by a steady decrease of viscosity with increasing shear strain rate from 0.1 to 1000 s−1. A difference among them was that the kaolinite suspension showed unstable flow behavior at high solid concentration, and the halloysite suspension had a similar behavior at low solid concentration. The shear stress at the beginning of flow—which represents the yield stress of the suspension—showed a power law correlation with the solid volumetric fraction, and that for kaolinite agreed well with previous static yield stress measurements. The stress of the halloysite suspension deviated from the power law curve at solid fraction < ~0.15. Dynamic viscoelasticity tests indicated that all suspensions showed a power law correlation between the modulus value and solid fraction. The crossover strain (when a solidlike-to-liquidlike transition occurs) of the kaolinite suspension was almost constant within the investigated solid fraction range, whereas that of the halloysite suspension decreased noticeably at solid fraction < ~0.15. Overall, the allophane suspension had the weakest strength and lowest resistance to oscillatory strain at a given solid fraction condition. The rheological properties of halloysite observed here may be related to the occurrence of flow-like, long-distance landslides in volcanic areas containing weathered tephra.

Study of particle packing and paste rheology in alkali activated mixtures to meet the rheology demands of 3D Concrete Printing

The rheological behavior of concrete mixtures made with alkali-activated fly ash-slag (AAFS) binder paste is investigated for varying aggregate content. The static yield stress, plastic viscosity and thixotropy of the mixtures are evaluated and related with the performance in 3D Concrete Printing (3DCP). The thixotropy of the concrete mixture is primarily influenced by AAFS binder paste composition and does not change with the aggregate content. Rheology control of the AAFS binder paste is achieved using additives like nano-clay, which enhance the buildup of internal structure and provide thixotropy in the concrete mixtures. The paste content, the surface area of aggregate, and the packing of solids in a concrete mixture influence its yield stress. The static yield stress increases sensitively in relation to the proportion of the surface area of the solids to the paste volume content in the concrete mixture. The minimum requirement of the paste content from packing of solids in the mixture is given by the Fuller-Thompson curve. Excess paste content in proportion to the demand determined from the surface area of aggregate and packing of solids in the concrete mixture produces a decrease in the static yield stress. For producing AAFS concrete mixtures suitable for 3DCP, the paste content in the concrete mixture should meet the requirement of paste demand, which depends on the aggregate content and packing of solids.