The aim of this paper is to present a model for the rheological behavior of simple liquids as a f... more The aim of this paper is to present a model for the rheological behavior of simple liquids as a function of the amplitude of the imposed shear stress or strain. The elastic mode theory is first generalized to take into account the fact that, during a flow experiment, mechanical energy is injected in a system initially at thermodynamic equilibrium. This generalized theory can be seen as a particular aspect of the general problem of perturbation by the measurement, associated with that of the coupling between fluctuation and dissipation. This generalization leads to a “finitary” character of the model. It is then combined with the inertial mode theory. The formalism thus obtained allows us to model the rheological behavior of liquids over a wide range of velocity gradients, including the intermediate narrow range corresponding to the Newtonian regime. As experimental tests, viscosity measurements with two kinds of moving rotor rheometers were performed. Only data obtained with liquid ...
Electron mobility in superfluid helium is modeled between 0.1 and 2.2 K by a van der Waals-type t... more Electron mobility in superfluid helium is modeled between 0.1 and 2.2 K by a van der Waals-type thermodynamic equation of state, which relates the free volume of solvated electrons to temperature, density, and phase dependent internal pressure.
IEEE Transactions on Dielectrics and Electrical Insulation
We report the results of the experiment aimed at measuring the mobility of O − 2 ions in dense ar... more We report the results of the experiment aimed at measuring the mobility of O − 2 ions in dense argon gas in the temperature range 180 K ≤ T ≤ 300 K. We show that an adequate theoretical description of the data is obtained by using the thermodynamic Free Volume (FV) model, originally developed to describe the electron bubble mobility in superfluid helium and successfully exploited for describing the O − 2 mobility in near critical neon gas. The model goal is to thermodynamically predict the free space available for ion motion. By implementing the FV model with the Millikan-Cunningham (MC) slip correction factor, we can describe the ion mobility in the crossover region bridging the dilute gas kinetic regime to the high-density hydrodynamic regime of ion transport. These results confirm the validity of the model and the universality of some of its features.
A novel general modeling of the viscoelastic properties of fluids: Application to mechanical rela... more A novel general modeling of the viscoelastic properties of fluids: Application to mechanical relaxation and low frequency oscillation measurements of liquid water Physics of Fluids 34, 043109 (2022);
Today, a large number of industrial processes involve the liquid state, very often at high pressu... more Today, a large number of industrial processes involve the liquid state, very often at high pressures. Among these, we can mention: (a) chemical preparations at high pressures; (b) determination of the efficiency and response time of servomechanisms (e.g. hydraulic press); (c) flows in porous rocks; (d) water hammer in pipelines; (e) evolution of viscosity as a function of pressure in lubrication processes
All these processes require a precise knowledge of the equation of state of liquids and consequently an experimental determination of the pressure isotherms; these can be deduced from the variation of volume with pressure. But when one wants to study the compressibility of fluids, one generally comes up against two major problems: on the one hand, the realization and the implementation of a measuring cell that resists the pressure that one wishes to apply, and on the other hand, the measurement of the pressure that one applies. It is the history of this evolution that we are going to present, by reproducing as often as possible the writings of the scientists who participated in it.
We report new measurements of the mobility µ of O − 2 ions in supercritical neon in the range 45 ... more We report new measurements of the mobility µ of O − 2 ions in supercritical neon in the range 45 K ≤ T ≤ 334 K for number density N ≥ 0.5 nm −3. We rationalize the experimental data of all isotherms with the Stokes-Cunningham formula by computing the ion hydrodynamic radius as a function of T and N with the thermodynamic free volume model developed for the ion mobility in superfluid He. The model parameters are determined by re-analyzing published data for T = 45 K for N up to N ≈ 1.65N c (N c ≈ 14.4 nm −3 is the critical number density), which roughly span four orders of magnitude of the Knudsen number (0.1 ≤ K n ≤ 1000), covering the transition from the kinetic-to the hydrodynamic transport regime. These parameters provide an excellent description of the dependence of µ on N for all higher isotherms and yield a strict test of the model validity, thereby bridging the gap between the kinetic-and the hydrodynamic transport regimes.
Experimental data on the viscosity and self-diffusion coefficient of two metallic compounds in th... more Experimental data on the viscosity and self-diffusion coefficient of two metallic compounds in their fluid phases, that is, potassium and thallium, are modeled using the translational elastic mode theory, which has been successfully applied to the case of water. It is shown that this theory allows the experimental data to be accounted for in accordance with their uncertainties and, above all, it allows the different variations observed between the different authors to be explained. Particularly in the case of thallium, this theory makes it possible to represent viscosity data with much better precision than the so-called reference equation of state. The dilute-gas limit laws connecting various parameters of the theory obtained in the case of water are confirmed here and thus give them a universal character. The elastic mode theory is accompanied by the development of new equations of state, mainly to describe properties along the saturated vapor pressure curve, which greatly extend the temperature range of application of these equations compared to those found in the literature. The whole analysis thus makes it possible to propose precise values of various thermodynamic parameters at the melting and boiling temperature corresponding to atmospheric pressure.
Positively charged ions were produced in supercritical helium at temperatures from 6 to 10 K and ... more Positively charged ions were produced in supercritical helium at temperatures from 6 to 10 K and up to 2 MPa using a corona discharge. Their mobility was measured via currentvoltage curves and the hydrodynamic radius was derived using Stokes law. An initial increase and subsequent decrease of hydrodynamic radius was observed and interpreted in terms of growth, compression and solidification of ion clusters. The mobility was modelled using a van der Waals-type thermodynamic state equation for the ion-in-helium mixed system and a temperature-dependent Millikan-Cunningham factor, describing experimental data both in the Knudsen and the Stokes flow region. Regions of maximum hydrodynamic radius and large
Positively charged helium clusters, also called ‘snowballs’, have been investigated within normal... more Positively charged helium clusters, also called ‘snowballs’, have been investigated within normal liquid helium.
Electron mobilities in supercritical and liquid helium were investigated as a function of the den... more Electron mobilities in supercritical and liquid helium were investigated as a function of the density. The mobilities were derived from I(V) curves measured in a high-pressure cryogenic cell using a corona discharge in point-plane electrode geometry for charge generation. The presented data spans a wide pressure and temperature range due to the versatility of our experimental set-up. Where data from previous investigations is available for comparison, very good agreement is found. We present a semi-empirical model to calculate electron mobilities both in the liquid and supercritical phase. This model requires the electron-helium scattering length and thermodynamic state equations as the only input and circumvents any need to consider surface tension. Our semi-empirical model reproduces experimental data very well, in particular towards lower densities where transitions from localised to delocalised electron states were observed.
A new method for assessing the site-specific emission from electronically excited helium droplets... more A new method for assessing the site-specific emission from electronically excited helium droplets is presented. The fluorescence features of helium droplets show sharp rotationally resolved lines indicating desorption of excimers and emission far outside the droplets as well as blue-shifted and strongly broadened features due to emission of excimers confined in cavities within the droplets. A third feature is identified: slightly broadened rotational lines that we attribute to emission from excimers bound to the droplet surface. The line broadening arises from collisions with the helium gas within the surface layer of the helium droplets. These conditions are simulated using a high pressure gas cell in which helium gas is electronically excited using a corona discharge. Rotational line broadening of similar magnitude to that of large droplets (N ∼ 10 7 atoms) is observed for gas pressures at about 5 bar and 80 K, corresponding to a number density of 4.52 × 10 −4Å−3. We conclude that the excimers are located within a shell separated by 6 to 7Å from the radius where the density has dropped to 50% of its centre value. Helium droplets that are smaller (N ∼ 10 4 atoms) exhibit rotational lines that are less broadened, which we attribute to the superposition of features originating from desorbed and from surface-bound excimers. A fit of the linewidths reveals that around 50% of the excimers are bound to the surface of the smaller droplets.
The Orsay-Trento bosonic density functional theory model is extended to include dissipation due t... more The Orsay-Trento bosonic density functional theory model is extended to include dissipation due to the viscous response of superfluid (4)He present at finite temperatures. The viscous functional is derived from the Navier-Stokes equation by using the Madelung transformation and includes the contribution of interfacial viscous response present at the gas-liquid boundaries. This contribution was obtained by calibrating the model against the experimentally determined electron mobilities from 1.2 K to 2.1 K along the saturated vapor pressure line, where the viscous response is dominated by thermal rotons. The temperature dependence of ion mobility was calculated for several different solvation cavity sizes and the data are rationalized in the context of roton scattering and Stokes limited mobility models. Results are compared to the experimentally observed "exotic ion" data, which provides estimates for the corresponding bubble sizes in the liquid. Possible sources of such ion...
The journal of physical chemistry letters, Jan 17, 2016
Evidence for helium excimers (He2(*)) in the lowest allowed rotational quantum state in liquid he... more Evidence for helium excimers (He2(*)) in the lowest allowed rotational quantum state in liquid helium is presented. He2(*) was generated by a corona discharge in the gas and normal liquid phases. Fluorescence spectra recorded in the visible region between 3.8 and 5.0 K and 0.2 and 5.6 bar showed the rotationally resolved d(3)Σu(+) → b(3)Πg transition of He2(*). Analysis of the pressure and temperature dependence of lineshifts and line intensities showed features of solvated He2(*) superimposed on its gas-phase spectrum and, in the liquid phase only, pressure-induced rotational cooling. These findings suggest that He2(*) can be used to investigate bulk helium in different phases at the nanoscale.
IEEE Transactions on Dielectrics and Electrical Insulation, 2020
We report data of the O2− ion mobility in neon gas over broad density and temperature ranges alon... more We report data of the O2− ion mobility in neon gas over broad density and temperature ranges along with its theoretical description in terms of the thermodynamic, free volume model that has successfully been adopted for the interpretation of electron and ion mobility in superfluid and normal helium. The free volume model, which is aimed at computing the free volume accessible for the ion motion, along with the Millikan-Cunningham slip factor correction, is able to describe the ion mobility in the crossover region connecting the dilute gas regime described by the classical kinetic theory to the high density region ruled by the laws of hydrodynamic transport.
A new equation of state for argon has been developed in view to extend the range of validity of t... more A new equation of state for argon has been developed in view to extend the range of validity of the equation of state previously proposed by Tegeler et al. (1999) and to obtain a better physical description of the experimental thermodynamic data for the whole fluid region (single-phase and coexistence states). As proposed by Tegeler et al., this equation is also based on a functional form of the residual part of the reduced Helmholtz free energy. However in this work, the fundamental equation for the Helmholtz free energy has been derived from the measured quantities CV(rho,T) and P(rho,T). The empirical description of the isochoric heat capacity CV is based on an original empirical description containing explicitly the metastable states. The new formulation is valid for the whole fluid region from the melting line to 2300 K and for pressures up to 50 000 MPa. It also predicts existence of a maximum of the isochoric heat capacity CV along isochors as experimentally observed in sever...
New Molecular Dynamics simulations have been carried out in order to get an insight on the physic... more New Molecular Dynamics simulations have been carried out in order to get an insight on the physical mechanisms that determine the drift mobility of negative Oxygen ions in very dense Neon gas in the supercritical phase close to the critical point. Two ion-neutral interaction potentials have been used that differ by their repulsive part. We have observed that the potential with a harder repulsive part gives much better agreement with the experimental data. The differences with the softer repulsive potential previously used are discussed. We propose that the behavior of the ion mobility as a function of the gas density is related to the number of neutral atoms loosely bound in the first solvation shell around the ion.
2017 IEEE 19th International Conference on Dielectric Liquids (ICDL), Jun 1, 2017
We report here the results of Molecular Dynamics simulations of the drift mobility of negative ox... more We report here the results of Molecular Dynamics simulations of the drift mobility of negative oxygen ions in very dense neon gas in the supercritical phase. The simulations relatively well reproduce the trend of the experimental data. The rationalization of the mobility behavior as a function of the gas density is given in terms of the number of atoms correlated in the first solvation shell around the ion.
The aim of this paper is to present a model for the rheological behavior of simple liquids as a f... more The aim of this paper is to present a model for the rheological behavior of simple liquids as a function of the amplitude of the imposed shear stress or strain. The elastic mode theory is first generalized to take into account the fact that, during a flow experiment, mechanical energy is injected in a system initially at thermodynamic equilibrium. This generalized theory can be seen as a particular aspect of the general problem of perturbation by the measurement, associated with that of the coupling between fluctuation and dissipation. This generalization leads to a “finitary” character of the model. It is then combined with the inertial mode theory. The formalism thus obtained allows us to model the rheological behavior of liquids over a wide range of velocity gradients, including the intermediate narrow range corresponding to the Newtonian regime. As experimental tests, viscosity measurements with two kinds of moving rotor rheometers were performed. Only data obtained with liquid ...
Electron mobility in superfluid helium is modeled between 0.1 and 2.2 K by a van der Waals-type t... more Electron mobility in superfluid helium is modeled between 0.1 and 2.2 K by a van der Waals-type thermodynamic equation of state, which relates the free volume of solvated electrons to temperature, density, and phase dependent internal pressure.
IEEE Transactions on Dielectrics and Electrical Insulation
We report the results of the experiment aimed at measuring the mobility of O − 2 ions in dense ar... more We report the results of the experiment aimed at measuring the mobility of O − 2 ions in dense argon gas in the temperature range 180 K ≤ T ≤ 300 K. We show that an adequate theoretical description of the data is obtained by using the thermodynamic Free Volume (FV) model, originally developed to describe the electron bubble mobility in superfluid helium and successfully exploited for describing the O − 2 mobility in near critical neon gas. The model goal is to thermodynamically predict the free space available for ion motion. By implementing the FV model with the Millikan-Cunningham (MC) slip correction factor, we can describe the ion mobility in the crossover region bridging the dilute gas kinetic regime to the high-density hydrodynamic regime of ion transport. These results confirm the validity of the model and the universality of some of its features.
A novel general modeling of the viscoelastic properties of fluids: Application to mechanical rela... more A novel general modeling of the viscoelastic properties of fluids: Application to mechanical relaxation and low frequency oscillation measurements of liquid water Physics of Fluids 34, 043109 (2022);
Today, a large number of industrial processes involve the liquid state, very often at high pressu... more Today, a large number of industrial processes involve the liquid state, very often at high pressures. Among these, we can mention: (a) chemical preparations at high pressures; (b) determination of the efficiency and response time of servomechanisms (e.g. hydraulic press); (c) flows in porous rocks; (d) water hammer in pipelines; (e) evolution of viscosity as a function of pressure in lubrication processes
All these processes require a precise knowledge of the equation of state of liquids and consequently an experimental determination of the pressure isotherms; these can be deduced from the variation of volume with pressure. But when one wants to study the compressibility of fluids, one generally comes up against two major problems: on the one hand, the realization and the implementation of a measuring cell that resists the pressure that one wishes to apply, and on the other hand, the measurement of the pressure that one applies. It is the history of this evolution that we are going to present, by reproducing as often as possible the writings of the scientists who participated in it.
We report new measurements of the mobility µ of O − 2 ions in supercritical neon in the range 45 ... more We report new measurements of the mobility µ of O − 2 ions in supercritical neon in the range 45 K ≤ T ≤ 334 K for number density N ≥ 0.5 nm −3. We rationalize the experimental data of all isotherms with the Stokes-Cunningham formula by computing the ion hydrodynamic radius as a function of T and N with the thermodynamic free volume model developed for the ion mobility in superfluid He. The model parameters are determined by re-analyzing published data for T = 45 K for N up to N ≈ 1.65N c (N c ≈ 14.4 nm −3 is the critical number density), which roughly span four orders of magnitude of the Knudsen number (0.1 ≤ K n ≤ 1000), covering the transition from the kinetic-to the hydrodynamic transport regime. These parameters provide an excellent description of the dependence of µ on N for all higher isotherms and yield a strict test of the model validity, thereby bridging the gap between the kinetic-and the hydrodynamic transport regimes.
Experimental data on the viscosity and self-diffusion coefficient of two metallic compounds in th... more Experimental data on the viscosity and self-diffusion coefficient of two metallic compounds in their fluid phases, that is, potassium and thallium, are modeled using the translational elastic mode theory, which has been successfully applied to the case of water. It is shown that this theory allows the experimental data to be accounted for in accordance with their uncertainties and, above all, it allows the different variations observed between the different authors to be explained. Particularly in the case of thallium, this theory makes it possible to represent viscosity data with much better precision than the so-called reference equation of state. The dilute-gas limit laws connecting various parameters of the theory obtained in the case of water are confirmed here and thus give them a universal character. The elastic mode theory is accompanied by the development of new equations of state, mainly to describe properties along the saturated vapor pressure curve, which greatly extend the temperature range of application of these equations compared to those found in the literature. The whole analysis thus makes it possible to propose precise values of various thermodynamic parameters at the melting and boiling temperature corresponding to atmospheric pressure.
Positively charged ions were produced in supercritical helium at temperatures from 6 to 10 K and ... more Positively charged ions were produced in supercritical helium at temperatures from 6 to 10 K and up to 2 MPa using a corona discharge. Their mobility was measured via currentvoltage curves and the hydrodynamic radius was derived using Stokes law. An initial increase and subsequent decrease of hydrodynamic radius was observed and interpreted in terms of growth, compression and solidification of ion clusters. The mobility was modelled using a van der Waals-type thermodynamic state equation for the ion-in-helium mixed system and a temperature-dependent Millikan-Cunningham factor, describing experimental data both in the Knudsen and the Stokes flow region. Regions of maximum hydrodynamic radius and large
Positively charged helium clusters, also called ‘snowballs’, have been investigated within normal... more Positively charged helium clusters, also called ‘snowballs’, have been investigated within normal liquid helium.
Electron mobilities in supercritical and liquid helium were investigated as a function of the den... more Electron mobilities in supercritical and liquid helium were investigated as a function of the density. The mobilities were derived from I(V) curves measured in a high-pressure cryogenic cell using a corona discharge in point-plane electrode geometry for charge generation. The presented data spans a wide pressure and temperature range due to the versatility of our experimental set-up. Where data from previous investigations is available for comparison, very good agreement is found. We present a semi-empirical model to calculate electron mobilities both in the liquid and supercritical phase. This model requires the electron-helium scattering length and thermodynamic state equations as the only input and circumvents any need to consider surface tension. Our semi-empirical model reproduces experimental data very well, in particular towards lower densities where transitions from localised to delocalised electron states were observed.
A new method for assessing the site-specific emission from electronically excited helium droplets... more A new method for assessing the site-specific emission from electronically excited helium droplets is presented. The fluorescence features of helium droplets show sharp rotationally resolved lines indicating desorption of excimers and emission far outside the droplets as well as blue-shifted and strongly broadened features due to emission of excimers confined in cavities within the droplets. A third feature is identified: slightly broadened rotational lines that we attribute to emission from excimers bound to the droplet surface. The line broadening arises from collisions with the helium gas within the surface layer of the helium droplets. These conditions are simulated using a high pressure gas cell in which helium gas is electronically excited using a corona discharge. Rotational line broadening of similar magnitude to that of large droplets (N ∼ 10 7 atoms) is observed for gas pressures at about 5 bar and 80 K, corresponding to a number density of 4.52 × 10 −4Å−3. We conclude that the excimers are located within a shell separated by 6 to 7Å from the radius where the density has dropped to 50% of its centre value. Helium droplets that are smaller (N ∼ 10 4 atoms) exhibit rotational lines that are less broadened, which we attribute to the superposition of features originating from desorbed and from surface-bound excimers. A fit of the linewidths reveals that around 50% of the excimers are bound to the surface of the smaller droplets.
The Orsay-Trento bosonic density functional theory model is extended to include dissipation due t... more The Orsay-Trento bosonic density functional theory model is extended to include dissipation due to the viscous response of superfluid (4)He present at finite temperatures. The viscous functional is derived from the Navier-Stokes equation by using the Madelung transformation and includes the contribution of interfacial viscous response present at the gas-liquid boundaries. This contribution was obtained by calibrating the model against the experimentally determined electron mobilities from 1.2 K to 2.1 K along the saturated vapor pressure line, where the viscous response is dominated by thermal rotons. The temperature dependence of ion mobility was calculated for several different solvation cavity sizes and the data are rationalized in the context of roton scattering and Stokes limited mobility models. Results are compared to the experimentally observed "exotic ion" data, which provides estimates for the corresponding bubble sizes in the liquid. Possible sources of such ion...
The journal of physical chemistry letters, Jan 17, 2016
Evidence for helium excimers (He2(*)) in the lowest allowed rotational quantum state in liquid he... more Evidence for helium excimers (He2(*)) in the lowest allowed rotational quantum state in liquid helium is presented. He2(*) was generated by a corona discharge in the gas and normal liquid phases. Fluorescence spectra recorded in the visible region between 3.8 and 5.0 K and 0.2 and 5.6 bar showed the rotationally resolved d(3)Σu(+) → b(3)Πg transition of He2(*). Analysis of the pressure and temperature dependence of lineshifts and line intensities showed features of solvated He2(*) superimposed on its gas-phase spectrum and, in the liquid phase only, pressure-induced rotational cooling. These findings suggest that He2(*) can be used to investigate bulk helium in different phases at the nanoscale.
IEEE Transactions on Dielectrics and Electrical Insulation, 2020
We report data of the O2− ion mobility in neon gas over broad density and temperature ranges alon... more We report data of the O2− ion mobility in neon gas over broad density and temperature ranges along with its theoretical description in terms of the thermodynamic, free volume model that has successfully been adopted for the interpretation of electron and ion mobility in superfluid and normal helium. The free volume model, which is aimed at computing the free volume accessible for the ion motion, along with the Millikan-Cunningham slip factor correction, is able to describe the ion mobility in the crossover region connecting the dilute gas regime described by the classical kinetic theory to the high density region ruled by the laws of hydrodynamic transport.
A new equation of state for argon has been developed in view to extend the range of validity of t... more A new equation of state for argon has been developed in view to extend the range of validity of the equation of state previously proposed by Tegeler et al. (1999) and to obtain a better physical description of the experimental thermodynamic data for the whole fluid region (single-phase and coexistence states). As proposed by Tegeler et al., this equation is also based on a functional form of the residual part of the reduced Helmholtz free energy. However in this work, the fundamental equation for the Helmholtz free energy has been derived from the measured quantities CV(rho,T) and P(rho,T). The empirical description of the isochoric heat capacity CV is based on an original empirical description containing explicitly the metastable states. The new formulation is valid for the whole fluid region from the melting line to 2300 K and for pressures up to 50 000 MPa. It also predicts existence of a maximum of the isochoric heat capacity CV along isochors as experimentally observed in sever...
New Molecular Dynamics simulations have been carried out in order to get an insight on the physic... more New Molecular Dynamics simulations have been carried out in order to get an insight on the physical mechanisms that determine the drift mobility of negative Oxygen ions in very dense Neon gas in the supercritical phase close to the critical point. Two ion-neutral interaction potentials have been used that differ by their repulsive part. We have observed that the potential with a harder repulsive part gives much better agreement with the experimental data. The differences with the softer repulsive potential previously used are discussed. We propose that the behavior of the ion mobility as a function of the gas density is related to the number of neutral atoms loosely bound in the first solvation shell around the ion.
2017 IEEE 19th International Conference on Dielectric Liquids (ICDL), Jun 1, 2017
We report here the results of Molecular Dynamics simulations of the drift mobility of negative ox... more We report here the results of Molecular Dynamics simulations of the drift mobility of negative oxygen ions in very dense neon gas in the supercritical phase. The simulations relatively well reproduce the trend of the experimental data. The rationalization of the mobility behavior as a function of the gas density is given in terms of the number of atoms correlated in the first solvation shell around the ion.
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Papers by F Aitken
All these processes require a precise knowledge of the equation of state of liquids and consequently an experimental determination of the pressure isotherms; these can be deduced from the variation of volume with pressure. But when one wants to study the compressibility of fluids, one generally comes up against two major problems: on the one hand, the realization and the implementation of a measuring cell that resists the pressure that one wishes to apply, and on the other hand, the measurement of the pressure that one applies. It is the history of this evolution that we are going to present, by reproducing as often as possible the writings of the scientists who participated in it.
All these processes require a precise knowledge of the equation of state of liquids and consequently an experimental determination of the pressure isotherms; these can be deduced from the variation of volume with pressure. But when one wants to study the compressibility of fluids, one generally comes up against two major problems: on the one hand, the realization and the implementation of a measuring cell that resists the pressure that one wishes to apply, and on the other hand, the measurement of the pressure that one applies. It is the history of this evolution that we are going to present, by reproducing as often as possible the writings of the scientists who participated in it.