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Settling behavior of non-spherical particles in power-law fluids:Experimental study and model development

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Particuology 2019年第5期17卷 30-39页

作者： Zhengming Xu Xianzhi Song Gensheng Li Zhaoyu Pang Zhaopeng Zhu State Key Laboratory of Petroleum Resources and Prospecting China University of Petroleum Beijing 102249 China

Solid-particle settling occurs in many natural and industrial processes, such as in the transportation of drilling cuttings and fracturing proppant. Knowledge of the drag coefficient and settling velocity of cuttings and proppant is of significance to hydraulics design, wellbore cleanout, and fracture optimization. We conducted 553 tests to investigate the settling characteristics of spherical and non-spherical particles in power-law fluids. Three major particle shapes (spherical, cubic, and cylindrical) and eight different particle sphericities were used to simulate cuttings and proppant, and power-law fluids were applied to simulate drilling and fracturing fluids. Based on the data analysis, a new drag coefficient-particle Reynolds number correlation was developed to determine the drag coefficient in a power-law fluid for spherical and non-spherical particles. The drag coefficient increases as the sphericity decreases for the same particle Reynolds number. For a specific particle shape, the drag coefficient decreases as the particle Reynolds number increases, but the decreasing trend is reduced at high particle Reynolds number conditions. An explicit settling-velocity equation was proposed to calculate the settling velocity of spherical and non-spherical particles in power-law fluids by considering the effect of sphericity. A suitable range for the proposed model is 0.0001 power-law fluids with given particle and fluid properties.

关键词： Settling velocity Drag coefficient Non-spherical particle Spherical particle power-law fluids

Mixture flow of particles and power-law fluid in round peristaltic tube

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Applied Mathematics and Mechanics(English Edition) 2019年第6期40卷 805-822页

作者： Hailin YANG Jianzhong LIN Xiaoke KU Institute of Fluid Engineering School of Aeronautics and AstronauticsZhejiang University

The erythrocyte and blood flowing in the blood vessel can be treated as the two-phase flow of the mixture of particles and a power-law fluid in a peristaltic *** the present work, the peristaltic transport of a power-law fluid and the suspension of particles in a tube is investigated by a perturbation method using the long wavelength approximation. The influence of different parameters on the velocity profile and streamlines is explored. Results show that there is a deflection of the flow field when the power-law index n = 0.5 or 1.5 compared with the Newtonian fluid where the trapping zone is symmetric to a certain cross section. The flux rate and reflux of the material are identified,and the conditions under which the reflux appears are determined. Moreover, a reflux phenomenon occurs near the wall. The trapping zone is related to not only the tube geometry and the flow flux but also the fluid properties. Both the length and width of the trapping zone increase with an increase in θ or φ. The trapping zone is more difficult to produce in the shear-thinning fluid than the shear-thickening fluid.

关键词： peristaltic transport two-phase flow power-law fluid perturbation method trapping phenomenon

Stability of core-annular flow of power-law fluids in the presence of interfacial surfactant

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Science China(Physics,Mechanics & Astronomy) 2010年第5期53卷 933-943页

作者： SUN XueWei,PENG Jie & ZHU KeQin Department of Engineering Mechanics,Tsinghua University,Beijing 100084,China Department of Engineering Mechanics Tsinghua University Beijing 100084 China

The shear-thinning influence on the core-annular flow stability of two immiscible power-law fluids is considered by making a linear stability *** flow is driven by an axial pressure gradient in a straight pipe with the interface between the two fluids occupied by an insoluble *** the basic flow for this core-annular arrangement,the analytical solution is obtained with respect to the power-law fluid *** linearized equations for the evolution of infinitesimal disturbances are derived and the stability problem is formulated as a generalized matrix eigenvalue problem,which is solved by using the software package Matlab based on the QZ *** shear-thinning property is found to have marked influence on the power-law fluid core-annular flow stability,which is reflected in various ***,the capillary instability is magnified by the shear-thinning property,which may lead to an essential difference between power-law and Newtonian fluid *** when the interface is close to the pipe wall,the power-law fluid flow may be unstable while the Newtonian fluid flow is ***,under disturbances to the interface a velocity discontinuity at the interface appears which is destabilizing to the *** magnitude of this velocity discontinuity is affected by the power-law index and the flow stability is influenced ***,the shear-thinning property may induce new stability modes which do not appear in the Newtonian fluid *** flow stability shows much dependence on the interface location,the role of which was neglected in most previous *** shear-thinning fluid flow is more unstable to long wave disturbances when the interface is close to the pipe wall,while the Newtonian fluid flow is more unstable when the interface is close to the pipe *** this trend is changed by the addition of interfacial surfactant,for which the power-law fluid flow is more stable no matter where the interface is loca

关键词： core-annular flow power-law fluid interfacial surfactant linear stability analysis

MHD Boundary Layer Flow of a power-law Nanofluid Containing Gyrotactic Microorganisms Over an Exponentially Stretching Surface

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Computers, Materials & Continua 2020年第2期62卷 525-549页

作者： Mohamed Abd El-Aziz A.M.Aly Department of Mathematics Faculty of ScienceKing Khalid UniversityAbha61411Saudi Arabia Department of Mathematics Faculty of ScienceHelwan UniversityHelwan-Cairo11795Egypt Department of Mathematics Faculty of ScienceSouth Valley UniversityQena83523Egypt

This study focusses on the numerical investigations of boundary layer flow for magnetohydrodynamic(MHD)and a power-law nanofluid containing gyrotactic microorganisms on an exponentially stretching surface with zero nanoparticle mass flux and convective *** nonlinear system of the governing equations is transformed and solved by Runge-Kutta-Fehlberg *** impacts of the transverse magnetic field,bioconvection parameters,Lewis number,nanofluid parameters,Prandtl number and power-law index on the velocity,temperature,nanoparticle volume fraction,density of motile microorganism profiles is *** addition,the impacts of these parameters on local skin-friction coefficient,local Nusselt,local Sherwood numbers and local density number of the motile microorganisms are *** results reveal that the power law index is considered an important factor in this *** to neglecting the buoyancy force term,the bioconvection and nanofluid parameters have slight effects on the velocity *** resultant Lorentz force,from increasing the magnetic field parameter,try to decrease the velocity profiles and increase the rescaled density of motile microorganisms,temperature and nanoparticle volume fraction ***,an augmentation of power-law index drops the reduced local skin-friction and reduced Sherwood number,while it increases reduced Nusselt number and reduced local density number of motile microorganisms.

关键词： Bioconvection gyrotactic microorganisms magnetohydrodynamic nanofluid boundary layer power-law

NEW METHOD TO ESTIMATE SCALING EXPONENTS OF power-law DEGREE DISTRIBUTION AND HIERARCHICAL CLUSTERING FUNCTION FOR COMPLEX NETWORKS

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Applied Mathematics and Mechanics(English Edition) 2006年第11期27卷 1475-1479页

作者：杨波段文奇陈忠 Antai College of Economics and Management Shanghai Jiaotong UniversityShanghai 200030P. R. China School of Business Administration Zhejiang Normal UniversityJinhua 321004Zhejiang ProvinceP. R. China

A new method and corresponding numerical procedure are introduced to estimate scaling exponents of power-law degree distribution and hierarchical clustering function for complex networks. This method can overcome the biased and inaccurate faults of graphical linear fitting methods commonly used in current network research. Furthermore, it is verified to have higher goodness-of-fit than graphical methods by comparing the KS （Kolmogorov-Smirnov） test statistics for 10 CNN （Connecting Nearest-Neighbor） networks.

关键词： parameter estimation complex networks power-law degree distribution hierarchical modularity

Effects of power-law spectrum behaviors of nonthermal electrons on a ring-beam maser instability

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Science China(Physics,Mechanics & Astronomy) 2012年第4期55卷 744-750页

作者： TANG JianFei WU DeJin YAN YiHua Purple Mountain Observatory Chinese Academy of SciencesNanfing 210008China Key Laboratory of Solar Activity National Astronomical ObservatoriesChinese Academy of SciencesBeijing 100012China Graduate University of Chinese Academy of Sciences Beijing 100039China

The electron-cyclotron maser （ECM） emission driven by nonthermal electrons is one of the most crucial mechanisms responsible for radio emissions in magnetized planets, for the interplanetary medium （IPM） and for the laboratory microwave generation devices. Major astrophysical observations demonstrate that nonthermal electrons frequently have a negative power-law spectrum with a lower energy cutoff and anisotropic distribution in the velocity space. In this paper, the effects of power-law spectrum behaviors of electrons on a ring-beam maser emission are considered. The results show that the growth rates of O1 and X2 modes decrease rapidly for small A （the dispersion of momentum u）. Because of the lower energy cutoff behavior, the nonthermal electrons with large a still can excite the ECM instability efficiently. The present analysis also includes the effects of parameter β （βu0 is the dispersion of perpendicular momentum ui, u0 the average value of u） on the instability. The growth rate of X2 mode decreases with parameter v0 （v0 = u⊥o/uo, U⊥0 is the average value of u⊥）. But for O1 mode, the relationship between the growth rate and v0 is complicated. It also shows that the growth rates are very sensitive to frequency ratio Ω （frequency ratio of electron cyclotron frequency to plasma frequency）.

关键词： power-law lower energy cutoff ring-beam maser emission

power-law Behavior in Signal Scattering Process in Vertical Granular Chain with Light Impurities

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Communications in Theoretical Physics 2001年第12期36卷 699-704页

作者： XU Ai-Guo Department of Physics and Center for Strongly Correlated Materials Research Seoul National University Seoul 151-742.Korea

We investigate the scattering process of impulse in vertical granular chain with light impurities. When the perturbation is weak, the quantities describing the reflection rate exhibit power-law behavior with the impurity depth. The exponent is nearly independent of vi. When the perturbation is very strong, the vertical chain shows similar behavior to that of the horizontal chain, so the exponent is nearly zero. Our numerical investigation begins from the weak perturbation region and extends to the nonlinear region and found a peak of the exponent. The difficulty in extending the numerical investigation to a stronger perturbation region is *** numbers: 45.70.-n, 43.25.+y, 46.40.

关键词： granular chain, scattering process, power-law behavior, reflection rate

Modulation Equations for Roll Waves on Vertically Falling Films of a power-law Fluid

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World Journal of Mechanics 2012年第1期2卷 1-8页

作者： Abdelaziz Boudlal Valery Liapidevskii Laboratoire de Mecanique de Lille UMR CNRS 8107 Villeneuve d’Ascq France Lavrentyev Institute of Hydrodynamics Novosibirsk State University Novosibirsk Russia

Waves of finite amplitude on a thin layer of non-Newtonian fluid modelled as a power-law fluid are considered. In the long wave approximation, the system of equations taking into account the viscous and nonlinear effects has the hyper- bolic type. For the two-parameter family of periodic waves in the film flow on a vertical wall the modulation equations for nonlinear wave trains are derived and investigated. The stability criterium for roll waves based on the hyperbolicity of the modulation equations is suggested. It is shown that the evolution of stable roll waves can be described by self-similar solutions of the modulation equations.

关键词： power-law Fluid Thin Film Flow Vertical Wall Modulation Equations Nonlinear Stability Roll Wave

Microwave-Assisted Transition Metal Nanostructure Synthesis: power-law Signature Verification

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American Journal of Analytical Chemistry 2023年第8期14卷 326-349页

作者： Victor J. law Denis P. Dowling School of Mechanical and Materials Engineering University College Dublin Dublin Ireland

A power-law (y = cxn) signature between process energy budget (kJ) and process energy density (kJ·ml-1) of microwave-assisted synthesis of silver and gold nanostructures has been recently described [law and Denis. AJAC, 14(4), 149-174, (2023)]. This study explores this relation further for palladium, platinum, and zinc oxide nanostructures. Parametric cluster analysis and statistical analysis is used to test the power-law signature of over four orders of magnitude as a function of six microwave applicator-types metal precursor, non-Green Chemistry synthesis and claimed Green Chemistry. It is found that for the claimed Green Chemistry, process energy budget ranges from 0.291 to 900 kJ, with a residual error ranging between −33 to +25.9 kJ·ml-1. The non-Green Chemistry synthesis has a higher process energy budget range from 3.2 kJ to 3.3 MJ, with a residual error of −33.3 to +245.3 kJ·ml-1. It is also found that the energy profile over time produced by software controlled digestion applicators is poorly reported which leads to residual error problematic outliers that produce possible phase-transition in the power-law signature. The original Au and Ag database and new Pd, Pt and ZnO database (with and without problematic outliers) yield a global microwave-assisted synthesis power-law signature constants of c = 0.7172 ± 0.3214 kJ·ml-1 at x-axes = 0.001 kJ, and the exponent, n = 0.791 ± 0.055. The information in this study is aimed to understand variations in historical microwave-assisted synthesis processes, and develop new scale-out synthesis through process intensification.

关键词： Microwave-Assisted Synthesis Pd Ag Pt Au ZnO power-law Residual Error Statistical Analysis Parametric Cluster Analysis