Rheology of suspensions of spherical particles in a newtonian and a non-newtonian fluid

Properties of suspensions of spherical glass beads (25–38 μm dia.) in a Newtonian fluid and a non-Newtonian (NBS Fluid 40) fluid were measured at volume fractions, φ, of 0%, 10%, 20% and 30%. Measurements were made using a modified and computerized Weissenberg Rheogoniometer. Properties measured included steady shear viscosity, η($\text{γ}\text{.}$), first normal stress difference, N₁($\text{γ}\text{.}$), linear viscoelastic properties, η′(ω) and G′(ω), shear stress relaxation, σ^? ($\text{γ}\text{.}$, t), and growth, σ⁺($\text{γ}\text{.}$, t) and normal stress relaxation, N₁^?($\text{γ}\text{.}$, t).For a the Newtonian fluid, increasing φ causes both η and η′ to increase, with η′ showing a slight frequency dependence. Both N₁ and G′ are zero and stress relaxation and growth occur essentially instantaneously. For the NBS fluid, both η and η′ increse with φ at all $\text{γ}\text{.}$ and ω, respectively, the increase being greater as $\text{γ}\text{.}$ and ω approach zero. N₁ and G′ are less affected by the presence of the particles than η and η′ with the effect on G′ being more pronounced than on N₁. For fixed $\text{γ}\text{.}$, stress relaxation and growth exhibit greater non-linear effects as φ is increased. A model for predicting a priori the linear viscoelastic properties for suspensions was found to yeild reasonable estimates up to φ = 20%.     

Time-domain finite difference calculations for interaction of an ultrasonic wave with a surface-breaking crack

Four two-dimensional configurations are considered in this paper. The first two concern a homogeneous slab (0⩽y⩽H, −∞<x<∞), with a surface-breaking crack (x=0, 0⩽y⩽a), and without such a crack. The other two configurations concern semi-infinite slabs of different mechanical properties which are in welded contact over x=0, 0⩽y⩽H. One of these has a surface-breaking crack in the interface (x=0, 0⩽y⩽a), and the other has perfect contact over the whole interface. Results are presented for diffraction and corner reflection of an ultrasonic displacement pulse. Time-domain calculations have been carried out bu the use of the finite difference method. The results are presented as full-field snapshots of the displacement fields at specified times, and as time histories of the particle velocity at the midpoint of the transducer-specimen interface at x=−H, y=H.     

Electrorheologial properties of hematite/silicone oil suspensions under DC fields

Electrorheological (ER) fluids composed of α-Fe₂O₃ (hematite) particles suspended in silicone oil are studied in this work. The rheological response has been characterized as a function of field strength, shear rate and volume fraction. Rheological tests under DC electric fields elucidated the influence of the electric field strength, E, and volume fraction, ϕ, on the field-dependent yield stress, τ_y. It was found that this quantity scales with E and ϕ with a linear and parabolic dependence, respectively. The viscosities of electrified suspensions were found to increase by several orders of magnitude as compared to the unelectrified suspension at low shear rates, although at high-shear rates hydrodynamic effects become dominant and no effects of the electric field on the viscosity are observed. The work is completed with the analysis of microscopic observations of the structure acquired by the ER fluid upon application of a constant electric field. Electrohydrodynamic convection is found to be the origin of the ER response rather than the commonly admitted particle fibrillation. This fact can provide an explanation to the relationship between yield stress and electric field strength as well as the pattern of periodic structures observed in the measurement geometries.     

Effect of laden solid particles on the turbulent flow structure of a round free jet

The effect of solid particles on the flow structure of a round air jet in a stagnant surrounding was investigated experimentally. Information on the averaged two-component velocities, the kinetic energies, and the u′ v′-properties were obtained for both phases by means of a monochromatic three beam laser Doppler anemometer. The particle number density was also measured by this system. Glass beads of 64 μm and 132 μm diameter were used for a constant mass loading ratio of 0.3 in a jet with a Reynolds number of 20 000. The lateral mean velocity and number density profiles were expressed by best fitting functions and several invariable coefficients were found. The standard drag force coefficient C _D for a single particle was applicable for a dilute particle cloud even in a non-uniform air velocity field.     

New type of equation for the relation between viscosity and particle content in suspensions

Many disperse systems show a typical non-Newtonian flow at relatively high concentrations of the disperse particle. However, two Newtonian viscosities η_∞ and η₀ can be, respectively, determined at high and low rates of shear. Expect for very low particle content, η_∞/η_s is proportional to exp(mϕ), where η_s is a medium viscosity, m a constant which might reflect the particle-particle interaction and ϕ the volume fraction. In considering this relationship, a new type of equation which describes the relation between the zero shear relative viscosity η_r0( ≡ η₀/η_s) of the disperse system and ϕ is proposed as follows. ln η_r0 = A(p)ϕ + am³ϕ², where A(p), the Einstein-Simha constant, is a function of the axial ratio p of dispersing particles, and a is a constant (⋍ 0.03) which depends slightly on the particle shape.The equation has been compared with the experimental results obtained for several disperse systems. A number of disperse systems of spherical particles are described well by the choice A(p) = 2.5 and a = 0.027, and a system of rod-like particles with p = 50 by the choice A(p) = 215.6 and a = 0.033. m for rod-like particles is larger than that for spherical particles.     

Experimental investigation on flow asymmetry in solid entrance region of a square circulating fluidized bed

To study the influence of back feeding particles on gas-solid flow in the riser, this paper investigated the flow asymmetry in the solid entrance region of a fluidized bed by particle concentration/velocity measurements in a cold square circulating fluidized beds （CFB）. The pressure drop distribution along the riser and the saturation carrying capacity of gas for Geldart-B type particles were first analyzed. Under the condition of u0 = 4 m/s and Gs = 21 kg/（m^2 s）, the back feeding particles were found to penetrate the lean gas-solid flow near the entrance （rear） wall before reaching the opposite （front） wall, thus leading to a relatively denser region near the front wall in the bottom bed. Higher solid circulation rate （u0 =4 m/s, Gs = 33 kg/（m^2 s）） resulted in a higher particle concentration in the riser. However the back feeding particles with higher momentum increased the asymmetry of the particle concentration/velocity profile in the solid entrance region. Lower air velocity （u0 =3.2 m/s） and Gs =21 kg/（m2 s）, beyond the saturation carrying capacity of gas, induced an S-shaped axial solid distribution with a denser bottom zone. This limited the penetration of the back feeding particles and forced the flnidizing air to flow in the central region, thus leading to a higher solid holdup near the rear wall. Under the conditions of uo = 4 m/s and Gs = 21 kg/（m^2 s）, addition of coarse particles （dp= 1145 μm） into the bed made the radial distribution of solids more symmetrical.     

Rheological properties and dispersion stability of magnetorheological (MR) suspensions

In the present article, the rheological responses and dispersion stability of magnetorheological (MR) fluids were investigated experimentally. Suspensions of magnetite and carbonyl iron particles were prepared as model MR fluids. Under an external magnetic field (H ₀) and a steady shear flow, the yield stress depends upon H ₀ ^3/2. The Yield stress depended on the volume fraction of the particle (φ) linearly only at low concentration and increased faster at high fraction. Rheological behavior of MR fluids subjected to a small-strain oscillatory shear flow was investigated as a function of the strain amplitude, frequency, and the external magnetic field. In order to improve the stability of MR fluid, ferromagnetic Co-γ-Fe₂O₃ and CrO₂ particles were added as the stabilizing and thickening agent in the carbonyl iron suspension. Such needle-like particles seem to play a role in the steric repulsion between the relatively large carbonyl iron particles, resulting in improved stability against rapid sedimentation of dense iron particles. Furthermore, the additive-containing MR suspensions exhibited larger yield stress, especially at higher magnetic field strength. Received: 4 April 2000 Accepted: 6 November 2000     

Dual yielding in capillary suspensions

Rheological measurements were performed to examine the yielding behavior of capillary suspensions prepared by mixing cocoa powder as dispersed phase, vegetable oil as the continuous primary fluid, and water as the secondary fluid. Here, we investigated the yielding behavior of solid-fluid-fluid systems with varying particle volume fraction, ?, spanning the regime from a low volume fraction (? = 0.25) to a highly filled regime (? = 0.65) using dynamic oscillatory measurements. While for ? ≤ 0.4 with a fixed water volume fraction (? _w ) of 0.06 as the secondary fluid, capillary suspensions exhibited a single yield point due to rupturing of aqueous capillary bridges between the particles, while capillary suspensions with ? ≥ 0.45 showed a two-step yielding behavior. On plotting elastic stress (G^′ γ) as a function of applied strain (γ), two distinct peaks, indicating two yield stresses, were observed. Both the yield stresses and storage modulus at low strains were found to increase with ? following a power law dependence. With increasing ? _w (0 – 0.08) at a fixed ? = 0.65, the system shifted to a frustrated, jammed state with particles strongly held together shown by rapidly increasing first and second yield stresses. In particular, the first yield stress was found to increase with ? _w following a power law dependence, while the second yield stress was found to increase exponentially with ? _w . Transient steady shear tests were also performed. The single stress overshoot for ? ≤ 0.4 with ? _w = 0.06 reflected one-step yielding behavior. In contrast, for high ? (≥ 0.45) values with ? _w = 0.06, two stress overshoots were observed in agreement with the two-step yielding behavior shown in the dynamic oscillatory measurements. Experiments on the effect of resting time on microstructure recovery demonstrated that aggregates could reform after resting under quiescent conditions.     

Effects of multi-dopants (Zn and Ho) in stabilizing spinel structure for cathode materials in lithium rechargeable batteries—Novel chelated sol–gel synthesis

Multi-doped spinels, namely LiMn₂O₄ and LiZn_xHo_yMn_2−x−yO₄ (x = 0.10–0.18; y = 0.02–0.10), for use as cathode materials for lithium-ion rechargeable batteries were synthesized via sol–gel method, using lauric acid as the chelating agent, to obtain micron-sized particles. The physical properties of the synthesized samples were investigated using differential thermal analysis, Fourier-transform infrared spectroscopy, X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy, energy-dispersive X-ray analysis, and electrochemical methods. XRD showed that LiMn₂O₄ and LiZn_xHo_yMn_2−x−yO₄ have high degrees of crystallinity and good phase purities. The SEM images of LiMn₂O₄ showed an ice-cube morphology with particles of size 1 μm. Charge–discharge studies showed that undoped LiMn₂O₄ delivered the discharge capacity of 124 mA h/g with coulombic efficiency of 95% during the first cycle, whereas doped spinels delivered discharge capacities of 125, 120, and 127 mA h/g in the first cycle with coulombic efficiencies of 96%, 91%, and 91%, respectively.     

A rheological approach to the stability of humic acid/clay colloidal suspensions

Steady-state, oscillatory, and transient rheological determinations were used to assess the stability of homoionic sodium montmorillonite (NaMt) suspensions at constant ionic strength (10^–2 mol/l NaCl) and different pH values, after adsorption of humic acid (HA) on the particles. The adsorption of the latter was first spectrophotometrically determined, at pH 3 and 9. While at pH 9 adsorption saturation was observed, at pH 3 the adsorption density continued to grow up to the maximum equilibrium HA concentration reached (∼200 mg/l). Considering the similarity between the structure of edge surfaces of NaMt particles and the surfaces of silica and alumina, the adsorption of HA was also investigated on the latter solids. The results suggest that at pH 3 humic acids adsorb preferentially on edge surfaces, mainly through electrostatic attraction with positively charged aluminol groups. This hypothesis is indirectly confirmed by zeta potential, ζ, values: while HA concentration has little effect on ζ for silica, the addition of HA yields the zeta potential of alumina increasingly negative for all pH values. Using shear stress vs shear rate plots, the yield stress of NaMt was determined as a function of particle concentration, C, for pH 3, 5, 7, and 9, with and without addition of 50 mg/l HA. The yield stress, σ_y, was fitted with a power law σ_y∝C ⁿ ; it was found that n values as high as 12 are characteristic of NaMt suspensions at pH 9 in the presence of HA. This indicates a strong stabilizing effect of humic acid. This stabilization was confirmed by oscillometric measurements, as the storage modulus G′ in the viscoelastic linear region also scales with C, displaying large n values at neutral and basic pHs in the presence of HA. The modulus (in the viscoelastic linear region, for a frequency ν=1 Hz) was found to increase with time, but G′ was lower at any time when HA was added, a consequence of the stabilization provided by HA. Similarly, creep-recovery experiments demonstrated that NaMt suspensions containing HA displayed a less elastic behavior, and a permanent deformation. Modeling the results as a Kelvin-Voigt model allowed one to establish a new scaling law of the reciprocal instantaneous deformation with C. As before, high values of n were found for suspensions at pH 9 in the presence of HA.     

Yield stress and flow behavior of concentrated ferrofluid-based magnetorheological fluids: the influence of composition

In this paper, the magnetorheological (MR) and magnetoviscous properties of ferrofluid-based iron particle suspensions were investigated. The 2.1-µm mean size Fe particles were dispersed in high-concentration transformer oil-based ferrofluid, the iron particle volume fraction in the resulting nano-micro composite magnetorheological fluid samples varying from Φ _Fe = 5 to 40 %. The ferrofluid carrier has φ _p = 23 % solid volume fraction of magnetic nanoparticles stabilized with chemisorbed oleic acid monolayer and without any excess surfactant. In the absence of the field, the ferrofluid has a quasi-Newtonian behavior with a weak shear thinning tendency. The static yield stress shows an increase of about 3 orders of magnitude for an iron particle content of approx. Φ _Fe = 25 % (Φ _tot = 42.25 %), while above this value, a saturation tendency is observed. The dynamic yield stress (Bingham model) also increases with the magnetic induction and the particle volume fraction; however, the saturation of the MR effect is less pronounced. The relative viscosity change has a maximum at Φ _Fe = (10–15) % due to the accelerated increase of the effective viscosity of the composite for higher Fe content. Addition of micrometer-sized iron particles to a concentrated ferrofluid without any supplementary stabilizing agent proved to be a direct and simple way to control the magnetorheological and magnetoviscous behavior, as well as the saturation magnetization of the resulting nano-micro composite fluid to fulfill the requirements of their use in various MR control and rotating seal devices.     

Rheology of colloidal particles in lyotropic hexagonal liquid crystals: the role of particle loading,shape, and phase transition kinetics

The rheology of self-assembled elongated iron oxyhydroxide (FeOOH) and spherical silica (SiO₂) particles in hexagonal (H₁) liquid crystal (LC) phase of water and non-ionic surfactant C₁₂E₉ is investigated by varying particle concentration and cooling rate. The rheology data shows that both SiO₂/H₁ and FeOOH/ H₁ LC composites exhibit a higher G^′ when compared to the particle-free H₁ phase, with increasing particle loading and cooling rate. FeOOH particles improve G^′ of the H₁ phase more significantly than SiO₂ particles due to the formation of an interconnected network at H₁ domain boundaries at cooling rates of 1 and 2 ^°C/min. We hypothesize that self-assembly of particles at domain boundaries leads to a decreased mobility of defects causing an increase in elasticity of particle-laden H₁ phase. Dynamic strain sweep and creep experiments show a non-linear stress–strain relationship attributed to the alignment of micellar cylindrical rods under shear.     

Wettability and impact dynamics of water droplets on rice (Oryza sativa L.) leaves

A displacement-shifted approach is introduced to the vision-based particle tracking velocimetry (VB-PTV) technique described in Lei et al. (Exp Fluids 53(5):1251–1268, 2012), using translational and angular displacements. The particle matching algorithm in VB-PTV is based on a proximity matrix, G _ij , which favors short distance particle matches over long distance matches. By modifying the formula used in constructing G _ij , particles that lie at the expected location of the match are favored. Two displacement-shifted methods are introduced: the first of which relies on particle image velocimetry estimates of particle displacements and the second of which relies on both the expected displacement and direction of the correct match to construct the proximity matrix. These displacement-shifted algorithms improve performance in high gradient (0.3 px/px and above), high displacement flows (upwards of 20 pixels), broadening the range of flows for which VB-PTV can be used. RMS errors in PTV results are reduced by 33 % or more when these displacement-shifted algorithms are made to the VB-PTV algorithm which is used to process Oseen vortex images. Experimental images of shear layer and the wake region of vortex shedding were used to verify the performances of the proposed methods, and the results are in agreement with the synthetic tests.     

Extensional rheology of concentrated emulsions as probed by capillary breakup elongational rheometry (CaBER)

Elongational flow behavior of w/o emulsions has been investigated using a capillary breakup elongational rheometer (CaBER) equipped with an advanced image processing system allowing for precise assessment of the full filament shape. The transient neck diameter D(t), time evolution of the neck curvature κ(t), the region of deformation l _def and the filament lifetime t _c are extracted in order to characterize non-uniform filament thinning. Effects of disperse volume fraction ?, droplet size d _sv , and continuous phase viscosity η _c on the flow properties have been investigated. At a critical volume fraction ? _c , strong shear thinning, and an apparent shear yield stress τ _y,s occur and shear flow curves are well described by a Herschel–Bulkley model. In CaBER filaments exhibit sharp necking and t _c as well as κ _max ?=?κ (t?=?t _c ) increase, whereas l _def decreases drastically with increasing ?. For ? <?? _c , D(t) data can be described by a power-law model based on a cylindrical filament approximation using the exponent n and consistency index k from shear experiments. For ??≥?? _c , D(t) data are fitted using a one-dimensional Herschel–Bulkley approach, but k and τ _y,s progressively deviate from shear results as ? increases. We attribute this to the failure of the cylindrical filament assumption. Filament lifetime is proportional to η _c at all ?. Above ? _c, κ _max as well as t _c /η _c scale linearly with τ _y,s . The Laplace pressure at the critical stretch ratio ε _c which is needed to induce capillary thinning can be identified as the elongational yield stress τ _y,e , if the experimental parameters are chosen such that the axial curvature of the filament profile can be neglected. This is a unique and robust method to determine this quantity for soft matter with τ _y ?< 1,000 Pa. For the emulsion series investigated here a ratio τ _y,e /τ _y,s = 2.8 ± 0.4 is found independent of ?. This result is captured by a generalized Herschel–Bulkley model including the third invariant of the strain-rate tensor proposed here for the first time, which implies that τ _y,e and τ _y,s are independent material parameters.     

Power-law creep and residual stresses in a carbopol gel

We report on the interplay between creep and residual stresses in a carbopol microgel. When a constant shear stress σ is applied below the yield stress σ _y, the strain is shown to increase as a power law of time, γ(t) = γ ₀ + (t/τ) ^α , with an exponent α = 0.39 ± 0.04 that is strongly reminiscent of Andrade creep in hard solids. For applied shear stresses lower than some typical value σ _c ? 0.2σ _y, the microgel experiences a more complex, anomalous creep behavior, characterized by an initial decrease of the strain, that we attribute to the existence of residual stresses of the order of σ _c that persist after a rest time under a zero shear rate following preshear. The influence of gel concentration on creep and residual stresses are investigated as well as possible aging effects. We discuss our results in light of previous works on colloidal glasses and other soft glassy systems.     

Anisotropic deformation of thin films comprised of helical nanosprings

We investigate the mechanical anisotropy of thin films that consist of tantalum oxide (Ta₂O₅) helical nanosprings fabricated by dynamic oblique deposition. Not only the vertical but also the lateral stiffness of thin films is evaluated using specimens in which nanosprings are sandwiched between solid Ta₂O₅ layers. Lateral or vertical force is applied to the upper solid layer by a diamond tip built into an AFM. In particular, the lateral stiffness of a nanospring has never been reported before. Apparent shear and Young’s moduli, G′ and E′, of the thin films are 2–3 orders smaller than those of solid Ta₂O₅ film. Ratio E′/G′ of the two different nanosprings is 3.4 and 6.2, and about 2.5 for the solid film. The thin films show strong characteristic anisotropy that the solid one could hardly attain. The stiffness and its anisotropy strongly depend on nanospring shape.     

A cell model theory of the shear viscosity of a concentrated suspension of interacting spheres in a non-Newtonian fluid

A theoretical approach to the shear viscosity of concentrated suspensions of small particles in a non-Newtonian fluid has been developed using a cell theory model involving particle-particle interaction. The cell theory of Frankel and Acrivos was first generalized to power-law fluid matrices without particle interaction. Particle-particle interaction was then taken into consideration. The theory suggests that the flow behavior of such systems at low shear rates is chiefly dependent upon non-hydrodynamics interparticle interaction such as van der Waals—London and electrostatic forces which induce flocculation and yield stresses. The flow properties at high shear rates are determined by hydrodynamics interaction essentially dependent upon particle concentration and shape.     

Wall slip and multi-tier yielding in capillary suspensions

Impact of wall slip on the yield stress measurement is examined for capillary suspensions consisting of cocoa powder as the dispersed phase, vegetable oil as the continuous primary fluid, and water as the secondary fluid using smooth and serrated parallel plates. Using dynamic oscillatory measurements, we investigated the yielding behavior of this ternary solid-fluid-fluid system with varying particle volume fraction, ?, from 0.45 to 0.65 and varying water volume fraction, ?_w, from 0.02 to 0.08. Yield stress is defined as the maximum in the elastic stress (G^′γ), which is obtained by plotting the product of elastic modulus (G^′) and strain amplitude (γ) as a function of applied strain amplitude. With serrated plates, which offer minimal slippage, capillary suspensions with ? ≥?0.45 and a fixed ?_w =?0.06 showed a two-step yielding behavior as indicated by two peaks in the plots of elastic stress as a function of strain amplitude. On the other hand with smooth plates, the capillary suspensions showed strong evidence of wall slip as evident by the presence of three distinct peaks and lowered first yield stresses for all ? and ?_w. These results can be interpreted based on the fact that a particle-depleted layer, which is known to be responsible for slip, is present in the vicinity of the smooth surfaces. The slip layer presents itself as an additional “pseudo-microstructure” (characteristic length scale) besides the two microstructures, aqueous bridges and solid particle agglomerates, that may occur in the system. With serrated plates, both the yield stresses (σ₁σ₂) and storage moduli plateau at lower strain (before the first yield point) and at higher strain (before the second yield point) (G\(^{\prime }_{p1}\), G\(^{\prime }_{p2}\)) were found to increase with ? (at a fixed ?_w =?0.06) following power-law dependences. Similarly with increasing ?_w (0.02 – 0.08) at a fixed ? =?0.62, the system behaved as a solid-like material in a jammed state with particles strongly held together as manifested by rapidly increasing σ₁ and σ₂. The usage of smooth surfaces primarily affected σ₁ which was reflected by an approximately 70–90% decrement in the measured σ₁ for all values of ?. By contrast, σ₂ and G\(^{\prime }_{p2}\) were found to be unaffected as shown by close agreement of values obtained using serrated geometry due to vanishing slip layers at higher strain amplitudes.     

A single-camera technique for simultaneous measurement of large solid particles transported in rapid shallow channel flows

This paper describes a measurement technique that was successfully applied in a study of bed load transport of large spherical solid particles in a shallow and supercritical flow (Fr?=?2.59–3.17) down a steep slope. The experimental condition was characterized by the relatively large solid particle size compared to the flow depth (d _p /h?=?0.23–0.35), and compared to the tracer diameter (d _p /d _t ?≈?130). The technique incorporated particle image velocimetry and particle tracking velocimetry (PTV) to simultaneously measure the characteristics of the two phases. In order to detect true solid particles and to distinguish them from each other and the unwanted objects, a particle characterization (PCR) algorithm based on Hough transform was employed. The output from the PCR process was utilized for PTV, as well as to generate the corresponding tracer images for special needs. Validation tests have confirmed the pixel accuracy and high reliability of the combined technique. Experimental results obtained with the developed technique include flow velocities, particle velocities, and concentration. The analysis has shown that the particle concentration profile followed an exponential relationship of the form similar to that of Rouse’s profiles, despite the large d _p /h ratio. It also revealed the effect of phase interaction, as a low loading rate of light particles on the order of O(10^?3) could yield a noticeable slowdown in the streamwise fluid velocity.     

Flow fields and packing states in the discharge flow of noncircular particles—A SIPHPM simulation

Although the discharge flow of spherical materials has been extensively explored, the effect of particle shape on discharge is still poorly understood. The present work explores the two-dimensional discharge flow fields of noncircular particles using the soft-sphere-imbedded pseudo-hard particle model method. Rectangular particles having different aspect ratios (R_a = 1, 1.5, 2–5) and regular polygonal particles having different numbers of sides (N_s = 3–8, 10) are discharged through hopper beds having different orifice widths (D_i = 40, 70.77, 99.13, 125.74, 151.13 mm). The discharge rates of differently shaped particles in different beds are consistent with Beverloo’s relation. Moreover, the flow fields are computed and evaluated to study the effects of R_a, N_s, and D_i on particle discharge. The characteristics of particle–particle connections in the discharge process are evaluated according to the temporal evolution and spatial distribution of the contact points. Additionally, the effect of the initial packing on the discharge profile is investigated. The findings help clarify the discharge of noncircular particles.