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
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
The solution diffusion coefficient is a great important intrinsical parameter in crystal growth.On earth,it is impossible to accurately determine the diffusion coefficient since there is nature convection.One of the m...The solution diffusion coefficient is a great important intrinsical parameter in crystal growth.On earth,it is impossible to accurately determine the diffusion coefficient since there is nature convection.One of the marked charateristics of space-crystal growth is to eleminate nature convection,so that purely diffusion-controlled condition of crystal growth could be realized and precise measurement of the diffusion coefficient should be approved.展开更多
The performance of gas diffusion porous electrode starved of electrolyte solution can be significantly increased by decreasing the thickness of uneven liquid film covering the catalyst agglomerates.
In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.
In this paper we are interested in the large time behavior of the nonlinear diffusion equationWe consider functions which allow the equation to possess traveling wave solutions. We first present an existence and uniqu...In this paper we are interested in the large time behavior of the nonlinear diffusion equationWe consider functions which allow the equation to possess traveling wave solutions. We first present an existence and uniqueness as well as some comparison principle result of generalized solutions to the Cauchy problem. Then we give for some threshold results, from which we can see that u=a is stable, while u= 0 or u=1 is unstable under some assumptions, etc.展开更多
Cu-Cr alloys are widely applied in electronic,aerospace and nuclear industries,due to their high strength and high conductivity.However,their terrible softening resistance limits wider applications.This paper presents...Cu-Cr alloys are widely applied in electronic,aerospace and nuclear industries,due to their high strength and high conductivity.However,their terrible softening resistance limits wider applications.This paper presents a novel strategy of integrating mechanism features into interpretable machine learning(ML)to develop softening-resistant Cu-Cr alloys and to understand their mechanisms.First,the mechanism features were specially designed to describe mechanisms potentially vital to softening resistance,and they were obtained through first-principles calculations.Those mechanism features that described interfacial segregation and solute diffusion exhibited significant Gini importance during feature selection.Only integrated with them,did ML models achieve great performance,accurate predictions,and successful development of Cu-0.4Cr-0.10La/Ce(wt.%)alloys with excellent softening resistance.Then,the contributions of these mechanism features to the predictions were interpreted by a game theoretic approach,but unexpectedly,they were not fully consistent with interpretations that we expected from mechanism features.Finally,investigation targeted at these inconsistencies gave novel insights into softening resistance mechanisms.The Cu-Cr-La/Ce alloys’excellent softening resistance was not induced by a prevailing mechanism of La/Ce atoms segregating at phase interfaces,nor by an expected mechanism of La/Ce atoms improving the Cr atom jump energy barriers.Instead,it was caused by a unique mechanism in which La/Ce atoms competed with Cr atoms for vacancies and therefore depleted the available vacancies for the Cr atom jump.This paper demonstrates a new paradigm of developing softening-resistant Cu-Cr alloys and understanding their mechanisms via mechanism-informed interpretable ML.展开更多
Solute diffusion controlled solidification model was used to simulate the initial stage cellular to dendrite transition of Ti44Al alloys during directional solidification at different velocities. The simulation result...Solute diffusion controlled solidification model was used to simulate the initial stage cellular to dendrite transition of Ti44Al alloys during directional solidification at different velocities. The simulation results show that during this process, a mixed structure composed of cells and dendrites was observed, where secondary dendrites are absent at facing surface with parallel closely spaced dendrites, which agrees with the previous experimental observation. The dendrite spacings are larger than cellular spacings at a given rate, and the columnar grain spacing sharply increases to a maximum as solidification advance to coexistence zone. In addition, simulation also revealed that decreasing the numbers of the seed causes the trend of unstable dendrite transition to increase. Finally, the main influence factors affecting cell/dendrite transition were analyzed, which could be the change of growth rates resulting in slight fluctuations of liquid composition occurred at growth front. The simulation results are in reasonable agreement with the results of previous theoretical models and experimental observation at low cooling rates.展开更多
The microstructural evolution of Ti-45 at.%Al alloy during directional solidification was simulated by applying a solute diffusion controlled solidification model.The obtained results have shown that under high therma...The microstructural evolution of Ti-45 at.%Al alloy during directional solidification was simulated by applying a solute diffusion controlled solidification model.The obtained results have shown that under high thermal gradients the stable primary spacing can be adjusted via branching or competitive growth.For dendritic structures formed under a high thermal gradient,the secondary dendrite arms are developed not very well in many cases due to the branching mechanism under a constrained dendritic growth condition.Furthermore,it has been observed that,with increasing pulling velocity,there exists a cell/dendrite transition region consisting of cells and dendrites,which varies with the thermal gradient in a contradicting way,i.e.increase of the thermal gradient leading to the decrease of the range of the transition region.The simulations agree reasonably well with experiment results.展开更多
The magnetohydrodynamic(MHD)boundary layer slipflow and solute transfer over a porous plate in the presence of a chemical reaction are investigated.The governing equations were transformed into self-similar ordinary di...The magnetohydrodynamic(MHD)boundary layer slipflow and solute transfer over a porous plate in the presence of a chemical reaction are investigated.The governing equations were transformed into self-similar ordinary differential equations by adopting the similarity transformation technique.Then the numerical solutions are obtained by a shooting technique using the fourth order Runge-Kutta method.The study reveals that due to the increase in the boundary slip,the concentration decreases and the velocity increases.On the other hand,with an increase in the magneticfield and mass suction,both boundary layer thicknesses decreased.As the Schmidt number and the reaction rate parameter increases,the concentration decreases and the mass transfer increases.展开更多
The sample preparation of samples conlaining bovine serum albumin（BSA）,e.g..as used in transdermal Franz diffusion cell（FDC） solutions,was evaluated using an analytical qualily-by-design（QbD）approach.Traditional...The sample preparation of samples conlaining bovine serum albumin（BSA）,e.g..as used in transdermal Franz diffusion cell（FDC） solutions,was evaluated using an analytical qualily-by-design（QbD）approach.Traditional precipitation of BSA by adding an equal volume of organic solvent,often successfully used with conventional HPLC-PDA,was found insufficiently robust when novel fused-core HPLC and/or UPLC-MS methods were used.In this study,three factors（acetonitrile（%）.formic acid（%） and boiling time（min）） were included in the experimental design to determine an optimal and more suitable sample treatment of BSAcontaining FDC solutions.Using a QbD and Derringer desirability（D） approach,combining BSA loss,dilution factor and variability,we constructed an optimal working space with the edge of failure defined as D〈0.9.The design space is modelled and is confirmed to have an ACN range of 83 ± 3% and FA content of 1 ±0.25%.展开更多
A mathematical modeling is explored to scrutinize the unsteady stagnation point flow of Oldroyd-B nanofluid under the thermal conductivity and solutal diffusivity with bioconvection mechanism.Impacts of Joule heating ...A mathematical modeling is explored to scrutinize the unsteady stagnation point flow of Oldroyd-B nanofluid under the thermal conductivity and solutal diffusivity with bioconvection mechanism.Impacts of Joule heating and Arrhenius activation energy including convective boundary conditions are studied,and the specified surface temperature and constant temperature of wall(CTW)are discussed.The consequences of thermal conductivity and diffusivity are also taken into account.The flow is generated through stretchable disk geometry,and the behavior of non-linear thermal radiation is incorporated in energy equation.The partial differential equations governing the fluid flow in the structure is reduced into dimensionless nonlinear ODEs by applying suitable similarity variables.The obtained system of non-dimensional nonlinear ODEs is treated numerically with the help of bvp4c solver in Matlab under shooting algorithm.The impact of various prominent parameters on velocity profile,thermal profile,volumetric nanoparticle concentration and microorganism distribution is depicted in graphical form.The numerical outcomes for skin friction coefficient,heat transfer rate,Sherwood number as well as microorganism density number versus various parameters are listed in the tables.The results show that fluid velocity is reduced by increasing buoyancy ratio parameter,while the fluid flow increases with mixed convective parameter.The temperature profile is enhanced with the amount of nonlinear thermal radiation and temperature dependent thermal conductivity.Furthermore,concentration profiles of nanoparticles have opposite behavior for Brownian motion coefficient and thermophoresis diffusion parameter,and it is noticed that by varying Peclet number the microorganisms profile is declined.The proposed study is useful to control and optimize heat transfer in industrial applications.展开更多
In this paper we consider the initial-boundary value problems for a class ofapplications, such as biomathematics and biochemistry.Applying the method ofcomposile expansion we construct the formally asymptotic solution...In this paper we consider the initial-boundary value problems for a class ofapplications, such as biomathematics and biochemistry.Applying the method ofcomposile expansion we construct the formally asymptotic solution of the problemdescribed. With the help of theory of upper and lower solutions we prove the uniformlyvalidity of the formal solution and the existence of solution of the original problem.展开更多
By using a general symmetry theory related to invariant functions,strong symmetry operators and hereditary operators,we find a general integrable hopf heirarchy with infinitely many general symmetries and Lax pairs.Fo...By using a general symmetry theory related to invariant functions,strong symmetry operators and hereditary operators,we find a general integrable hopf heirarchy with infinitely many general symmetries and Lax pairs.For the first order Hopf equation,there exist infinitely many symmetries which can be expressed by means of an arbitrary function in arbitrary dimensions.The general solution of the first order Hopf equation is obtained via hodograph transformation.For the second order Hopf equation,the Hopf-diffusion equation,there are five sets of infinitely many symmetries.Especially,there exist a set of primary branch symmetry with which contains an arbitrary solution of the usual linear diffusion equation.Some special implicit exact group invariant solutions of the Hopf-diffusion equation are also given.展开更多
In this paper ,in the space that possesses restoring nucleus, we obtain analyticsolutions in the series form for the steady-state convection diffusion equation The solutions have the following characteristics: (1) the...In this paper ,in the space that possesses restoring nucleus, we obtain analyticsolutions in the series form for the steady-state convection diffusion equation The solutions have the following characteristics: (1) they ave given in the accurate form:(2)they can be calculated in the explicit way, without solving the eguations;(3) the error of the approximate solution will be monotonically decreased under the meaning of the norm of the spaces when a cardinal term is added in the procedure of numerical solution .Finally, we calculated the example in [2] the result shows that our solution is more accurate than that in [2].展开更多
Slot-die coating with halogen-free solvents is a promising scalable fabrication strategy for organic solar cells(OSCs).However,the complex interplay between long-time-scale solute diffusion and microstructural evoluti...Slot-die coating with halogen-free solvents is a promising scalable fabrication strategy for organic solar cells(OSCs).However,the complex interplay between long-time-scale solute diffusion and microstructural evolution during the coating process remains poorly understood,limiting further optimization of morphology and device performance.In this study,we elucidate the critical role of solution viscosity in regulating phase separation and aggregation kinetics.Specifically,lower solution viscosity enhances solute diffusion,accelerating molecular aggregation while suppressing liquid-liquid phase separation(LLPS).Notably,we observe that in three different systems with varying crystallinity and immiscibility(PM6:Y6,PTQ10:Y6,and D18:Y6),the optimal processing conditions for peak device efficiency consistently correspond to a nearly identical solution viscosity(∼0.8 mPa s),despite variations in optimal processing temperatures.In situ characterizations reveal that at this viscosity,all three systems exhibit constrained LLPS and rapid molecular aggregation,promoting the formation of finely structured,continuous nanoscale domains.These findings establish solution viscosity as a universal governing parameter for morphology control in printed active layers.By providing a fundamental framework for understanding viscosity-mediated phase separation,this work offers valuable insights for advancing high-throughput,environmentally friendly printing techniques for high-efficiency OSCs.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.
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
文摘The solution diffusion coefficient is a great important intrinsical parameter in crystal growth.On earth,it is impossible to accurately determine the diffusion coefficient since there is nature convection.One of the marked charateristics of space-crystal growth is to eleminate nature convection,so that purely diffusion-controlled condition of crystal growth could be realized and precise measurement of the diffusion coefficient should be approved.
文摘The performance of gas diffusion porous electrode starved of electrolyte solution can be significantly increased by decreasing the thickness of uneven liquid film covering the catalyst agglomerates.
文摘In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.
文摘In this paper we are interested in the large time behavior of the nonlinear diffusion equationWe consider functions which allow the equation to possess traveling wave solutions. We first present an existence and uniqueness as well as some comparison principle result of generalized solutions to the Cauchy problem. Then we give for some threshold results, from which we can see that u=a is stable, while u= 0 or u=1 is unstable under some assumptions, etc.
基金supported by the National Key Research and Development Program of China(Grant No.2021YFB3803100)the National Natural Science Foundation of China(Grant No.U2202255)+3 种基金the Science and Technology Innovation Program of Hunan Province(Grant No.2021GK2016)the Major Science and Technology Pro-gram of Wuhu,China(Grant No.2021zd02)the Hunan Natural Science Fund for Distinguished Young Scholars(No.2024JJ2076)the Project of Innovation-Driven Plan and the Project of State Key Laboratory of Powder Metallurgy,Central South University,Changsha,China.
文摘Cu-Cr alloys are widely applied in electronic,aerospace and nuclear industries,due to their high strength and high conductivity.However,their terrible softening resistance limits wider applications.This paper presents a novel strategy of integrating mechanism features into interpretable machine learning(ML)to develop softening-resistant Cu-Cr alloys and to understand their mechanisms.First,the mechanism features were specially designed to describe mechanisms potentially vital to softening resistance,and they were obtained through first-principles calculations.Those mechanism features that described interfacial segregation and solute diffusion exhibited significant Gini importance during feature selection.Only integrated with them,did ML models achieve great performance,accurate predictions,and successful development of Cu-0.4Cr-0.10La/Ce(wt.%)alloys with excellent softening resistance.Then,the contributions of these mechanism features to the predictions were interpreted by a game theoretic approach,but unexpectedly,they were not fully consistent with interpretations that we expected from mechanism features.Finally,investigation targeted at these inconsistencies gave novel insights into softening resistance mechanisms.The Cu-Cr-La/Ce alloys’excellent softening resistance was not induced by a prevailing mechanism of La/Ce atoms segregating at phase interfaces,nor by an expected mechanism of La/Ce atoms improving the Cr atom jump energy barriers.Instead,it was caused by a unique mechanism in which La/Ce atoms competed with Cr atoms for vacancies and therefore depleted the available vacancies for the Cr atom jump.This paper demonstrates a new paradigm of developing softening-resistant Cu-Cr alloys and understanding their mechanisms via mechanism-informed interpretable ML.
基金National Natural Science Foundation of China (50434030)
文摘Solute diffusion controlled solidification model was used to simulate the initial stage cellular to dendrite transition of Ti44Al alloys during directional solidification at different velocities. The simulation results show that during this process, a mixed structure composed of cells and dendrites was observed, where secondary dendrites are absent at facing surface with parallel closely spaced dendrites, which agrees with the previous experimental observation. The dendrite spacings are larger than cellular spacings at a given rate, and the columnar grain spacing sharply increases to a maximum as solidification advance to coexistence zone. In addition, simulation also revealed that decreasing the numbers of the seed causes the trend of unstable dendrite transition to increase. Finally, the main influence factors affecting cell/dendrite transition were analyzed, which could be the change of growth rates resulting in slight fluctuations of liquid composition occurred at growth front. The simulation results are in reasonable agreement with the results of previous theoretical models and experimental observation at low cooling rates.
文摘The microstructural evolution of Ti-45 at.%Al alloy during directional solidification was simulated by applying a solute diffusion controlled solidification model.The obtained results have shown that under high thermal gradients the stable primary spacing can be adjusted via branching or competitive growth.For dendritic structures formed under a high thermal gradient,the secondary dendrite arms are developed not very well in many cases due to the branching mechanism under a constrained dendritic growth condition.Furthermore,it has been observed that,with increasing pulling velocity,there exists a cell/dendrite transition region consisting of cells and dendrites,which varies with the thermal gradient in a contradicting way,i.e.increase of the thermal gradient leading to the decrease of the range of the transition region.The simulations agree reasonably well with experiment results.
基金gratefully acknowledges the financial support from the National Board for Higher Mathematics(NBHM),DAE,Mumbai,India to pursue this work.
文摘The magnetohydrodynamic(MHD)boundary layer slipflow and solute transfer over a porous plate in the presence of a chemical reaction are investigated.The governing equations were transformed into self-similar ordinary differential equations by adopting the similarity transformation technique.Then the numerical solutions are obtained by a shooting technique using the fourth order Runge-Kutta method.The study reveals that due to the increase in the boundary slip,the concentration decreases and the velocity increases.On the other hand,with an increase in the magneticfield and mass suction,both boundary layer thicknesses decreased.As the Schmidt number and the reaction rate parameter increases,the concentration decreases and the mass transfer increases.
基金the Special Research Fund of Ghent University(BOF 01D23812 to Lien Taevernier and BOF O1J22510 to Evelien Wynendaele and Professor Bart De Spiegeleer)the Institute for the Promotion of Innovation through Science and Technology in Flanders(IWT 101529 to Matthias D'Hondt)for their financial funding
文摘The sample preparation of samples conlaining bovine serum albumin（BSA）,e.g..as used in transdermal Franz diffusion cell（FDC） solutions,was evaluated using an analytical qualily-by-design（QbD）approach.Traditional precipitation of BSA by adding an equal volume of organic solvent,often successfully used with conventional HPLC-PDA,was found insufficiently robust when novel fused-core HPLC and/or UPLC-MS methods were used.In this study,three factors（acetonitrile（%）.formic acid（%） and boiling time（min）） were included in the experimental design to determine an optimal and more suitable sample treatment of BSAcontaining FDC solutions.Using a QbD and Derringer desirability（D） approach,combining BSA loss,dilution factor and variability,we constructed an optimal working space with the edge of failure defined as D〈0.9.The design space is modelled and is confirmed to have an ACN range of 83 ± 3% and FA content of 1 ±0.25%.
基金the National Natural Science Foundation of China(Nos.51876170,12072257)the Natural Science Basic Research Plan in Shaanxi Province of China(No.2019JM-343)the National Key Project(GJXM92579).
文摘A mathematical modeling is explored to scrutinize the unsteady stagnation point flow of Oldroyd-B nanofluid under the thermal conductivity and solutal diffusivity with bioconvection mechanism.Impacts of Joule heating and Arrhenius activation energy including convective boundary conditions are studied,and the specified surface temperature and constant temperature of wall(CTW)are discussed.The consequences of thermal conductivity and diffusivity are also taken into account.The flow is generated through stretchable disk geometry,and the behavior of non-linear thermal radiation is incorporated in energy equation.The partial differential equations governing the fluid flow in the structure is reduced into dimensionless nonlinear ODEs by applying suitable similarity variables.The obtained system of non-dimensional nonlinear ODEs is treated numerically with the help of bvp4c solver in Matlab under shooting algorithm.The impact of various prominent parameters on velocity profile,thermal profile,volumetric nanoparticle concentration and microorganism distribution is depicted in graphical form.The numerical outcomes for skin friction coefficient,heat transfer rate,Sherwood number as well as microorganism density number versus various parameters are listed in the tables.The results show that fluid velocity is reduced by increasing buoyancy ratio parameter,while the fluid flow increases with mixed convective parameter.The temperature profile is enhanced with the amount of nonlinear thermal radiation and temperature dependent thermal conductivity.Furthermore,concentration profiles of nanoparticles have opposite behavior for Brownian motion coefficient and thermophoresis diffusion parameter,and it is noticed that by varying Peclet number the microorganisms profile is declined.The proposed study is useful to control and optimize heat transfer in industrial applications.
文摘In this paper we consider the initial-boundary value problems for a class ofapplications, such as biomathematics and biochemistry.Applying the method ofcomposile expansion we construct the formally asymptotic solution of the problemdescribed. With the help of theory of upper and lower solutions we prove the uniformlyvalidity of the formal solution and the existence of solution of the original problem.
基金Supported by the National Natural Science Foundation of China Grant under Nos.11435005,11175092,and 11205092Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No.ZF1213K.C.Wong Magna Fund in Ningbo University
文摘By using a general symmetry theory related to invariant functions,strong symmetry operators and hereditary operators,we find a general integrable hopf heirarchy with infinitely many general symmetries and Lax pairs.For the first order Hopf equation,there exist infinitely many symmetries which can be expressed by means of an arbitrary function in arbitrary dimensions.The general solution of the first order Hopf equation is obtained via hodograph transformation.For the second order Hopf equation,the Hopf-diffusion equation,there are five sets of infinitely many symmetries.Especially,there exist a set of primary branch symmetry with which contains an arbitrary solution of the usual linear diffusion equation.Some special implicit exact group invariant solutions of the Hopf-diffusion equation are also given.
文摘In this paper ,in the space that possesses restoring nucleus, we obtain analyticsolutions in the series form for the steady-state convection diffusion equation The solutions have the following characteristics: (1) they ave given in the accurate form:(2)they can be calculated in the explicit way, without solving the eguations;(3) the error of the approximate solution will be monotonically decreased under the meaning of the norm of the spaces when a cardinal term is added in the procedure of numerical solution .Finally, we calculated the example in [2] the result shows that our solution is more accurate than that in [2].
基金the National Natural Science Foundation of China(W2411049,52303247,and 52173023)the Fundamental Research Funds for the Central Universities(xzy012023169)+2 种基金the Postdoctoral Research Project of Shaanxi Province(2023BSHEDZZ24)the 111 Project 2.0(BP0618008)the China Postdoctoral Science Foundation(2023TQ0273)。
文摘Slot-die coating with halogen-free solvents is a promising scalable fabrication strategy for organic solar cells(OSCs).However,the complex interplay between long-time-scale solute diffusion and microstructural evolution during the coating process remains poorly understood,limiting further optimization of morphology and device performance.In this study,we elucidate the critical role of solution viscosity in regulating phase separation and aggregation kinetics.Specifically,lower solution viscosity enhances solute diffusion,accelerating molecular aggregation while suppressing liquid-liquid phase separation(LLPS).Notably,we observe that in three different systems with varying crystallinity and immiscibility(PM6:Y6,PTQ10:Y6,and D18:Y6),the optimal processing conditions for peak device efficiency consistently correspond to a nearly identical solution viscosity(∼0.8 mPa s),despite variations in optimal processing temperatures.In situ characterizations reveal that at this viscosity,all three systems exhibit constrained LLPS and rapid molecular aggregation,promoting the formation of finely structured,continuous nanoscale domains.These findings establish solution viscosity as a universal governing parameter for morphology control in printed active layers.By providing a fundamental framework for understanding viscosity-mediated phase separation,this work offers valuable insights for advancing high-throughput,environmentally friendly printing techniques for high-efficiency OSCs.
