Diffusion of solutes significantly affects the coarsening rate of γ'precipitates in precipitation-hardened high entropy alloys(PH-HEAs).In this work,we systematically study the refractory solutes M(Hf,Nb,Ta,Mo,W,...Diffusion of solutes significantly affects the coarsening rate of γ'precipitates in precipitation-hardened high entropy alloys(PH-HEAs).In this work,we systematically study the refractory solutes M(Hf,Nb,Ta,Mo,W,Re,Ru)diffusion in face-centered-cubic(FCC)NiCoFeCr lattice through a combination of first-principles calculations,diffusion couples,and coarsening of γ'precipitates experiments.Our calculations reveal that there exists a stronger negative correlation between solute diffusivity and Young’s modulus than between solute diffusivity and atomic size;i.e.,the higher the Young’s modulus,the more difficult solute diffusion is.Based on the electronic structure analysis,the underlying origins for such a relation-ship could be ascribed to the fact that solutes with high Young’s modulus have stronger bonds with neighboring host atoms,less compressibility,and thus poor diffusivity.Afterwards,the main interdiffu-sion coefficients of three refractory elements with similar atomic sizes and increasing Young’s modulus,Mo,W,and Re,at 1150℃in(NiCoFeCr)_(92)Al_(3)Ti_(3)M_(2)are,in order of magnitude,D_(MoMo)^(Ni)>D_(WW)^(Ni)>D_(ReRe)^(Ni),as determined by the diffusion-couple experiments.Further investigations on the coarsening kinetics of precipitates confirmed the additions of refractory elements improve the coarsening resistance of γ'pre-cipitates in the order of Re>W>Mo.The trends in the diffusivity determined by experiment and simulation are in excellent agreement.More importantly,the Young’s modulus effect for the diffusion of refractory solutes in HEAs is also carefully analyzed and discussed.Our present findings will give new insights into future design of γ'-strengthened HEAs for high-temperature structural applications.展开更多
Poly(methacrylic acid co-poloxamer) hydrogel networks were synthesized by free radical solution polymerization and their equilibrium swelling and solute permeation properties were characterized. These gels exhibited p...Poly(methacrylic acid co-poloxamer) hydrogel networks were synthesized by free radical solution polymerization and their equilibrium swelling and solute permeation properties were characterized. These gels exhibited pH dependant swelling and solute diffusivity due to the formation or disruption of hydrogen bonded complexation between methacrylic acid (MAA) and etheric (EO). In neutral and basic conditions (above the swelling transition pH), the copolymer swelling was greatly higher than acid condition. In complexed hydrogels, the diffusion coefficients of vitamin B12 (VB12) were in the range of 10-10 to 10-7 cm2s-1; While in uncomplexed hydrogels, the values were about 210-6 cm2s-1. The comonomer composition and synthesis conditions have great effect on the structure, and thereby, swelling and solute diffusion characteristics of the resultant hydrogels. For the copolymers with composition of less than or more than 1:1 MAA/EO molar ratio, the plot of lnD vs 1/H-1 followed two different linear equations of 慺ree volume theory? respectively.展开更多
In practical engineering construction,multi-layered barriers containing geomembranes are extensively applied to retard the migration of pollutants.However,the associated analytical theory on pollutants diffusion still...In practical engineering construction,multi-layered barriers containing geomembranes are extensively applied to retard the migration of pollutants.However,the associated analytical theory on pollutants diffusion still needs to be further improved.In this work,general analytical solutions are derived for one-dimensional diffusion of degradable organic contaminant(DOC)in the multi-layered media containing geomembranes under a time-varying concentration boundary condition,where the variable substitution and separated variable approaches are employed.These analytical solutions with clear expressions can be used not only to study the diffusion behaviors of DOC in bottom and vertical composite barrier systems,but also to verify other complex numerical models.The proposed general analytical solutions are then fully validated via three comparative analyses,including comparisons with the experimental measurements,an existing analytical solution,and a finite-difference solution.Ultimately,the influences of different factors on the composite cutoff wall’s(CCW,which consists of two soil-bentonite layers and a geomembrane)service performance are investigated through a composite vertical barrier system as the application example.The findings obtained from this investigation can provide scientific guidance for the barrier performance evaluation and the engineering design of CCWs.This application example also exhibits the necessity and effectiveness of the developed analytical solutions.展开更多
The diffusion coefficients(Dapp) and the heterogeneous electron transfer rate constants(ks)for ferrocene in several polymer solvents were determined by using steady-stae voltammetry. Thetemperature dependence of the t...The diffusion coefficients(Dapp) and the heterogeneous electron transfer rate constants(ks)for ferrocene in several polymer solvents were determined by using steady-stae voltammetry. Thetemperature dependence of the two parameters indicates Arrhenius behavior. The polymer solventeffects on diffusion and electron transfer dynamics of ferrocene were discussed展开更多
The diffusion coefficients(Dapp) and the heterogeneous electron-transfer rate constants(ks)for ferrocene and its seven derivatives in MPEG/LiClO4 electrolyte were determined by using steadystate voltammetry. The two p...The diffusion coefficients(Dapp) and the heterogeneous electron-transfer rate constants(ks)for ferrocene and its seven derivatives in MPEG/LiClO4 electrolyte were determined by using steadystate voltammetry. The two parameters increase with increasing temperature, indicating Arrhenius behavior. The effects of the nature of electroactive solute molecules on Dapp, ks, and the half-wave potentials(E1/2) are discussed.展开更多
The ditheion coefficients(Dapp) and the heterogeneous electron-transfer rate constan(ks)for ferrocene in MPEG/salt electrolytes were determined by using Steady-stae voltammetry. The temperature dependence of the two p...The ditheion coefficients(Dapp) and the heterogeneous electron-transfer rate constan(ks)for ferrocene in MPEG/salt electrolytes were determined by using Steady-stae voltammetry. The temperature dependence of the two parameters obeys the Arrhenius equstion. The effect of the ionic size of sir supporting electrolytes on diffusion and electron transfer dynamics of fermcene was discussed展开更多
In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for th...In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.展开更多
By using the continuation theorem of coincidence theory,the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional response x_(1)(t)=x_(1)(t)a_(1)(t...By using the continuation theorem of coincidence theory,the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional response x_(1)(t)=x_(1)(t)a_(1)(t)-b_(1)(t)x_(1)(t)-c_(1)(t)y(t)1+m(t)x_(1)(t)+D_(1)(t)[x_(2)(t)-x_(1)(t)],x_(2)(t)=x_(2)(t)a_(2)(t)-b_(2)(t)x_(2)(t)-c_(2)(t)∫^(0)_(-τ)k(s)x_(2)(t+s)d s+D_(2)(t)[x_(1)(t)-x_(2)(t)],y′(t)=y(t)a_(3)(t)-b_(3)(t)y(t)-c_(3)(t)x_(1)(t)1+m(t)x_(1)(t)is established,where a i(t),b_(i)(t),c_(i)(t)(i=1,2,3),m(t)and D_(i)(t)(i=1,2)are all positive periodic continuous functions with period w>0,τis a nonnegative constant and k(s)is a continuous nonnegative function on[-τ,0].展开更多
Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solut...Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter ε and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of 0（ε^2）.展开更多
A class of singularly perturbed Robin problems for reaction diffusion equation is considered. Under suitable conditions the asymptotic behavior of the generalized solution for the problems are studied.
This study aims to develop a chloride diffusion simulation method that considers the hydration microstructure and pore solution properties during the hydration of tricalcium silicate(C3S).The method combines the hydra...This study aims to develop a chloride diffusion simulation method that considers the hydration microstructure and pore solution properties during the hydration of tricalcium silicate(C3S).The method combines the hydration simulation,thermodynamic calculation,and finite element analysis to examine the effects of pore solution,including effect of electrochemical potential,effect of chemical activity,and effect of mechanical interactions between ions,on the chloride effective diffusion coefficient of hydrated C3S paste.The results indicate that the effect of electrochemical potential on chloride diffusion becomes stronger with increasing hydration age due to the increase in the content of hydrated calcium silicate;as the hydration age increases,the effect of chemical activity on chloride diffusion weakens when the number of diffusible elements decreases;the effect of mechanical interactions between ions on chloride diffusion decreases with the increase of hydration age.展开更多
The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and...The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and porous effects are not taken into consideration but they can be immediately included by a simple rescaling of Prandtl number and magnetic parameter. Exact general solutions for the dimensionless velocity and concentration fields and the corresponding Sherwood number and skin friction coefficient are determined under integral form in terms of error function or complementary error function of Gauss. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any problem with technical relevance of this type. As an interesting completion, uncommon in the literature, the differential equations which describe the thermal, concentration and momentum boundary layer, as well as the exact expressions for the thicknesses of thermal, concentration or velocity boundary layers were determined.Numerical results have shown that the thermal boundary layer thickness decreases for increasing values of Prandtl number and the concentration boundary layer thickness is decreasing with Schmidt number. Finally, for illustration,three special cases are considered and the influence of physical parameters on some fundamental motions is graphically underlined and discussed. The required time to reach the flow according with post-transient solution(the steady-state),for cosine/sine oscillating concentrations on the boundary is graphically determined. It is found that, the presence of destructive chemical reaction improves this time for increasing values of chemical reaction parameter.展开更多
The functionally generalized variable separation of the generalized nonlinear diffusion equations ut = A（u, Ux）Uxx ＋ B（u, ux） is studied by using the conditional Lie-Blicklund symmetry method. The variant forms o...The functionally generalized variable separation of the generalized nonlinear diffusion equations ut = A（u, Ux）Uxx ＋ B（u, ux） is studied by using the conditional Lie-Blicklund symmetry method. The variant forms of the considered equations, which admit the corresponding conditional Lie--Biicklund symmetries, are characterized. To construct functionally gener- alized separable solutions, several concrete examples defined on the exponential and trigonometric invariant subspaces are provided.展开更多
A localized space-time method of fundamental solutions(LSTMFS)is extended for solving three-dimensional transient diffusion problems in this paper.The interval segmentation in temporal direction is developed for the a...A localized space-time method of fundamental solutions(LSTMFS)is extended for solving three-dimensional transient diffusion problems in this paper.The interval segmentation in temporal direction is developed for the accurate simulation of long-time-dependent diffusion problems.In the LSTMFS,the whole space-time domain with nodes arranged i divided into a series of overlapping subdomains with a simple geometry.In each subdomain,the conventional method of fundamental solutions is utilized and the coefficients associated with the considered domain can be explicitly determined.By calculating a combined sparse matrix system,the value at any node inside the space-time domain can be obtained.Numerical experi-ments demonstrate that high accuracy and efficiency can be simultaneously achieved via the LSTMFS,even for the problems defined on a long-time and quite complex computational domain.展开更多
A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. B...A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.展开更多
The diffusion behavior of Zn/Al interfaces in their powders sintering was investigated with SEM. The results show that Zn-Al eutectoid microstructure can be achieved through their powders sintering, and the diffusion ...The diffusion behavior of Zn/Al interfaces in their powders sintering was investigated with SEM. The results show that Zn-Al eutectoid microstructure can be achieved through their powders sintering, and the diffusion characteristic between Zn and Al is just a demonstration of Kirkendall effect, by which Zn can dissolve into Al and contrarily Al cannot dissolve into Zn. During sintering, a diffusion-solution zone α′ has formed and subsequently transforms into eutectoid microstructure in cooling process. The superplastic deformation mechanism of Zn-Al eutectic alloy is phase boundary sliding which is controlled by diffusion-solution zone α′. If diffusion-solution zone α′ is unsaturated, it will have much more crystal defects and the combination between α′ and β phase is weak, thus the process of phase boundary sliding becomes easily; on the contrary, if the diffusion-solution zone α′ becomes thick and saturated, the sliding will be difficult.展开更多
The coupled three-components liquid diffusion within a porous pellet was investigated. The coupled diffusion model was given according to irreversible thermodynamics, and the rigorous solutions of the model subject to...The coupled three-components liquid diffusion within a porous pellet was investigated. The coupled diffusion model was given according to irreversible thermodynamics, and the rigorous solutions of the model subject to the homogeneous boundary conditions of the first kind are derived by employing Hankel transform technique and the standard technique resolving ordinary differential system. The method can also be used to solve the other coupled diffusion problems within a pellet with different kinds of boundary conditions. Then the case computations were conducted. The calculation results show that the effect of interdiffussion on the concentration of components depends upon the diffusion time strongly, after a long diffusion period, a very small cross diffusion coefficient will induce the observable change of concentration profile, and that, when the cross coefficients are close to 5%7% of the main coefficients, the significant effect of coupled diffusion on the concentration profiles of components is observed. The case computations also show that interdiffussion can induce non-monotonous concentration profiles. So, for the diffusion taking place within ternary system, the concentration profiles obtained by the analysis of interdiffussion can be very different from that obtained by the equivalent binary system analysis method.展开更多
The dynamic density functional theory is applied to study the diffusion of nanoparticles in polymer solutions, in which different diffusion modes have been identified by exploiting the density and free energy evolutio...The dynamic density functional theory is applied to study the diffusion of nanoparticles in polymer solutions, in which different diffusion modes have been identified by exploiting the density and free energy evolutions. Under the condition of low polymer concentration, diffusion is controlled by particle free motion with a normal Gaussian type. As the concentration increases, the non- Gaussian behavior can be observed when the particle size is comparable to the correlation length of polymer chain. Particles need to penetrate through a cage and overcome an entropic barrier, where the hopping and the model-coupling diffusion coexist. Further increase of polymer concentration can result in complete restriction of the particle by surrounding polymer segments. In this case, the non-Gaussian process fades away, and particle diffusion is controlled by Rouse dynamics of polymer chains with the generalized Gaussian characteristics.展开更多
基金financially supported by the National Natural Science Foundation of China(No.51701061)the Natural Sci-ence Foundation of Hebei Province(No.E2019202059).
文摘Diffusion of solutes significantly affects the coarsening rate of γ'precipitates in precipitation-hardened high entropy alloys(PH-HEAs).In this work,we systematically study the refractory solutes M(Hf,Nb,Ta,Mo,W,Re,Ru)diffusion in face-centered-cubic(FCC)NiCoFeCr lattice through a combination of first-principles calculations,diffusion couples,and coarsening of γ'precipitates experiments.Our calculations reveal that there exists a stronger negative correlation between solute diffusivity and Young’s modulus than between solute diffusivity and atomic size;i.e.,the higher the Young’s modulus,the more difficult solute diffusion is.Based on the electronic structure analysis,the underlying origins for such a relation-ship could be ascribed to the fact that solutes with high Young’s modulus have stronger bonds with neighboring host atoms,less compressibility,and thus poor diffusivity.Afterwards,the main interdiffu-sion coefficients of three refractory elements with similar atomic sizes and increasing Young’s modulus,Mo,W,and Re,at 1150℃in(NiCoFeCr)_(92)Al_(3)Ti_(3)M_(2)are,in order of magnitude,D_(MoMo)^(Ni)>D_(WW)^(Ni)>D_(ReRe)^(Ni),as determined by the diffusion-couple experiments.Further investigations on the coarsening kinetics of precipitates confirmed the additions of refractory elements improve the coarsening resistance of γ'pre-cipitates in the order of Re>W>Mo.The trends in the diffusivity determined by experiment and simulation are in excellent agreement.More importantly,the Young’s modulus effect for the diffusion of refractory solutes in HEAs is also carefully analyzed and discussed.Our present findings will give new insights into future design of γ'-strengthened HEAs for high-temperature structural applications.
文摘Poly(methacrylic acid co-poloxamer) hydrogel networks were synthesized by free radical solution polymerization and their equilibrium swelling and solute permeation properties were characterized. These gels exhibited pH dependant swelling and solute diffusivity due to the formation or disruption of hydrogen bonded complexation between methacrylic acid (MAA) and etheric (EO). In neutral and basic conditions (above the swelling transition pH), the copolymer swelling was greatly higher than acid condition. In complexed hydrogels, the diffusion coefficients of vitamin B12 (VB12) were in the range of 10-10 to 10-7 cm2s-1; While in uncomplexed hydrogels, the values were about 210-6 cm2s-1. The comonomer composition and synthesis conditions have great effect on the structure, and thereby, swelling and solute diffusion characteristics of the resultant hydrogels. For the copolymers with composition of less than or more than 1:1 MAA/EO molar ratio, the plot of lnD vs 1/H-1 followed two different linear equations of 慺ree volume theory? respectively.
基金Project(2023YFC3707800)supported by the National Key Research and Development Program of China。
文摘In practical engineering construction,multi-layered barriers containing geomembranes are extensively applied to retard the migration of pollutants.However,the associated analytical theory on pollutants diffusion still needs to be further improved.In this work,general analytical solutions are derived for one-dimensional diffusion of degradable organic contaminant(DOC)in the multi-layered media containing geomembranes under a time-varying concentration boundary condition,where the variable substitution and separated variable approaches are employed.These analytical solutions with clear expressions can be used not only to study the diffusion behaviors of DOC in bottom and vertical composite barrier systems,but also to verify other complex numerical models.The proposed general analytical solutions are then fully validated via three comparative analyses,including comparisons with the experimental measurements,an existing analytical solution,and a finite-difference solution.Ultimately,the influences of different factors on the composite cutoff wall’s(CCW,which consists of two soil-bentonite layers and a geomembrane)service performance are investigated through a composite vertical barrier system as the application example.The findings obtained from this investigation can provide scientific guidance for the barrier performance evaluation and the engineering design of CCWs.This application example also exhibits the necessity and effectiveness of the developed analytical solutions.
文摘The diffusion coefficients(Dapp) and the heterogeneous electron transfer rate constants(ks)for ferrocene in several polymer solvents were determined by using steady-stae voltammetry. Thetemperature dependence of the two parameters indicates Arrhenius behavior. The polymer solventeffects on diffusion and electron transfer dynamics of ferrocene were discussed
文摘The diffusion coefficients(Dapp) and the heterogeneous electron-transfer rate constants(ks)for ferrocene and its seven derivatives in MPEG/LiClO4 electrolyte were determined by using steadystate voltammetry. The two parameters increase with increasing temperature, indicating Arrhenius behavior. The effects of the nature of electroactive solute molecules on Dapp, ks, and the half-wave potentials(E1/2) are discussed.
文摘The ditheion coefficients(Dapp) and the heterogeneous electron-transfer rate constan(ks)for ferrocene in MPEG/salt electrolytes were determined by using Steady-stae voltammetry. The temperature dependence of the two parameters obeys the Arrhenius equstion. The effect of the ionic size of sir supporting electrolytes on diffusion and electron transfer dynamics of fermcene was discussed
基金Supported by the National Natural Sciences Foundation of China(40676016 and 10471039)the National Key Project for Basic Research(2003CB415101-03 and 2004CB418304)+2 种基金the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)in part by E-Institutes of Shanghai Municipal Education Commission(N.E03004)the Natural Science Foundation of Zeijiang,China(Y606268).
文摘In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.
基金Supported by the National Natural Science Foundation of China(19531070)the Major and Youth Project Foundation of Hubei Province Education Department(2001Z06003)(2002B00002).
文摘By using the continuation theorem of coincidence theory,the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional response x_(1)(t)=x_(1)(t)a_(1)(t)-b_(1)(t)x_(1)(t)-c_(1)(t)y(t)1+m(t)x_(1)(t)+D_(1)(t)[x_(2)(t)-x_(1)(t)],x_(2)(t)=x_(2)(t)a_(2)(t)-b_(2)(t)x_(2)(t)-c_(2)(t)∫^(0)_(-τ)k(s)x_(2)(t+s)d s+D_(2)(t)[x_(1)(t)-x_(2)(t)],y′(t)=y(t)a_(3)(t)-b_(3)(t)y(t)-c_(3)(t)x_(1)(t)1+m(t)x_(1)(t)is established,where a i(t),b_(i)(t),c_(i)(t)(i=1,2,3),m(t)and D_(i)(t)(i=1,2)are all positive periodic continuous functions with period w>0,τis a nonnegative constant and k(s)is a continuous nonnegative function on[-τ,0].
基金supported by the E-Institutes of Shanghai Municipal Education Commission (Grant No.E03004)
文摘Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter ε and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of 0（ε^2）.
基金Supported by the National Natural Science Foundation of China(11371248)the Natural Science Foundation of the Education Department of Anhui Province 3(KJ2013A133,KJ2013B003)the Natural Science Foundation of Zhejiang Province(LY13A010005)
文摘A class of singularly perturbed Robin problems for reaction diffusion equation is considered. Under suitable conditions the asymptotic behavior of the generalized solution for the problems are studied.
基金Funded by the Natural Science Foundation of Jiangsu Province(No.BK20241529)China Postdoctoral Science Foundation(No.2024M750736)。
文摘This study aims to develop a chloride diffusion simulation method that considers the hydration microstructure and pore solution properties during the hydration of tricalcium silicate(C3S).The method combines the hydration simulation,thermodynamic calculation,and finite element analysis to examine the effects of pore solution,including effect of electrochemical potential,effect of chemical activity,and effect of mechanical interactions between ions,on the chloride effective diffusion coefficient of hydrated C3S paste.The results indicate that the effect of electrochemical potential on chloride diffusion becomes stronger with increasing hydration age due to the increase in the content of hydrated calcium silicate;as the hydration age increases,the effect of chemical activity on chloride diffusion weakens when the number of diffusible elements decreases;the effect of mechanical interactions between ions on chloride diffusion decreases with the increase of hydration age.
基金Abdus Salam School of Mathematical Sciences, GC University, Lahore, PakistanHigher Education Commission of Pakistan, for generous supporting and facilitating this research work
文摘The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and porous effects are not taken into consideration but they can be immediately included by a simple rescaling of Prandtl number and magnetic parameter. Exact general solutions for the dimensionless velocity and concentration fields and the corresponding Sherwood number and skin friction coefficient are determined under integral form in terms of error function or complementary error function of Gauss. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any problem with technical relevance of this type. As an interesting completion, uncommon in the literature, the differential equations which describe the thermal, concentration and momentum boundary layer, as well as the exact expressions for the thicknesses of thermal, concentration or velocity boundary layers were determined.Numerical results have shown that the thermal boundary layer thickness decreases for increasing values of Prandtl number and the concentration boundary layer thickness is decreasing with Schmidt number. Finally, for illustration,three special cases are considered and the influence of physical parameters on some fundamental motions is graphically underlined and discussed. The required time to reach the flow according with post-transient solution(the steady-state),for cosine/sine oscillating concentrations on the boundary is graphically determined. It is found that, the presence of destructive chemical reaction improves this time for increasing values of chemical reaction parameter.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11371293,11401458,and 11501438)the National Natural Science Foundation of China,Tian Yuan Special Foundation(Grant No.11426169)the Natural Science Basic Research Plan in Shaanxi Province of China(Gran No.2015JQ1014)
文摘The functionally generalized variable separation of the generalized nonlinear diffusion equations ut = A（u, Ux）Uxx ＋ B（u, ux） is studied by using the conditional Lie-Blicklund symmetry method. The variant forms of the considered equations, which admit the corresponding conditional Lie--Biicklund symmetries, are characterized. To construct functionally gener- alized separable solutions, several concrete examples defined on the exponential and trigonometric invariant subspaces are provided.
基金the Fundamental Research Funds for the Central Universities(Grants B200203009 and B200202126)the Natural Science Foundation of Jiangsu Province(Grant BK20190073)+2 种基金the State Key Laboratory of Acoustics,Chinese Academy of Sciences(Grant SKLA202001)the State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University(Grant KF2020-22)the China Postdoctoral Science Foundation(Grants 2017M611669 and 2018T110430).
文摘A localized space-time method of fundamental solutions(LSTMFS)is extended for solving three-dimensional transient diffusion problems in this paper.The interval segmentation in temporal direction is developed for the accurate simulation of long-time-dependent diffusion problems.In the LSTMFS,the whole space-time domain with nodes arranged i divided into a series of overlapping subdomains with a simple geometry.In each subdomain,the conventional method of fundamental solutions is utilized and the coefficients associated with the considered domain can be explicitly determined.By calculating a combined sparse matrix system,the value at any node inside the space-time domain can be obtained.Numerical experi-ments demonstrate that high accuracy and efficiency can be simultaneously achieved via the LSTMFS,even for the problems defined on a long-time and quite complex computational domain.
基金Supported by the National Natural Science Foundation of China (10961017)"Qinglan" Talent Programof Lanzhou Jiaotong University (QL-05-20A)
文摘A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.
文摘The diffusion behavior of Zn/Al interfaces in their powders sintering was investigated with SEM. The results show that Zn-Al eutectoid microstructure can be achieved through their powders sintering, and the diffusion characteristic between Zn and Al is just a demonstration of Kirkendall effect, by which Zn can dissolve into Al and contrarily Al cannot dissolve into Zn. During sintering, a diffusion-solution zone α′ has formed and subsequently transforms into eutectoid microstructure in cooling process. The superplastic deformation mechanism of Zn-Al eutectic alloy is phase boundary sliding which is controlled by diffusion-solution zone α′. If diffusion-solution zone α′ is unsaturated, it will have much more crystal defects and the combination between α′ and β phase is weak, thus the process of phase boundary sliding becomes easily; on the contrary, if the diffusion-solution zone α′ becomes thick and saturated, the sliding will be difficult.
基金Project (50136020) supported by the National Natural Science Foundation of China Project (01056) supported by theKey Project of Education Ministry of China
文摘The coupled three-components liquid diffusion within a porous pellet was investigated. The coupled diffusion model was given according to irreversible thermodynamics, and the rigorous solutions of the model subject to the homogeneous boundary conditions of the first kind are derived by employing Hankel transform technique and the standard technique resolving ordinary differential system. The method can also be used to solve the other coupled diffusion problems within a pellet with different kinds of boundary conditions. Then the case computations were conducted. The calculation results show that the effect of interdiffussion on the concentration of components depends upon the diffusion time strongly, after a long diffusion period, a very small cross diffusion coefficient will induce the observable change of concentration profile, and that, when the cross coefficients are close to 5%7% of the main coefficients, the significant effect of coupled diffusion on the concentration profiles of components is observed. The case computations also show that interdiffussion can induce non-monotonous concentration profiles. So, for the diffusion taking place within ternary system, the concentration profiles obtained by the analysis of interdiffussion can be very different from that obtained by the equivalent binary system analysis method.
基金financially supported by the National Natural Science Foundation of China (Nos. 51790502 and 51525301)the National Supercomputer Centre in GuangzhouChemcloudcomputing of Beijing University of Chemical Technology
文摘The dynamic density functional theory is applied to study the diffusion of nanoparticles in polymer solutions, in which different diffusion modes have been identified by exploiting the density and free energy evolutions. Under the condition of low polymer concentration, diffusion is controlled by particle free motion with a normal Gaussian type. As the concentration increases, the non- Gaussian behavior can be observed when the particle size is comparable to the correlation length of polymer chain. Particles need to penetrate through a cage and overcome an entropic barrier, where the hopping and the model-coupling diffusion coexist. Further increase of polymer concentration can result in complete restriction of the particle by surrounding polymer segments. In this case, the non-Gaussian process fades away, and particle diffusion is controlled by Rouse dynamics of polymer chains with the generalized Gaussian characteristics.
