Recently,foamed polymers have been widely used in the repair of underground engineering disasters by grouting(trenchless technology)due to controllable gelation time and self-expansion.However,the grouting process bec...Recently,foamed polymers have been widely used in the repair of underground engineering disasters by grouting(trenchless technology)due to controllable gelation time and self-expansion.However,the grouting process becomes more complicated due to the complex geological conditions and the self-expansion of slurry.Therefore,this paper adopts a self-made visual experimental device with peripheral pressure and water plugging rate(WPR)monitoring functions to study the influence of main influencing parameters(particle size distribution,grouting amount and dynamic water pump pressure(DWPP))on the spatiotemporal distribution of slurry WPR and diffusion dynamic response(peripheral pressure).The results show that:When grouting amount is 563 g and DWPP is 0.013 MPa,the expansion force of the slurry in the diffusion process is dominant and can significantly change the local sand and gravel skeleton structure.When grouting amount is 563 g,DWPP is 0.013 MPa,and particle size distribution type isⅢ,the flow time of the polymer is shortened,the pores of the gravel are rapidly blocked.Then,the peripheral pressure decreases rapidly with the increase of the distance,and the time to reach the inflection point WPR is shortened.The instantaneous blockage of the pores leads to the delayed transmission of flow field blockage information.展开更多
To calculate the diffusion law of chaff cloud launched by aircraft,taking rectangular chaff as an example,the diffusion model of chaff cloud is established in this paper.Firstly,the coordinate systems of chaff are def...To calculate the diffusion law of chaff cloud launched by aircraft,taking rectangular chaff as an example,the diffusion model of chaff cloud is established in this paper.Firstly,the coordinate systems of chaff are defined and the motion model of chaff is established.The motion model mainly includes chaff motion equation and rotation equation,which are obtained by combining the aerodynamic moment and aerodynamic damping.Then,the influence of multi-chaff aerodynamic interference on the movement of chaff is analyzed.Finally,considering the influence of overlap area between chaffs and chaff spacing on the aerodynamic coefficients,the multi-chaff motion model is obtained,and the simulation results are compared with the test results to verify the credibility of the model.展开更多
Shale gas reservoirs have poor physical properties and a large number of micro-nano pores have been developed.Shale gas wells have no natural productivity and need fracturing reconstruction measures to put into produc...Shale gas reservoirs have poor physical properties and a large number of micro-nano pores have been developed.Shale gas wells have no natural productivity and need fracturing reconstruction measures to put into production.However,the fracturing fluid will enter the reservoir space of shale matrix after fracturing and affect the production of shale gas.At present,there is no consensus on the influence of fracturing fluid retention on gas well production.Based on this,the paper adopts gas molecular transport analyzer to carry out experimental research on the influence of fracturing fluid on shale gas diffusion law after entering matrix pores.The results show that:(1)Compared with the diffusion capacity of single-phase shale gas,the diffusion capacity of shale gas decreases significantly when fracturing fluid is present in the reservoir;(2)In the process of fracturing fluid flowback,when the water saturation in the reservoir decreases from 50%to 0,the gas well productivity increases by about 60%.(3)When fracturing fluid exists in the reservoir,the pore diameter has an exponential relationship with the shale gas diffusion coefficient,and the diffusion coefficient increases exponentially with the increase of pore diameter.The research of this paper provides theoretical basis for guiding the efficient development of shale gas wells.展开更多
In this paper, a detailed Lie symmetry analysis of the(2+1)-dimensional coupled nonlinear extension of the reaction-diffusion equation is presented. The general finite transformation group is derived via a simple dire...In this paper, a detailed Lie symmetry analysis of the(2+1)-dimensional coupled nonlinear extension of the reaction-diffusion equation is presented. The general finite transformation group is derived via a simple direct method,which is equivalent to Lie point symmetry group actually. Similarity reduction and some exact solutions of the original equation are obtained based on the optimal system of one-dimensional subalgebras. In addition, conservation laws are constructed by employing the new conservation theorem.展开更多
According to the existing concrete core samples obtained in site, chloride concentration and porosity of existing normal hydraulic concrete were measured, and chloride diffusivity in existing hydraulic concrete was st...According to the existing concrete core samples obtained in site, chloride concentration and porosity of existing normal hydraulic concrete were measured, and chloride diffusivity in existing hydraulic concrete was studied. By Fick’s second law, the chloride diffusion coefficients in the steady diffusion area were calculated. The chloride diffusion of different mix proportion concrete was tested, and chloride diffusion coefficients and porosities of freshly concrete were measured, moreover, the relationship between diffusion coefficient and porosity was analyzed. The results show that the varying law of chloride diffusion coefficient with exposure time of existing concrete can be predicted in a better way by Fick’s second law and water-cement ratios or porosity of concrete and chloride concentration in existing concrete.展开更多
We explore the time evolution law of a two-mode squeezed light field(pure state)passing through twin diffusion channels,and we find that the final state is a squeezed chaotic light field(mixed state)with entanglement,...We explore the time evolution law of a two-mode squeezed light field(pure state)passing through twin diffusion channels,and we find that the final state is a squeezed chaotic light field(mixed state)with entanglement,which shows that even though the two channels are independent of each other,since the two modes of the initial state are entangled with each other,the final state remains entangled.Nevertheless,although the squeezing(entanglement)between the two modes is weakened after the diffusion,it is not completely removed.We also highlight the law of photon number evolution.In the calculation process used in this paper,we make full use of the summation method within the ordered product of operators and the generating function formula for two-variable Hermite polynomials.展开更多
Based on the divergence theorem, we reveal that the Fickian first law relevant to the diffusion flux |J(t,x,y,z) > in the time and space is incomplete without an integral constant |J0(t) > for the integral of Fi...Based on the divergence theorem, we reveal that the Fickian first law relevant to the diffusion flux |J(t,x,y,z) > in the time and space is incomplete without an integral constant |J0(t) > for the integral of Fickian second law. The new diffusion flux (NDF) taking it into account shows that we can systematically understand the problems of one-way diffusion, impurity diffusion and self-diffusion as a special case of the interdiffusion. Applying the NDF to the interdiffusion problem between metal plates, it is clarified that the Kirkenkall effect is caused by |J0(t) > and also that the interdiffusion coefficients in alloy can be easily obtained. The interdiffusion problems are reasonably solved regardless of the intrinsic diffusion conception. Thus the NDF to replace the Fickian first law is an essential equation in physics.展开更多
This article concentrates on the properties of three-dimensional magneto-hydrodynamic flow of a viscous fluid saturated with Darcy porous medium deformed by a nonlinear variable thickened surface.Analysis of flow is d...This article concentrates on the properties of three-dimensional magneto-hydrodynamic flow of a viscous fluid saturated with Darcy porous medium deformed by a nonlinear variable thickened surface.Analysis of flow is disclosed in the neighborhood of stagnation point.Features of heat transport are characterized with Newtonian heating and variable thermal conductivity.Mass transport is carried out with first order chemical reaction and variable mass diffusivity.Resulting governing equations are transformed by implementation of appropriate transformations.Analytical convergent series solutions are computed via homotopic technique.Physical aspects of numerous parameters are discussed through graphical data.Drag force coefficient,Sherwood and Nusselt numbers are illustrated through graphs corresponding to various pertinent parameters.Graphical discussion reveals that conjugate and constructive chemical reaction parameters enhance the temperature and concentration distributions,respectively.展开更多
The effects of vacancies on diffusion of interstitial and substitutional atoms as well as interaction between them in metals were discussed.In the interstitial alloy,a coupling between interstitial atoms and vacancy i...The effects of vacancies on diffusion of interstitial and substitutional atoms as well as interaction between them in metals were discussed.In the interstitial alloy,a coupling between interstitial atoms and vacancy is interrelated through the reaction of formation and dissociation of complex.For substitutional alloy with |E_b|<kT,if the atom diffusion is of the vacancies exchange mechanism,the vacancies may considerably affect atom diffusion.Based on the micromechanism of diffusion in these two alloys,their diffusion equations under general condition may be obtained,and the second Fick' s law is only an approximate form when neg- lecting vacancy influence.展开更多
The Nernst-Einstein equation is used to calculate the diffusion coefficient of calcium ion in the CaO-Al2O3-SiO2 system based on the data of the density and electrical conductivity.It is assumed that all the aluminium...The Nernst-Einstein equation is used to calculate the diffusion coefficient of calcium ion in the CaO-Al2O3-SiO2 system based on the data of the density and electrical conductivity.It is assumed that all the aluminium ions form tetrahedral structure and merge with chain or ring in the case of molar concentration of CaO higher than Al2O3.And in this case,calcium ion is assumed to be the conclusive charge carrier.A formula between the diffusion coefficient and concentration of calcium ion as well as temperature is deduced,which gives an increasing function relation between the diffusion coefficient and the concentration of calcium ions.展开更多
Formation and growth of the intermediate phases in the Ni-Al diffusion couples prepared by pouring technique were investigated. Electron probe microanalysis, scanning electron microscopy and X-ray diffraction were use...Formation and growth of the intermediate phases in the Ni-Al diffusion couples prepared by pouring technique were investigated. Electron probe microanalysis, scanning electron microscopy and X-ray diffraction were used to characterize the product phases in the joints. The results show that two intermediate phases form in the sequence of NiAl3 and Ni2Al3 during solidification. After annealed, Ni2Al3 and NiAl3 still exist in the joints of the couples. The reasons for the formation of Ni2Al3 and NiAl3, as well as the absence of NiAl, Ni5Al3 and Ni3Al were discussed, respectively. The growth kinetics of both product phase layers indicates that their growth obeys the parabolic rate law. The activation energies and frequency factors for NiAl3 and Ni2Al3 phases were also calculated according to the Arrhenius equation.展开更多
The exact solution of fractional diffusion model with a location-independent source term used in the study of the concentration of fission product in spherical uranium dioxide （U02） particle is built. The adsorption...The exact solution of fractional diffusion model with a location-independent source term used in the study of the concentration of fission product in spherical uranium dioxide （U02） particle is built. The adsorption effect of the fission product on the surface of the U02 particle and the delayed decay effect are also considered. The solution is given in terms of Mittag-Leffler function with finite Hankel integral transformation and Laplace transformation. At last, the reduced forms of the solution under some special physical conditions, which is used in nuclear engineering, are obtained and corresponding remarks are given to provide significant exact results to the concentration analysis of nuclear fission products in nuclear reactor.展开更多
Purpose:The goal of this study is to analyze the relationship between funded and unfunded papers and their citations in both basic and applied sciences.Design/methodology/approach:A power law model analyzes the relati...Purpose:The goal of this study is to analyze the relationship between funded and unfunded papers and their citations in both basic and applied sciences.Design/methodology/approach:A power law model analyzes the relationship between research funding and citations of papers using 831,337 documents recorded in the Web of Science database.Findings:The original results reveal general characteristics of the diffusion of science in research fields:a)Funded articles receive higher citations compared to unfunded papers in journals;b)Funded articles exhibit a super-linear growth in citations,surpassing the increase seen in unfunded articles.This finding reveals a higher diffusion of scientific knowledge in funded articles.Moreover,c)funded articles in both basic and applied sciences demonstrate a similar expected change in citations,equivalent to about 1.23%,when the number of funded papers increases by 1%in journals.This result suggests,for the first time,that funding effect of scientific research is an invariant driver,irrespective of the nature of the basic or applied sciences.Originality/value:This evidence suggests empirical laws of funding for scientific citations that explain the importance of robust funding mechanisms for achieving impactful research outcomes in science and society.These findings here also highlight that funding for scientific research is a critical driving force in supporting citations and the dissemination of scientific knowledge in recorded documents in both basic and applied sciences.Practical implications:This comprehensive result provides a holistic view of the relationship between funding and citation performance in science to guide policymakers and R&D managers with science policies by directing funding to research in promoting the scientific development and higher diffusion of results for the progress of human society.展开更多
The well-known Darken equation has been widely accepted in analyzing interdiffusion problems since 1948. The diffusion researchers have never conceived a doubt about the validity of Darken equation for such a long tim...The well-known Darken equation has been widely accepted in analyzing interdiffusion problems since 1948. The diffusion researchers have never conceived a doubt about the validity of Darken equation for such a long time. However, it is revealed that the Darken equation is inconsistent with the fundamental theory in mathematics. At the same time, it is clarified that the well-known intrinsic diffusion concept is an illusion. The present brief report will have a great influence on matters of the research and education relevant to diffusion problems not only in future but also in past, since the accumulated diffusivity data analyzed by the invalid Darken theory and the misjudged descriptions in existing text books should be revised or deleted as soon as possible.展开更多
The influence of an alternative magnetic field on the growth of the diffusionlayer in Al-Zn diffusion couple was studied. The thickness of the diffusion layer was examined. Theresults show that the alternative magneti...The influence of an alternative magnetic field on the growth of the diffusionlayer in Al-Zn diffusion couple was studied. The thickness of the diffusion layer was examined. Theresults show that the alternative magnetic field increases the thickness of the diffusion layer andthe effect increases with the intensity and frequency of the alternative magnetic field increasing. The growth of the diffusion layer obeys the parabolic rate law and the growth rateincreases with the application of the alternative magnetic field. This growth rate change ismanifested through a change in the frequency factor k_0 and not through a change in the activationenergy Q. The frequency factor k_0 for the diffusion layer growth with the alternative magneticfield is 5.03 cm^2/s and the one without the magnetic field is 3.84 cm^2/s.展开更多
This paper investigates the flow, heat andmass transfer of a power law fluid from a vertical plate in presence of a magnetic field. The resulting non-linear partial differential equations governing the flow together w...This paper investigates the flow, heat andmass transfer of a power law fluid from a vertical plate in presence of a magnetic field. The resulting non-linear partial differential equations governing the flow together with the boundary conditions are reduced to non-dimensional form. The governing equations are discretized using implicit finite difference scheme and solved numerically. The velocity, temperature and concentration profile are presented graphically while the skin friction, local Nusselt number and the Sherwood number are presented in tabular form for different values of parameters of the problem.展开更多
Certain prerequisite information on the component fluxes is necessary for solution of the Stefan-Maxwell equation in multicomponent diffusion systems and the Graham's law of diffusion and effusion is often resorte...Certain prerequisite information on the component fluxes is necessary for solution of the Stefan-Maxwell equation in multicomponent diffusion systems and the Graham's law of diffusion and effusion is often resorted for this purpose. This article addresses solution of the Stefan-Maxwell equation in binary gas systems and explores the necessary conditions for definite solution of concentration profiles and pertinent component fluxes. It is found that there are multiple solutions for component fluxes in contradiction to what specified by the Graham's law of diffusion.The theorem of minimum entropy production in the non-equilibrium thermodynamics is believed instructive in determining the stable steady state solution out of infinite multiple solutions possible under the specified conditions.It is suggested that only when the boundary condition of component concentration is symmetrical in an isothermal binary system, the counter-diffusion becomes equimolar. The Graham's law of diffusion seems not generally valid for the case of isothermal ordinary diffusion.展开更多
In accordance with the definition of diffusivity, the origin of coordinate system of the original diffusion equation is set at a point in the solvent material. Kirkendall revealed that Cu atoms, Zn atoms and vacancies...In accordance with the definition of diffusivity, the origin of coordinate system of the original diffusion equation is set at a point in the solvent material. Kirkendall revealed that Cu atoms, Zn atoms and vacancies move simultaneously in the interdiffusion region. This indicates that the original diffusion equation is a moving coordinate system for the experimentation system outside the diffusion region. The diffusion region space which means vacancies and interstices among atoms plays an important role in the diffusion phenomena. The theoretical equation of the Kirkendall effect is reasonably obtained as a shift between coordinate systems of the diffusion equation. The situation is similar to the well-known Doppler effect in the wave equation. Boltzmann transformed the original diffusion equation of a binary system into the nonlinear ordinary differential equation in accordance with the parabolic law. In the previous works, the solutions of the diffusion equation transformed by Boltzmann were analytically obtained and we found that the well-known Darken equation is mathematically wrong. In the present study, we found that the so-called intrinsic diffusivity corresponds in appearance to the physical solution obtained previously. However, the intrinsic diffusivity itself conceived in the diffusion research history is essentially nonexistent.展开更多
The elimination of intracranial hematomas has received widespread attention and the interactions between hemolytic agents and hematomas have become a hot research topic.In this study,we used the Navier-Stokes equation...The elimination of intracranial hematomas has received widespread attention and the interactions between hemolytic agents and hematomas have become a hot research topic.In this study,we used the Navier-Stokes equation to describe the flow control equation for hemolytic agents in a tube and used Fick’s law and the Maxwell-Stefan diffusion theory to describe the diffusion and mass transfer of hemolytic agents and hematomas.The physical fields and initial boundary conditions were set according to the parametric properties of the fluid and drainage tube.The COMSOL Multiphysics software was used to simulate the streamline distribution of hemolytic agents in a bifurcated drainage tube.Additionally,the diffusion behaviors of the hemolytic agents into hematomas were simulated and visual analysis of coupled multiphysics was performed to realize the digitization and visualization of engineering fluid problems and contribute to the field of medical engineering.展开更多
The having-been-used-for-50-year Boyd membrane diffusion Equation-In(1 - F) = R t can be deduced into F = kt through using Maclanrin expansion equation and the Lagerange remainders. The latter is a simple membrane dif...The having-been-used-for-50-year Boyd membrane diffusion Equation-In(1 - F) = R t can be deduced into F = kt through using Maclanrin expansion equation and the Lagerange remainders. The latter is a simple membrane diffusion equation, which is available to judge if the exchanging course of the resin obeys the rules of membrane-diffusion mechanism more conveniently.展开更多
基金Project(2022YFC3801000)supported by the National Key Research and Development Program of ChinaProject(232300421064)supported by the Natural Science Foundation of Henan Province,China+1 种基金Project(241111322700)supported by the Key Research and Development Projects in Henan Province,ChinaProject(52008379)supported by the National Natural Science Foundation of China。
文摘Recently,foamed polymers have been widely used in the repair of underground engineering disasters by grouting(trenchless technology)due to controllable gelation time and self-expansion.However,the grouting process becomes more complicated due to the complex geological conditions and the self-expansion of slurry.Therefore,this paper adopts a self-made visual experimental device with peripheral pressure and water plugging rate(WPR)monitoring functions to study the influence of main influencing parameters(particle size distribution,grouting amount and dynamic water pump pressure(DWPP))on the spatiotemporal distribution of slurry WPR and diffusion dynamic response(peripheral pressure).The results show that:When grouting amount is 563 g and DWPP is 0.013 MPa,the expansion force of the slurry in the diffusion process is dominant and can significantly change the local sand and gravel skeleton structure.When grouting amount is 563 g,DWPP is 0.013 MPa,and particle size distribution type isⅢ,the flow time of the polymer is shortened,the pores of the gravel are rapidly blocked.Then,the peripheral pressure decreases rapidly with the increase of the distance,and the time to reach the inflection point WPR is shortened.The instantaneous blockage of the pores leads to the delayed transmission of flow field blockage information.
基金This work is supported by the National Natural Science Foundation of China(grant number 61471390).
文摘To calculate the diffusion law of chaff cloud launched by aircraft,taking rectangular chaff as an example,the diffusion model of chaff cloud is established in this paper.Firstly,the coordinate systems of chaff are defined and the motion model of chaff is established.The motion model mainly includes chaff motion equation and rotation equation,which are obtained by combining the aerodynamic moment and aerodynamic damping.Then,the influence of multi-chaff aerodynamic interference on the movement of chaff is analyzed.Finally,considering the influence of overlap area between chaffs and chaff spacing on the aerodynamic coefficients,the multi-chaff motion model is obtained,and the simulation results are compared with the test results to verify the credibility of the model.
基金supported by the Science and Technology Innovation Foundation of CNPC“Multiscale Flow Law and Flow Field Coupling Study of Tight Sandstone Gas Reservoir”(2016D-5007-0208)13th Five-Year National Major Project“Multistage Fracturing Effect and Production of Fuling Shale Gas Horizontal Well Law Analysis Research”(2016ZX05060-009).
文摘Shale gas reservoirs have poor physical properties and a large number of micro-nano pores have been developed.Shale gas wells have no natural productivity and need fracturing reconstruction measures to put into production.However,the fracturing fluid will enter the reservoir space of shale matrix after fracturing and affect the production of shale gas.At present,there is no consensus on the influence of fracturing fluid retention on gas well production.Based on this,the paper adopts gas molecular transport analyzer to carry out experimental research on the influence of fracturing fluid on shale gas diffusion law after entering matrix pores.The results show that:(1)Compared with the diffusion capacity of single-phase shale gas,the diffusion capacity of shale gas decreases significantly when fracturing fluid is present in the reservoir;(2)In the process of fracturing fluid flowback,when the water saturation in the reservoir decreases from 50%to 0,the gas well productivity increases by about 60%.(3)When fracturing fluid exists in the reservoir,the pore diameter has an exponential relationship with the shale gas diffusion coefficient,and the diffusion coefficient increases exponentially with the increase of pore diameter.The research of this paper provides theoretical basis for guiding the efficient development of shale gas wells.
基金Supported by the National Natural Science Foundation of China under Grant No.11275072Research Fund for the Doctoral Program of Higher Education of China under Grant No.20120076110024+3 种基金Innovative Research Team Program of the National Natural Science Foundation of China under Grant No.61321064Shanghai Knowledge Service Platform Project under Grant No.ZF1213Shanghai Minhang District Talents of High Level Scientific Research ProjectTalent Fund and K.C.Wong Magna Fund in Ningbo University
文摘In this paper, a detailed Lie symmetry analysis of the(2+1)-dimensional coupled nonlinear extension of the reaction-diffusion equation is presented. The general finite transformation group is derived via a simple direct method,which is equivalent to Lie point symmetry group actually. Similarity reduction and some exact solutions of the original equation are obtained based on the optimal system of one-dimensional subalgebras. In addition, conservation laws are constructed by employing the new conservation theorem.
基金Funded by the National Natural Science Foundation of China (No.50879079)Science and Technology Plan Project of Zhejiang Province (No.2007C23058)
文摘According to the existing concrete core samples obtained in site, chloride concentration and porosity of existing normal hydraulic concrete were measured, and chloride diffusivity in existing hydraulic concrete was studied. By Fick’s second law, the chloride diffusion coefficients in the steady diffusion area were calculated. The chloride diffusion of different mix proportion concrete was tested, and chloride diffusion coefficients and porosities of freshly concrete were measured, moreover, the relationship between diffusion coefficient and porosity was analyzed. The results show that the varying law of chloride diffusion coefficient with exposure time of existing concrete can be predicted in a better way by Fick’s second law and water-cement ratios or porosity of concrete and chloride concentration in existing concrete.
基金supported by the National Natural Science Foundation of China(Grant No.11775208)the Foundation for Young Talents in College of Anhui Province,China(Grant No.gxyq2019077)the Natural Science Foundation of the Anhui Higher Education Institutions of China(Grant Nos.KJ2019A0688 and KJ2020A0638)。
文摘We explore the time evolution law of a two-mode squeezed light field(pure state)passing through twin diffusion channels,and we find that the final state is a squeezed chaotic light field(mixed state)with entanglement,which shows that even though the two channels are independent of each other,since the two modes of the initial state are entangled with each other,the final state remains entangled.Nevertheless,although the squeezing(entanglement)between the two modes is weakened after the diffusion,it is not completely removed.We also highlight the law of photon number evolution.In the calculation process used in this paper,we make full use of the summation method within the ordered product of operators and the generating function formula for two-variable Hermite polynomials.
文摘Based on the divergence theorem, we reveal that the Fickian first law relevant to the diffusion flux |J(t,x,y,z) > in the time and space is incomplete without an integral constant |J0(t) > for the integral of Fickian second law. The new diffusion flux (NDF) taking it into account shows that we can systematically understand the problems of one-way diffusion, impurity diffusion and self-diffusion as a special case of the interdiffusion. Applying the NDF to the interdiffusion problem between metal plates, it is clarified that the Kirkenkall effect is caused by |J0(t) > and also that the interdiffusion coefficients in alloy can be easily obtained. The interdiffusion problems are reasonably solved regardless of the intrinsic diffusion conception. Thus the NDF to replace the Fickian first law is an essential equation in physics.
文摘This article concentrates on the properties of three-dimensional magneto-hydrodynamic flow of a viscous fluid saturated with Darcy porous medium deformed by a nonlinear variable thickened surface.Analysis of flow is disclosed in the neighborhood of stagnation point.Features of heat transport are characterized with Newtonian heating and variable thermal conductivity.Mass transport is carried out with first order chemical reaction and variable mass diffusivity.Resulting governing equations are transformed by implementation of appropriate transformations.Analytical convergent series solutions are computed via homotopic technique.Physical aspects of numerous parameters are discussed through graphical data.Drag force coefficient,Sherwood and Nusselt numbers are illustrated through graphs corresponding to various pertinent parameters.Graphical discussion reveals that conjugate and constructive chemical reaction parameters enhance the temperature and concentration distributions,respectively.
文摘The effects of vacancies on diffusion of interstitial and substitutional atoms as well as interaction between them in metals were discussed.In the interstitial alloy,a coupling between interstitial atoms and vacancy is interrelated through the reaction of formation and dissociation of complex.For substitutional alloy with |E_b|<kT,if the atom diffusion is of the vacancies exchange mechanism,the vacancies may considerably affect atom diffusion.Based on the micromechanism of diffusion in these two alloys,their diffusion equations under general condition may be obtained,and the second Fick' s law is only an approximate form when neg- lecting vacancy influence.
基金Item Sponsored by National Natural Science Foundation of China(50774004)
文摘The Nernst-Einstein equation is used to calculate the diffusion coefficient of calcium ion in the CaO-Al2O3-SiO2 system based on the data of the density and electrical conductivity.It is assumed that all the aluminium ions form tetrahedral structure and merge with chain or ring in the case of molar concentration of CaO higher than Al2O3.And in this case,calcium ion is assumed to be the conclusive charge carrier.A formula between the diffusion coefficient and concentration of calcium ion as well as temperature is deduced,which gives an increasing function relation between the diffusion coefficient and the concentration of calcium ions.
基金Funded by the National Natural Science Foundation of China(No.10477006)the Key Project of Chinese Ministry of Education(No.106055)
文摘Formation and growth of the intermediate phases in the Ni-Al diffusion couples prepared by pouring technique were investigated. Electron probe microanalysis, scanning electron microscopy and X-ray diffraction were used to characterize the product phases in the joints. The results show that two intermediate phases form in the sequence of NiAl3 and Ni2Al3 during solidification. After annealed, Ni2Al3 and NiAl3 still exist in the joints of the couples. The reasons for the formation of Ni2Al3 and NiAl3, as well as the absence of NiAl, Ni5Al3 and Ni3Al were discussed, respectively. The growth kinetics of both product phase layers indicates that their growth obeys the parabolic rate law. The activation energies and frequency factors for NiAl3 and Ni2Al3 phases were also calculated according to the Arrhenius equation.
基金Supported by the National S&T Major Project under Grant No.ZX06901
文摘The exact solution of fractional diffusion model with a location-independent source term used in the study of the concentration of fission product in spherical uranium dioxide （U02） particle is built. The adsorption effect of the fission product on the surface of the U02 particle and the delayed decay effect are also considered. The solution is given in terms of Mittag-Leffler function with finite Hankel integral transformation and Laplace transformation. At last, the reduced forms of the solution under some special physical conditions, which is used in nuclear engineering, are obtained and corresponding remarks are given to provide significant exact results to the concentration analysis of nuclear fission products in nuclear reactor.
文摘Purpose:The goal of this study is to analyze the relationship between funded and unfunded papers and their citations in both basic and applied sciences.Design/methodology/approach:A power law model analyzes the relationship between research funding and citations of papers using 831,337 documents recorded in the Web of Science database.Findings:The original results reveal general characteristics of the diffusion of science in research fields:a)Funded articles receive higher citations compared to unfunded papers in journals;b)Funded articles exhibit a super-linear growth in citations,surpassing the increase seen in unfunded articles.This finding reveals a higher diffusion of scientific knowledge in funded articles.Moreover,c)funded articles in both basic and applied sciences demonstrate a similar expected change in citations,equivalent to about 1.23%,when the number of funded papers increases by 1%in journals.This result suggests,for the first time,that funding effect of scientific research is an invariant driver,irrespective of the nature of the basic or applied sciences.Originality/value:This evidence suggests empirical laws of funding for scientific citations that explain the importance of robust funding mechanisms for achieving impactful research outcomes in science and society.These findings here also highlight that funding for scientific research is a critical driving force in supporting citations and the dissemination of scientific knowledge in recorded documents in both basic and applied sciences.Practical implications:This comprehensive result provides a holistic view of the relationship between funding and citation performance in science to guide policymakers and R&D managers with science policies by directing funding to research in promoting the scientific development and higher diffusion of results for the progress of human society.
文摘The well-known Darken equation has been widely accepted in analyzing interdiffusion problems since 1948. The diffusion researchers have never conceived a doubt about the validity of Darken equation for such a long time. However, it is revealed that the Darken equation is inconsistent with the fundamental theory in mathematics. At the same time, it is clarified that the well-known intrinsic diffusion concept is an illusion. The present brief report will have a great influence on matters of the research and education relevant to diffusion problems not only in future but also in past, since the accumulated diffusivity data analyzed by the invalid Darken theory and the misjudged descriptions in existing text books should be revised or deleted as soon as possible.
基金This work was financially supported by the National 863 Foundation of China (No. 2001AA332030)the National Key Basic Research Program (973) (No. G1999064905)
文摘The influence of an alternative magnetic field on the growth of the diffusionlayer in Al-Zn diffusion couple was studied. The thickness of the diffusion layer was examined. Theresults show that the alternative magnetic field increases the thickness of the diffusion layer andthe effect increases with the intensity and frequency of the alternative magnetic field increasing. The growth of the diffusion layer obeys the parabolic rate law and the growth rateincreases with the application of the alternative magnetic field. This growth rate change ismanifested through a change in the frequency factor k_0 and not through a change in the activationenergy Q. The frequency factor k_0 for the diffusion layer growth with the alternative magneticfield is 5.03 cm^2/s and the one without the magnetic field is 3.84 cm^2/s.
文摘This paper investigates the flow, heat andmass transfer of a power law fluid from a vertical plate in presence of a magnetic field. The resulting non-linear partial differential equations governing the flow together with the boundary conditions are reduced to non-dimensional form. The governing equations are discretized using implicit finite difference scheme and solved numerically. The velocity, temperature and concentration profile are presented graphically while the skin friction, local Nusselt number and the Sherwood number are presented in tabular form for different values of parameters of the problem.
基金Supported by the National Natural Science Foundation of China(No.29792074)and SINOPEC.
文摘Certain prerequisite information on the component fluxes is necessary for solution of the Stefan-Maxwell equation in multicomponent diffusion systems and the Graham's law of diffusion and effusion is often resorted for this purpose. This article addresses solution of the Stefan-Maxwell equation in binary gas systems and explores the necessary conditions for definite solution of concentration profiles and pertinent component fluxes. It is found that there are multiple solutions for component fluxes in contradiction to what specified by the Graham's law of diffusion.The theorem of minimum entropy production in the non-equilibrium thermodynamics is believed instructive in determining the stable steady state solution out of infinite multiple solutions possible under the specified conditions.It is suggested that only when the boundary condition of component concentration is symmetrical in an isothermal binary system, the counter-diffusion becomes equimolar. The Graham's law of diffusion seems not generally valid for the case of isothermal ordinary diffusion.
文摘In accordance with the definition of diffusivity, the origin of coordinate system of the original diffusion equation is set at a point in the solvent material. Kirkendall revealed that Cu atoms, Zn atoms and vacancies move simultaneously in the interdiffusion region. This indicates that the original diffusion equation is a moving coordinate system for the experimentation system outside the diffusion region. The diffusion region space which means vacancies and interstices among atoms plays an important role in the diffusion phenomena. The theoretical equation of the Kirkendall effect is reasonably obtained as a shift between coordinate systems of the diffusion equation. The situation is similar to the well-known Doppler effect in the wave equation. Boltzmann transformed the original diffusion equation of a binary system into the nonlinear ordinary differential equation in accordance with the parabolic law. In the previous works, the solutions of the diffusion equation transformed by Boltzmann were analytically obtained and we found that the well-known Darken equation is mathematically wrong. In the present study, we found that the so-called intrinsic diffusivity corresponds in appearance to the physical solution obtained previously. However, the intrinsic diffusivity itself conceived in the diffusion research history is essentially nonexistent.
基金This research was funded by the National Science Foundation of China,Nos.51674121 and 61702184the Returned Overseas Scholar Funding of Hebei Province,No.C2015005014the Hebei Key Laboratory of Science and Application,and Tangshan Innovation Team Project,No.18130209B.
文摘The elimination of intracranial hematomas has received widespread attention and the interactions between hemolytic agents and hematomas have become a hot research topic.In this study,we used the Navier-Stokes equation to describe the flow control equation for hemolytic agents in a tube and used Fick’s law and the Maxwell-Stefan diffusion theory to describe the diffusion and mass transfer of hemolytic agents and hematomas.The physical fields and initial boundary conditions were set according to the parametric properties of the fluid and drainage tube.The COMSOL Multiphysics software was used to simulate the streamline distribution of hemolytic agents in a bifurcated drainage tube.Additionally,the diffusion behaviors of the hemolytic agents into hematomas were simulated and visual analysis of coupled multiphysics was performed to realize the digitization and visualization of engineering fluid problems and contribute to the field of medical engineering.
文摘The having-been-used-for-50-year Boyd membrane diffusion Equation-In(1 - F) = R t can be deduced into F = kt through using Maclanrin expansion equation and the Lagerange remainders. The latter is a simple membrane diffusion equation, which is available to judge if the exchanging course of the resin obeys the rules of membrane-diffusion mechanism more conveniently.
