The Henry’s law constant of volatiles in polymer systems is a crucial parameter reflecting the gas-liquid equilibrium,which is very important for devolatilization.In this research,polyolefin elastomer(POE)-cyclohexan...The Henry’s law constant of volatiles in polymer systems is a crucial parameter reflecting the gas-liquid equilibrium,which is very important for devolatilization.In this research,polyolefin elastomer(POE)-cyclohexane and polydimethylsiloxane(PDMS)-hexane systems were studied,and the Henry’s law constant was obtained by measuring the gas phase equilibrium partial pressure when polymer solutions containing different mass fractions of volatiles reached a saturated state.The effects of temperature,type of volatiles,and polymer viscosity on the gas phase equilibrium partial pressure and Henry’s law constant of the volatiles were investigated.The results indicate that,with the increase of temperature and polymer viscosity,the gas phase equilibrium partial pressure and Henry’s law constant of volatiles increase.As temperature increases,the solubility of gas in liquid decreases.The relationship between the Henry’s law constant and temperature is consistent with the Arrhenius law.In the PDMS-hexane system,the gas phase equilibrium partial pressure and Henry’s law constant of n-hexane are higher than those of cyclohexane.The obtained Henry’s law constants can be used as a reference for perfecting the devolatilization process and improving the devolatilization effect.展开更多
Laboratory experiments and field observations show that the equilibrium range of wind wave spectra presents a – 4 power law when it is scaled properly. This feature has been attributed to energy balance in spectral s...Laboratory experiments and field observations show that the equilibrium range of wind wave spectra presents a – 4 power law when it is scaled properly. This feature has been attributed to energy balance in spectral space by many researchers. In this paper we point out that white noise on an oscillation system can also lead to a similar inverse power law in the corresponding displacement spectrum, implying that the – 4 power law for the equilibrium range of wind wave spectra may probably only reflect the randomicity of the wind waves rather than any other dynamical processes in physical space. This explanation may shed light on the mechanism of other physical processes with spectra also showing an inverse power law, such as isotropic turbulence, internal waves, etc.展开更多
Considering Brinkman⁃Forchheimer extended Darcy flow and local thermal non⁃equilibrium effect,a general model of forced convection with viscous dissipation in power⁃law fluid saturated porous media channel was establi...Considering Brinkman⁃Forchheimer extended Darcy flow and local thermal non⁃equilibrium effect,a general model of forced convection with viscous dissipation in power⁃law fluid saturated porous media channel was established.The dimensionless temperature profiles and Nusselt number were numerically solved using the classical fourth⁃order Runge Kutta method under a constant heat flux boundary condition.The conclusion showed that the fluid⁃solid temperature distributions were significantly affected by dimensionless Bi,k,Da,Br,and F,and the effects of power⁃law indexes on convection heat transfer characteristics were also non⁃negligible.展开更多
Based on the basis of the two stage dynamic game of complete information and purely tactful perfect equilibrium theory, the non cooperative gaming between the police department and the criminals is analyzed. Dyn...Based on the basis of the two stage dynamic game of complete information and purely tactful perfect equilibrium theory, the non cooperative gaming between the police department and the criminals is analyzed. Dynamic game can be proved to forecast and explain potential tactful choices of the police department and the criminals at various stages, so as to analyze the essence of the law enforcement by the theoretical models.展开更多
This contribution presents an outline of a new mathematical formulation for Classical Non-Equilibrium Thermodynamics (CNET) based on a contact structure in differential geometry. First a non-equilibrium state space is...This contribution presents an outline of a new mathematical formulation for Classical Non-Equilibrium Thermodynamics (CNET) based on a contact structure in differential geometry. First a non-equilibrium state space is introduced as the third key element besides the first and second law of thermodynamics. This state space provides the mathematical structure to generalize the Gibbs fundamental relation to non-equilibrium thermodynamics. A unique formulation for the second law of thermodynamics is postulated and it showed how the complying concept for non-equilibrium entropy is retrieved. The foundation of this formulation is a physical quantity, which is in non-equilibrium thermodynamics nowhere equal to zero. This is another perspective compared to the inequality, which is used in most other formulations in the literature. Based on this mathematical framework, it is proven that the thermodynamic potential is defined by the Gibbs free energy. The set of conjugated coordinates in the mathematical structure for the Gibbs fundamental relation will be identified for single component, closed systems. Only in the final section of this contribution will the equilibrium constraint be introduced and applied to obtain some familiar formulations for classical (equilibrium) thermodynamics.展开更多
Humans spend 64% - 94% of their time indoors;therefore, indoor air quality is very important for potential exposure to volatile organic compounds (VOC). The source of VOC in the subsurface may come from accidental or ...Humans spend 64% - 94% of their time indoors;therefore, indoor air quality is very important for potential exposure to volatile organic compounds (VOC). The source of VOC in the subsurface may come from accidental or intentional releases, leaking landfills or leaking underground and above-ground storage tanks. Once these contaminants are present near or beneath buildings, they may move as a vapour through soil gas and enter the building. A large number of vapour intrusion (VI) algorithms have been published in peer-reviewed publications that link indoor VOC concentrations to the contamination of soils. These models typically include phase partitioning calculations of VOC based on Henry’s law to estimate the concentration of a particular contaminant in soil gas. This paper presents the results from a series of laboratory experiments concerning the use of the Henry’s Law constant for the calculation of toluene concentrations in equilibrium between ground water and soil air. A series of column experiments were conducted with various toluene concentrations in artificial (ground) water to contrast the predicted and observed (soil) air concentrations. The experiments which exclude soil material show a toluene fugacity behaviour roughly in line with Henry’s law whereas the experiments which include soil material result in equilibrium soil concentrations which were around one order-of-magnitude lower than was expected from a Henry Law-based estimation. It is concluded that for toluene inclusion of Henry’s Law in VI algorithms does not provide an adequate description of volatilisation in soils and may lead to an overestimation of health risk. Instead, a model based on a simple description of the relevant intermolecular interactions could be explored.展开更多
The paper deals with the existence of equilibrium points in the restricted three-body problem when the smaller primary is an oblate spheroid and the infinitesimal body is of variable mass. Following the method of smal...The paper deals with the existence of equilibrium points in the restricted three-body problem when the smaller primary is an oblate spheroid and the infinitesimal body is of variable mass. Following the method of small parameters;the co-ordinates of collinear equilibrium points have been calculated, whereas the co-ordinates of triangular equilibrium points are established by classical method. On studying the surface of zero-velocity curves, it is found that the mass reduction factor has very minor effect on the location of the equilibrium points;whereas the oblateness parameter of the smaller primary has a significant role on the existence of equilibrium points.展开更多
In a recent publication the author derived and experimentally tested several theoretical models, distinguished by different boundary conditions at the contacts with horizontal and vertical supports, that predicted the...In a recent publication the author derived and experimentally tested several theoretical models, distinguished by different boundary conditions at the contacts with horizontal and vertical supports, that predicted the forces of reaction on a fixed (i.e. inextensible) ladder. This problem is statically indeterminate since there are 4 forces of reaction and only 3 equations of static equilibrium. The model that predicted the empirical reactions correctly used a law of static friction to complement the equations of static equilibrium. The present paper examines in greater theoretical and experimental detail the role of friction in accounting for the forces of reaction on a fixed ladder. The reported measurements confirm that forces parallel and normal to the support at the top of the ladder are linearly proportional with a constant coefficient of friction irrespective of the magnitude or location of the load, as assumed in the theoretical model. However, measurements of forces parallel and normal to the support at the base of the ladder are linearly proportional with coefficients that depend sensitively on the location (although not the magnitude) of the load. This paper accounts quantitatively for the different effects of friction at the top and base of the ladder under conditions of usual use whereby friction at the vertical support alone is insufficient to keep the ladder from sliding. A theoretical model is also proposed for the unusual circumstance in which friction at the vertical support can keep the ladder from sliding.展开更多
The literature reports that equality of temperature, equality of potential and equality of pressure between a system and a reservoir are necessary conditions for the stable equilibrium of the system-reservoir composit...The literature reports that equality of temperature, equality of potential and equality of pressure between a system and a reservoir are necessary conditions for the stable equilibrium of the system-reservoir composite or, in the opposite and equivalent logical inference, that stable equilibrium is a sufficient condition for equality. The aim and the first novelty of the present study is to prove that equality of temperature, potential and pressure is also a sufficient condition for stable equilibrium, in addition to necessity, implying that stable equilibrium is a condition also necessary, in addition to sufficiency, for equality. The second novelty is that the proof of the sufficiency of equality (or the necessity of stable equilibrium) is attained by means of the generalization of the entropy property, derived from the generalization of exergy property, which is used to demonstrate that stable equilibrium is a logical consequence of equality of generalized potential. This proof is underpinned by the Second Law statement and the Maximum-Entropy Principle based on generalized entropy which depends on temperature, potential and pressure of the reservoir. The conclusion, based on these two novel concepts, consists of the theorem of necessity and sufficiency of stable equilibrium for equality of generalized potentials within a composite constituted by a system and a reservoir.展开更多
Among all statements of Second Law, the existence and uniqueness of stable equilibrium, for each given value of energy content and composition of constituents of any system, have been adopted to define thermodynamic e...Among all statements of Second Law, the existence and uniqueness of stable equilibrium, for each given value of energy content and composition of constituents of any system, have been adopted to define thermodynamic entropy by means of the impossibility of Perpetual Motion Machine of the Second Kind (PMM2) which is a consequence of the Second Law. Equality of temperature, chemical potential and pressure in many-particle systems are proved to be necessary conditions for the stable equilibrium. The proofs assume the stable equilibrium and derive, by means of the Highest-Entropy Principle, equality of temperature, chemical potential and pressure as a consequence. A first novelty of the present research is to demonstrate that equality is also a sufficient condition, in addition to necessity, for stable equilibrium implying that stable equilibrium is a condition also necessary, in addition to sufficiency, for equality of temperature potential and pressure addressed to as generalized potential. The second novelty is that the proof of sufficiency of equality, or necessity of stable equilibrium, is achieved by means of a generalization of entropy property, derived from a generalized definition of exergy, both being state and additive properties accounting for heat, mass and work interactions of the system underpinning the definition of Highest-Generalized-Entropy Principle adopted in the proof.展开更多
基金Polyolefin Elastomer Technology Development project(2020B-2619).
文摘The Henry’s law constant of volatiles in polymer systems is a crucial parameter reflecting the gas-liquid equilibrium,which is very important for devolatilization.In this research,polyolefin elastomer(POE)-cyclohexane and polydimethylsiloxane(PDMS)-hexane systems were studied,and the Henry’s law constant was obtained by measuring the gas phase equilibrium partial pressure when polymer solutions containing different mass fractions of volatiles reached a saturated state.The effects of temperature,type of volatiles,and polymer viscosity on the gas phase equilibrium partial pressure and Henry’s law constant of the volatiles were investigated.The results indicate that,with the increase of temperature and polymer viscosity,the gas phase equilibrium partial pressure and Henry’s law constant of volatiles increase.As temperature increases,the solubility of gas in liquid decreases.The relationship between the Henry’s law constant and temperature is consistent with the Arrhenius law.In the PDMS-hexane system,the gas phase equilibrium partial pressure and Henry’s law constant of n-hexane are higher than those of cyclohexane.The obtained Henry’s law constants can be used as a reference for perfecting the devolatilization process and improving the devolatilization effect.
基金This study was financially supported by the National Natural Science Foundation of China （Grant No. 40406008）the Foundation for 0pen Projects of the Key Lab of Physical 0ceanography, the Ministry of Education, China （Grant No. 200309）.
文摘Laboratory experiments and field observations show that the equilibrium range of wind wave spectra presents a – 4 power law when it is scaled properly. This feature has been attributed to energy balance in spectral space by many researchers. In this paper we point out that white noise on an oscillation system can also lead to a similar inverse power law in the corresponding displacement spectrum, implying that the – 4 power law for the equilibrium range of wind wave spectra may probably only reflect the randomicity of the wind waves rather than any other dynamical processes in physical space. This explanation may shed light on the mechanism of other physical processes with spectra also showing an inverse power law, such as isotropic turbulence, internal waves, etc.
基金Sponsored by the Liaoning Provincial Doctoral Initiation Fund Project(Grant No.2019-BS-030).
文摘Considering Brinkman⁃Forchheimer extended Darcy flow and local thermal non⁃equilibrium effect,a general model of forced convection with viscous dissipation in power⁃law fluid saturated porous media channel was established.The dimensionless temperature profiles and Nusselt number were numerically solved using the classical fourth⁃order Runge Kutta method under a constant heat flux boundary condition.The conclusion showed that the fluid⁃solid temperature distributions were significantly affected by dimensionless Bi,k,Da,Br,and F,and the effects of power⁃law indexes on convection heat transfer characteristics were also non⁃negligible.
文摘Based on the basis of the two stage dynamic game of complete information and purely tactful perfect equilibrium theory, the non cooperative gaming between the police department and the criminals is analyzed. Dynamic game can be proved to forecast and explain potential tactful choices of the police department and the criminals at various stages, so as to analyze the essence of the law enforcement by the theoretical models.
文摘This contribution presents an outline of a new mathematical formulation for Classical Non-Equilibrium Thermodynamics (CNET) based on a contact structure in differential geometry. First a non-equilibrium state space is introduced as the third key element besides the first and second law of thermodynamics. This state space provides the mathematical structure to generalize the Gibbs fundamental relation to non-equilibrium thermodynamics. A unique formulation for the second law of thermodynamics is postulated and it showed how the complying concept for non-equilibrium entropy is retrieved. The foundation of this formulation is a physical quantity, which is in non-equilibrium thermodynamics nowhere equal to zero. This is another perspective compared to the inequality, which is used in most other formulations in the literature. Based on this mathematical framework, it is proven that the thermodynamic potential is defined by the Gibbs free energy. The set of conjugated coordinates in the mathematical structure for the Gibbs fundamental relation will be identified for single component, closed systems. Only in the final section of this contribution will the equilibrium constraint be introduced and applied to obtain some familiar formulations for classical (equilibrium) thermodynamics.
文摘Humans spend 64% - 94% of their time indoors;therefore, indoor air quality is very important for potential exposure to volatile organic compounds (VOC). The source of VOC in the subsurface may come from accidental or intentional releases, leaking landfills or leaking underground and above-ground storage tanks. Once these contaminants are present near or beneath buildings, they may move as a vapour through soil gas and enter the building. A large number of vapour intrusion (VI) algorithms have been published in peer-reviewed publications that link indoor VOC concentrations to the contamination of soils. These models typically include phase partitioning calculations of VOC based on Henry’s law to estimate the concentration of a particular contaminant in soil gas. This paper presents the results from a series of laboratory experiments concerning the use of the Henry’s Law constant for the calculation of toluene concentrations in equilibrium between ground water and soil air. A series of column experiments were conducted with various toluene concentrations in artificial (ground) water to contrast the predicted and observed (soil) air concentrations. The experiments which exclude soil material show a toluene fugacity behaviour roughly in line with Henry’s law whereas the experiments which include soil material result in equilibrium soil concentrations which were around one order-of-magnitude lower than was expected from a Henry Law-based estimation. It is concluded that for toluene inclusion of Henry’s Law in VI algorithms does not provide an adequate description of volatilisation in soils and may lead to an overestimation of health risk. Instead, a model based on a simple description of the relevant intermolecular interactions could be explored.
文摘The paper deals with the existence of equilibrium points in the restricted three-body problem when the smaller primary is an oblate spheroid and the infinitesimal body is of variable mass. Following the method of small parameters;the co-ordinates of collinear equilibrium points have been calculated, whereas the co-ordinates of triangular equilibrium points are established by classical method. On studying the surface of zero-velocity curves, it is found that the mass reduction factor has very minor effect on the location of the equilibrium points;whereas the oblateness parameter of the smaller primary has a significant role on the existence of equilibrium points.
文摘In a recent publication the author derived and experimentally tested several theoretical models, distinguished by different boundary conditions at the contacts with horizontal and vertical supports, that predicted the forces of reaction on a fixed (i.e. inextensible) ladder. This problem is statically indeterminate since there are 4 forces of reaction and only 3 equations of static equilibrium. The model that predicted the empirical reactions correctly used a law of static friction to complement the equations of static equilibrium. The present paper examines in greater theoretical and experimental detail the role of friction in accounting for the forces of reaction on a fixed ladder. The reported measurements confirm that forces parallel and normal to the support at the top of the ladder are linearly proportional with a constant coefficient of friction irrespective of the magnitude or location of the load, as assumed in the theoretical model. However, measurements of forces parallel and normal to the support at the base of the ladder are linearly proportional with coefficients that depend sensitively on the location (although not the magnitude) of the load. This paper accounts quantitatively for the different effects of friction at the top and base of the ladder under conditions of usual use whereby friction at the vertical support alone is insufficient to keep the ladder from sliding. A theoretical model is also proposed for the unusual circumstance in which friction at the vertical support can keep the ladder from sliding.
文摘The literature reports that equality of temperature, equality of potential and equality of pressure between a system and a reservoir are necessary conditions for the stable equilibrium of the system-reservoir composite or, in the opposite and equivalent logical inference, that stable equilibrium is a sufficient condition for equality. The aim and the first novelty of the present study is to prove that equality of temperature, potential and pressure is also a sufficient condition for stable equilibrium, in addition to necessity, implying that stable equilibrium is a condition also necessary, in addition to sufficiency, for equality. The second novelty is that the proof of the sufficiency of equality (or the necessity of stable equilibrium) is attained by means of the generalization of the entropy property, derived from the generalization of exergy property, which is used to demonstrate that stable equilibrium is a logical consequence of equality of generalized potential. This proof is underpinned by the Second Law statement and the Maximum-Entropy Principle based on generalized entropy which depends on temperature, potential and pressure of the reservoir. The conclusion, based on these two novel concepts, consists of the theorem of necessity and sufficiency of stable equilibrium for equality of generalized potentials within a composite constituted by a system and a reservoir.
文摘Among all statements of Second Law, the existence and uniqueness of stable equilibrium, for each given value of energy content and composition of constituents of any system, have been adopted to define thermodynamic entropy by means of the impossibility of Perpetual Motion Machine of the Second Kind (PMM2) which is a consequence of the Second Law. Equality of temperature, chemical potential and pressure in many-particle systems are proved to be necessary conditions for the stable equilibrium. The proofs assume the stable equilibrium and derive, by means of the Highest-Entropy Principle, equality of temperature, chemical potential and pressure as a consequence. A first novelty of the present research is to demonstrate that equality is also a sufficient condition, in addition to necessity, for stable equilibrium implying that stable equilibrium is a condition also necessary, in addition to sufficiency, for equality of temperature potential and pressure addressed to as generalized potential. The second novelty is that the proof of sufficiency of equality, or necessity of stable equilibrium, is achieved by means of a generalization of entropy property, derived from a generalized definition of exergy, both being state and additive properties accounting for heat, mass and work interactions of the system underpinning the definition of Highest-Generalized-Entropy Principle adopted in the proof.
