Magnetic field assisted fluidization Dimensional analysis addressing the physical basis

This paper originates a discussion on dimensional analysis and scaling in magnetically assisted fluidized beds. Basic examination of process variables, merging mechanical and magnetic units, allows the conversion of mixed sets of variables into unified terms representing surface forces as effects of the fields contributing to the assisted fluidization behaviour. This transformation is termed ＂pressure transform＂ since the new variables are all characteristic pressures generated by three basic fields： gravity, magnetic and fluid flow. This approach addresses the physical basis in terms of dimensionless groups rather than formal algebraic manipulations pertinent to classical dimensional analysis. Basic dimensionless group termed granular magnetic Bond number is introduced as the ratio of characteristic pressures of gravity and of magnetic field. This analysis also provides a set of named dimensionless numbers characterizing magnetic field assisted fluidization such as Filippov number, Rosensweig number, Kwauk number and Siegell number, derived as ratios of characteristic pressures.     

In Memory of Prof.Mooson Kwauk

Prof.Mooson Kwauk,founder and Editor-in-Chief of Particuology, passed away peacefully due to illness on November 20,2012 in Beijing at the age of 92.His funeral was held at Beijing Babaoshan Cemetery on November 26,attended by more than 1000 mourners. Mooson was born in Hanyang,Hubei Province,China,on June 24,1920,and raised in Shanghai.His father was a senior engineer and government official;his mother was a teacher.After graduating from the University of Shanghai with a degree in chemistry in 1943, he completed his master’s degree in chemical engineering under the supervision of Prof.Richard H.Wilhelm at Princeton University in 1946,publishing a paper entitled "Fluidization of Solid Particles" in 1948.It was this paper that was to prove his greatest success in fluidization,classifying the first time two distinctive modes of fluidization:aggregative and particulate. Leaving Princeton,Mooson joined Hydrocarbon Research Inc.in New York in 1946,working as an engineer in the Process Development Department on projects for coal gasification,air separation,     

Handbook of Fluidization,Mooson Kwauk,Hongzhong Li

Fluidization is an important process technology and isubiquitously present in the process industry.The phenomena of fluidization also represent one of the most     

APPLIED MATHEMATICS AND MECHANICS

This journal is on applied mathematics and mechanics published in the People' s Republic of China. Our editorial committee, headed by Professor Chien Wei-zang, Academician of Chinese Academy of Sciences, President of Shanghai University, and Professor Zhou Zhe-wei, consists of scientists in the fields of applied mathematics and mechanics all over China. Founded by Professor Chien Wei-zang in May 1980 as a quarterly, AMM became a bimonthly in 1981 and then a monthly in 1985. It is a comprehensive journal carrying original research papers     

MULTISCALE MECHANICS OF BIOLOGICAL AND BIOLOGICALLY INSPIRED MATERIALS AND STRUCTURES

The world of natural materials and structures provides an abundance of applications in which mechanics is a critical issue for our understanding of functional material properties. In particular, the mechanical properties of biological materials and structures play an important role in virtually all physiological processes and at all scales, from the molecular and nanoscale to the macroscale, linking research fields as diverse as genetics to structural mechanics in an approach referred to as materiomics. Example cases that illustrate the importance of mechanics in biology include mechanical support provided by materials like bone, the facilitation of locomotion capabilities by muscle and tendon, or the protection against environmental impact by materials as the skin or armors. In this article we review recent progress and case studies, relevant for a variety of applications that range from medicine to civil engineering. We demonstrate the importance of fundamental mechanistic insight at multiple time- and length-scales to arrive at a systematic understanding of materials and structures in biology, in the context of both physiological and disease states and for the development of de novo biomaterials. Three particularly intriguing issues that will be discussed here include： First, the capacity of biological systems to turn weakness to strength through the utilization of multiple structural levels within the universality-diversity paradigm. Second, material breakdown in extreme and disease conditions. And third, we review an example where the hierarchical design paradigm found in natural protein materials has been applied in the development of a novel hiomaterial based on amyloid protein.     

Changes in the natural frequency of a ferromagnetic rod in a magnetic field due to magnetoelastic interaction

Based on the magnetoelastic generalized variational principle and Hamilton＇s principle, a dynamic theoretical model characterizing the magnetoelastic interaction of a soft ferromagnetic medium in an applied magnetic field is developed in this paper. From the variational manipulation of magnetic scale potential and elastic displacement, all the fundamental equations for the magnetic field and mechanical deformation, as well as the magnetic body force and magnetic traction for describing magnetoelastic interaction are derived. The theoretical model is applied to a ferromagnetic rod vibrating in an applied magnetic field using a perturbation technique and the Galerkin method. The results show that the magnetic field will change the natural frequencies of the ferromagnetic rod by causing a decrease with the bending motion along the applied magnetic field where the magnetoelastic buckling will take place, and by causing an increase when the bending motion of the rod is perpendicular to the field. The prediction by the mode presented in this paper qualitatively agrees with the natural frequency changes of the ferromagnetic rod observed in the experiment.     

Magnetically assisted gas-solid fluidization in a tapered vessel： Part II Dimensionless bed expansion scaling

The article presents an effort to create dimensionless scaling correlations of the overall bed porosity in the case of magnetically assisted fluidization in a tapered vessel with external transverse magnetic field. This is a stand of portion of new branch in the magnetically assisted fluidization recently created concerning employment of tapered vessels. Dimensional analysis based on ＂pressure transform＂ of the initial set of variables and involving the magnetic granular Bond number has been applied to develop scaling relationships of dimensionless groups representing ratios of pressures created by the fluid flow, gravity and the magnetic field over an elementary volume of the fluidized bed. Special attention has been paid on the existing data correlations developed for non-magnetic beds and the links to the new ones especially developed for tapered magnetic counterparts. A special dimensionless variable Xp = （Ar△Dbt）1/3√RgMQ combining Archimedes and Rosensweig numbers has been conceived for porosity correlation. Data correlations have been performed by power-law, exponential decay and asymptotic functions with analysis of their adequacies and accuracies of approximation.     

Focusing on the meso-scales of multi-scale phenomena—In search for a new paradigm in chemical engineering

To celebrate the 90th birthday of Professor Mooson Kwauk, who supervised the multi-scale research at this Institute in the last three decades, we dedicate this paper outlining our thoughts on this subject accumulated from our previous studies. In the process of developing, improving and extending the energy- minimization multi-scale （EMMS） method, we have gradually recognized that meso-scales are critical to the understanding of the different kinds of multi-scale structures and systems. It is a common challenge not only for chemical engineering but also for almost all disciplines of science and engineering, due to its importance in bridging micro- and macro-behaviors and in displaying complexity and diversity. It is believed that there may exist a common law behind meso-scales of different problems, possibly even in different fields. Therefore, a breakthrough in the understanding of meso-scales will help materialize a revolutionary progress, with respect to modeling, computation and application.     

Analysis of shock wave reflection from fixed and moving boundaries using a stabilized particle method

In the present paper, the efficiency of an enhanced formulation of the stabilized corrective smoothed particle method （CSPM） for simulation of shock wave propagation and reflection from fixed and moving solid boundaries in compressible fluids is investigated. The Lagrangian nature and its accuracy for imposing the boundary conditions are the two main reasons for adoption of CSPM. The governing equations are further modified for imposition of moving solid boundary conditions. In addition to the traditional artificial viscosity, which can remove numerically induced abnormal jumps in the field values, a velocity field smoothing technique is introduced as an efficient method for stabilizing the solution. The method has been implemented for one- and two-dimensional shock wave propagation and reflection from fixed and moving boundaries and the results have been compared with other available solutions. The method has also been adopted for simulation of shock wave propagation and reflection from infinite and finite solid boundaries.     

DYNAMIC BEHAVIORS OF CONDUCTIVE CIRCULAR PLATE IN TIME-VARYING MAGNETIC FIELDS

In this study, we proposed an analytical solution for eddy currents as well as electromagnetic forces of a conductive circular plate in a time varying magnetic field. Specifically, an analytical series solution for eddy currents in a circular plate subjected to an axisymmetrie time varying magnetic field has been proposed based on the T-method that has been widely used in the eddy current analysis of conductive and superconductive structures. Accordingly, the dynamic response, the dynamic instability and the magnetic damping of a circular plate in a transverse transient magnetic field as well as a stationary in-plane magnetic field have also been obtained. The analytical series solution proposed in this work as well as the subsequent numerical analysis not only confirmed the emergence of dynamic instability of a circular plate in a strong transverse magnetic field, but also demonstrated the existence of magneto-damping of a circular conductive plate in an in-plane magnetic field. The method developed in this paper provides a potential new possible way by which the analysis of the electromagnetic coupling problems of conductive structures can be simplified.     

Analytical investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method

In this study, the effects of magnetic field and nanoparticle on the Jeffery-Hamel flow are studied using a powerful analytical method called the Adomian decomposition method (ADM). The traditional Navier-Stokes equation of fluid mechanics and Maxwell’s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The obtained results are well agreed with that of the Runge-Kutta method. The present plots confirm that the method has high accuracy for different α, Ha, and Re numbers. The flow field inside the divergent channel is studied for various values of Hartmann number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated.     

Process,mechanism and impacts of scale formation in alkaline flooding by a variable porosity and permeability model

In spite of the role of alkali in enhancing oil recovery (EOR), the formation of precipitation during alkaline-surfactant-polymer (ASP) flooding can severely do harm to the stratum of oil reservoirs, which has been observed in situ tests of oil fields such as scale deposits found in oil stratum and at the bottom of oil wells. On the other hand, remarkable variation of stratum parameters, e.g., pore radius, porosity, and permeability due to scale formation consider-ably affects seepage flow and alkaline flooding process in return. The objective of this study is to firstly examine these mutual influential phenomena and corresponding mecha-nisms along with EOR during alkaline flooding when the effects of precipitation are no longer negligible. The chem-ical kinetic theory is applied for the specific fundamental reactions to describe the process of rock dissolution in silica-based reservoirs. The solubility product principle is used to analyze the mechanism of alkali scale formation in flooding. Then a 3D alkaline flooding coupling model accounting for the variation of porosity and permeability is established to quantitatively estimate the impact of alkali scales on reser-voir stratum. The reliability of the present model is verified in comparison with indoor experiments and field tests of the Daqing oil field. Then, the numerical simulations on a 1/4 well group in a 5-spot pattern show that the precipitation grows with alkali concentration, temperature, and injection pressure and, thus, reduces reservoir permeability and oil recovery correspondingly. As a result, the selection of alkali with a weak base is preferable in ASP flooding by tradeoff strategy.     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅸ)— THERMOMECHANICS

The existing fundamental laws of thermodynamics for micropolar continuum field theories are restudied and their incompleteness is pointed out. New first and second fundamental laws for thermostatics and thermodynamics for micropolar continua are postulated. From them all equilibrium equations and the entropy inequality of thermostatics as well as all balance equations and the entropy rate inequalities are naturally and simultaneously deduced. The comparisons between the new results presented here and the corresponding results demonstrated in existing monographs and textbooks concerning micropolar continuum mechanics are made at any time. It should be emphasized to note that, the problem of why the local balance equation of energy and the local entropy inequality could not be obtained from the existing fundamental laws of thermodynamics for micropolar continua, is believed to be clarified.     

The Solution for Axisymmetrical Shells with Abrupt Curvature Change(Corrugated Shells)by the Finite Element Method

It has been noted in the present paper that the finite element method using linear elements for solving axisymmetrical shells cannot be applied to the analysis of axisymmetrical shells with abrupt curvature change,owing to the fact that the influence of the curvature upon the angular displace-ments has been neglected.The present paper provides a finite element method using linear elements in which the influence of curvature is considered and the angular displacements are treated as continuous parameters.This method has been applied to the calculation of corrugated shells of the type C,and compared with the experimental results obtained by Turner-Ford as well as with the analytical solution given by Prof.Chien Wei-zang.The compari-sons have been proved that this theory is correct.     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES(Ⅸ)—THERMOMECHANICS

The existing fundamental laws of thermodynamics for micropolar continuum field theories are restudied and their incompleteness is pointed out. New first and second fundamental laws for thermostatics and thermodynamics for micropolar continua are postulated. From them all equilibrium equations and the entropy inequality of thermostatics as well as all balance equations and the entropy rate inequalities are naturally and simultaneously deduced. The comparisons between the new results presented here and the corresponding results demonstrated in existing monographs and textbooks concerning micropolar continuum mechanics are made at any time. It should be emphasized to note that, the problem of why the local balance equation of energy and the local entropy inequality could not be obtained from the existing fundamental laws of thermodynamics for micropolar continua, is believed to be clarified.     

SURFACE STRESS EFFECT IN MECHANICS OF NANOSTRUCTURED MATERIALS

This review article summarizes the advances in the surface stress effect in mechanics of nanostructured elements,including nanoparticles,nanowires,nanobeams,and nanofilms,and heterogeneous materials containing nanoscale inhomogeneities.It begins with the fundamental formulations of surface mechanics of solids,including the definition of surface stress as a surface excess quantity,the surface constitutive relations,and the surface equilibrium equations.Then,it depicts some theoretical and experimental studies of the mechanical properties of nanostructured elements,as well as the static and dynamic behaviour of cantilever sensors caused by the surface stress which is influenced by adsorption.Afterwards,the article gives a summary of the analytical elasto-static and dynamic solutions of a single as well as multiple inhomogeneities embedded in a matrix with the interface stress prevailing.The effect of surface elasticity on the diffraction of elastic waves is elucidated.Due to the difficulties in the analytical solution of inhomogeneities of complex shapes and configurations,finite element approaches have been developed for heterogeneous materials with the surface stress.Surface stress and surface energy are inherently related to crack propagation and the stress field in the vicinity of crack tips.The solutions of crack problems taking into account surface stress effects are also included.Predicting the effective elastic and plastic responses of heterogeneous materials while taking into account surface and interface stresses has received much attention.The advances in this topic are inevitably delineated.Mechanics of rough surfaces appears to deserve special attention due to its theoretical and practical implications.Some most recent work is reviewed.Finally,some challenges are pointed out.They include the characterization of surfaces and interfaces of real nanomaterials,experimental measurements and verification of mechanical parameters of complex surfaces,and the effects of the physical and chemical processes on the surface properties,etc.     

SIF-based fracture criterion for interface cracks

The complex stress intensity factor K governing the stress field of an interface crack tip may be split into two parts, i.e.,■ and s~(-iε), so that K = ■ s~(-iε), s is a characteristic length and ε is the oscillatory index. ■ has the same dimension as the classical stress intensity factor and characterizes the interface crack tip field. That means a criterion for interface cracks may be formulated directly with■, as Irwin(ASME J. Appl. Mech. 24:361–364, 1957) did in 1957 for the classical fracture mechanics. Then, for an interface crack,it is demonstrated that the quasi Mode I and Mode II tip fields can be defined and distinguished from the coupled mode tip fields. Built upon SIF-based fracture criteria for quasi Mode I and Mode II, the stress intensity factor(SIF)-based fracture criterion for mixed mode interface cracks is proposed and validated against existing experimental results.     

Mathematical problems in the integral-transformation method of dynamic crack

In the investigation on fracture mechanics, the potential function was introduced,and the moving differential equation was constructed. By making Laplace and Fourier transformation as well as sine and cosine transformation to moving differential equations and various responses, the dual equation which is constructed from boundary conditions lastly was solved. This method of investigating dynamic crack has become a more systematic one that is used widely. Some problems are encountered when the dynamic crack is studied.After the large investigation on the problems, it is discovered that during the process of mathematic derivation, the method is short of precision, and the derived results in this method are accidental and have no credibility. A model for example is taken to explain the problems existing in initial deriving process of the integral-transformation method of dynamic crack.     

THE PLANE PISTON PROBLEM IN A WEAK GRAVITATIONAL FIELD

We analyze a gasdynamical process in the stellar atmosphere that is driven by a"piston" moving with constant velocity in a weak gravitational field. Ahead of the piston.the gas is compressed. and this compressed gas uses part of its internal energy andsomewhere its kinetic energy to overcome the applied gravity.If we expand the quantities as a series of a small parameter which is the ratio of atypical escape velocity to the plasma velocity, the basic state gives a uniform flow.as shownby the case of gasdynamical theory without gravity. The first-order relationships show theinfluence of the applied gravity on the flow fields.that is.the strength of the shock wavechanges slightly.the internal energy of the gas exhausts. For the cases of strong shock waveand near the piston, an analytical solution may be approximately obtained and has thesimilar features.Because of the importance of the applied gravity in the astrophysical and atmosphericphysical processes. these results may shed light on the mechanics of