The effect of alcohols as the third component on diffusion in mixtures of aromatics and ketones

With laboratory and numerical work, we demonstrate that one of the main diffusion coefficients and the smaller eigenvalue of the Fick diffusion matrix are invariant to the number of methylene groups of the alcohol in ternary mixtures composed of an aromatic (benzene), a ketone (acetone) and one of three different alcohols (methanol, ethanol or 2-propanol). A critical analysis of the relationship between the kinetic and thermodynamic contributions to the diffusion coefficients allows us to explain this intriguing behaviour of this class of mixture. These findings are reflected by the diffusive behaviour of the according binary subsystems. Our approach provides a promising systematic framework for future investigations into the important and challenging problem of transport diffusion in multicomponent liquids.

The Fick diffusion coefficient matrix of three ternary mixtures composed of an aromatic (benzene), a ketone (acetone) and one of three different alcohols (methanol, ethanol or 2-propanol) is investigated with laboratory and numerical work.

Multicomponent diffusion plays a crucial role in various natural and industrial processes involving mass transfer.^1–3 Liquids appearing in nature and technical applications are essentially multicomponent. However, only data on binary diffusion coefficients are relatively abundant because the diffusion behavior of ternary and higher mixtures is much more complex.^4,5 Describing the isothermal–isobaric diffusion of a ternary mixture by Fick’s law requires four different diffusion coefficients that are composition dependent. The presence of cross diffusion coefficients aggravates the interpretation and data processing in experimental work, resulting in large uncertainties.^6,7 Thus, efforts are being made to develop new methods for analysis of multicomponent diffusion explicitly addressing various degrees of complexity.^8–10 Predictive equations for multicomponent diffusion of liquids mostly rely on extensions of the Darken relation,^11–13 which is only valid for ideal mixtures.¹⁴ The underlying physical phenomena in non-ideal mixtures are not well understood and the lack of experimental data impedes the development and verification of new predictive equations.The objective of this study was not only to measure and predict the Fick diffusion coefficient matrix for a series of ternary liquid mixtures, rather, the emphasis lied on understanding common features and whether they can be related to the behavior of the pure components and binary subsystems. Three ternary mixtures that are composed of organic compounds were selected, i.e. an aromatic, a ketone and an alcohol. Throughout, the first two components were benzene (1) and acetone (2) and the third component was one of the alcohols, methanol, ethanol or 2-propanol. For each mixture, nine state points along a composition path with a constant content of benzene, x₁ = 0.33 mol mol⁻¹, were studied under ambient conditions (298.15 K and 0.1 MPa). Seven of the state points were ternary mixtures and two were binary subsystems. To obtain reliable results for the Fick diffusion coefficient matrix, two complementary approaches were used, i.e. experiments and predictive molecular simulations. This combination allows for a critical analysis and leads to a deeper understanding of the underlying phenomena.^14,15The Taylor dispersion technique was utilized for the experiments.^16,17 In this method, a small quantity of mixture with a slightly different composition is injected into a laminar stream. It disperses due to convection and diffusion while flowing through a capillary tube and the refractive index is measured at its end to sample the concentration distribution. We have used the same apparatus as in previous works.^6,7 The Fick diffusion matrix is obtained by fitting working equations to the measured signal, i.e. the Taylor peak. The mathematical model of the Taylor dispersion technique was originally developed on the basis of Fick’s law in the volume reference frame. In a ternary mixture, two molar fluxes J^v_i relative to a volume averaged velocity are related to gradients of molar concentration ∇C_i with four diffusion coefficients D^v_ij. Alternatively, fluxes expressed in the molar reference frame J_i are relative to a molar averaged velocity and the mole fraction gradients ∇x_i act as a driving force1with molar density ρ. The fluxes of all three components are constrained by ΣJ_i = 0. The main diffusion coefficients D₁₁ and D₂₂ relate the flux of one component to its own mole fraction gradient and the cross diffusion coefficients D₁₂ and D₂₁ describe the coupling of the flux of one component with the gradient of the other. The third component does not appear in eqn (1) explicitly, but in general it affects all four diffusion coefficients. The transformation of experimental data from the volume to the molar reference frame (D^v_ij to D_ij) could be done here on the basis of the pure component volumes (see the ESI^†).Equilibrium molecular dynamics (MD) simulations were employed in this work, allowing for examination at the microscopic scale. The underlying molecular models were rigid, non-polarizable force fields of united atom type, consisting of a varying number of Lennard–Jones, point charge, dipole and quadrupole sites (see the ESI^†). Note that the force field parameters were adjusted to pure fluid properties only so that all simulation results for the mixtures are strictly predictive. Diffusion coefficients were sampled with the Green–Kubo formalism, based on integrated correlation functions of net velocities of the contained species.^11,15 Thereby, phenomenological coefficients Δ_ij were obtained, associating the diffusive fluxes with the chemical potential gradients ∇μ_i2with gas constant R and temperature T. Fluxes J_i correspond to the molar reference frame as in eqn (1).The diffusion coefficients from experiment and simulation are related to different driving forces so that the chemical potential gradients have to be transformed to the mole fraction gradients for their comparison.¹⁸ This transformation is contained in the thermodynamic factor matrix Γ3with the activity coefficient of species i being γ_i, which expresses the non-ideality of a mixture with respect to the composition. This relationship shows that the Fick diffusion coefficients are actually the product of two contributions, a kinetic Δ_ij and a thermodynamic Γ_ij. The separate observation of these two contributions promotes understanding of the underlying physical phenomena. In the present study, the thermodynamic factor was calculated using the Wilson excess Gibbs energy (g^E) model, using parameters fitted to experimental vapor–liquid equilibrium data of the binary subsystems (see the ESI^†). This combination of MD simulation results with a g^E model was successfully used in previous work to predict Fick diffusion coefficients, including several binary subsystems of the ternary mixtures studied here.¹⁹The four elements of the Fick diffusion coefficient matrix were determined for the three ternary mixtures, benzene + acetone + methanol/ethanol/2-propanol, for nine different compositions, each at ambient temperature and pressure.Results for the first main element of the diffusion matrix D₁₁, which relates the flux of benzene to its own mole fraction gradient, are shown in Fig. 1(a). The experimental data agree quantitatively with the molecular simulation data. D₁₁ increases with the acetone content in the ternary mixture. Since mixtures with a constant mole fraction of benzene (x₁ = 0.33 mol mol⁻¹) were studied throughout, the left edge of Fig. 1(a) corresponds to the binary limit of benzene + alcohol, while the right edge corresponds to that of benzene + acetone. Analysis of the ternary diffusive fluxes implies the following asymptotic behavior of the diffusion coefficients towards the binary limits:⁷ (i) at the infinite dilution limit, x₂ → 0, the ternary coefficient D₁₁ tends to the binary Fick diffusion coefficient of benzene + alcohol; (ii) at the other limit, x₃ → 0, D₁₁ − D₁₂ = D₂₂ − D₂₁ → D_bin (benzene + acetone) should hold. The present experimental and simulation results for D₁₁ are consistent with these asymptotic limits.Open in a separate windowFig. 1Top: The main Fick diffusion coefficient (molar reference frame) of benzene D₁₁ in the three ternary mixtures benzene (1) + acetone (2) + alcohol (3) at a constant benzene mole fraction x₁ = 0.33 mol mol⁻¹ from experiment (triangles) and MD simulation combined with the Wilson g^E model (circles). Both data sets were sampled at the same compositions, but are slightly shifted in the plot for visibility reasons. The symbols at the edges of this plot are the binary diffusion coefficients of benzene + alcohol (x₂ → 0) and of benzene + acetone (x₃ → 0). Bottom: The binary Fick diffusion coefficient of the subsystems benzene + alcohol and benzene + acetone. Most of the binary experimental data were taken from the literature.^20–27An inspection of Fig. 1(a) provides an unexpected finding: the main element D₁₁ is almost identical for all three mixtures along the examined composition path, i.e. it is independent of the contained type of alcohol. To explain this intriguing behavior of D₁₁, the properties of the pure components are considered first (see

The length‐dependent activation of contraction is equally impaired in impuberal male and female rats in monocrotaline‐induced right ventricular failure

The length‐dependent activation of contraction is attenuated in the failing myocardium of adult male rats. This pathological change is not seen in adult female rats, possibly because of a protective effect of sex hormones. The present study evaluated length‐dependent changes in isometric twitch, Ca²⁺ transient (CaT) and action potential (AP) in the right ventricular myocardium of impuberal healthy male and female rats (control) and in rats treated with a single injection of 50 mg/kg monocrotaline (MCT). Compared with sex‐matched control rats, MCT‐treated male and female rats exhibited increased right ventricular weight (134% and 142% of control, respectively), decreased left ventricular weight (72% and 79%), twitch attenuation (48.8 ± 2.7% and 57.5 ± 1.2%) and prolongation (125 ± 3% and 127 ± 2%), CaT attenuation (37.8 ± 0.4% and 39.1 ± 1.1%) and prolongation (114 ± 1% and 116 ± 1%) and AP prolongation at 90% repolarization (195 ± 2% and 203 ± 1%). The MCT‐treated male rats exhibited a 50% lower integral magnitude and an approximately 25% larger time‐to‐peak ‘bump’ compared with control male rats. These parameters in MCT‐treated female rats tended to show similar changes to those seen in the control female rats, with no significant difference between the two groups. In all groups, integral magnitude and time‐to‐peak ‘bump’ increased with length. In conclusion, the length‐dependent activation of contraction was equally blunted in the failing right ventricular myocardium of impuberal male and female rats. This was related to changes in CaT and AP, which were similar between male and female rats. Therefore, puberty is necessary for manifestation of the protective effects of sex hormones on this remodelling.     

Ventilatory efficiency during ramp exercise in relation to age and sex in a healthy Japanese population

BackgroundThe current understanding of ventilator efficiency variables during ramp exercise testing in the normal Japanese population is insufficient, and the responses of tidal volume (VT) and minute ventilation (V?E) to the ramp exercise test in the normal Japanese population are not known.MethodsA total of 529 healthy Japanese subjects aged 20–78 years underwent cardiopulmonary exercise testing using a cycle ergometer with ramp protocols. VT and V?E at rest, at anaerobic threshold, and at peak exercise were determined. The slope of V?E versus carbon dioxide (V?CO₂) (V?E vs. V?CO₂ slope), minimum V?E/V?CO₂, and oxygen uptake efficiency slope (OUES) were determined.ResultsFor males and females in their 20 s, peak VT (VTpeak) was 2192 ± 376 and 1509 ± 260 mL (p < 0.001), peak V?E (V?Epeak) was 80.6 ± 18.7 and 57.7 ± 13.9 L/min (sex differences p < 0.001), the V?E vs. V?CO₂ slope was 24.4 ± 3.2 and 25.7 ± 3.2 (p = 0.035), the minimum V?E/V?CO₂ was 24.2 ± 2.3 and 27.0 ± 2.8 (p < 0.001), and the OUES was 2452 ± 519 and 1991 ± 315 (p < 0.001), respectively. VTpeak and V?Epeak decreased with age and increased with weight and height. The V?E vs. V?CO₂ slope and minimum V?E/V?CO₂ increased with age, while conversely, the OUES decreased with age.ConclusionsWe have established the normal range of VT and V?E responses, the V?E vs. V?CO₂ slope, the minimum V?E/V?CO₂, and the OUES for a healthy Japanese population. Some of these parameters were influenced by weight, height, sex, and age. These results provide useful reference values for interpreting the results of cardiopulmonary exercise testing in cardiac patients.