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A vibrational model of transport properties of dense fluids assumes that solid-like oscillations of atoms around their temporary equilibrium positions dominate the dynamical picture. The temporary equilibrium positions of atoms do not form any regular structure and are not fixed, unlike in solids. Instead, they are allowed to diffuse and this is why liquids can flow. However, this diffusive motion is characterized by much longer time scales compared to those of solid-like oscillations. Although this general picture is not particularly new, only in a recent series of works it has been possible to construct a coherent and internally consistent quantitative description of transport properties such as self-diffusion, shear viscosity, and thermal conductivity. Moreover, the magnitudes of these transport coefficients have been related to the properties of collective excitations in dense fluids. Importantly, the model is simple and no free parameters are involved. Recent achievements are summarized in this overview. Application of the vibrational model to various single-component model systems such as plasma-related Coulomb and screened Coulomb (Yukawa) fluids, the Lennard-Jones fluid, and the hard-sphere fluid is considered in detail. Applications to real liquids are also briefly discussed. Overall, good to excellent agreement with available numerical and experimental data is demonstrated. Conditions of applicability of the vibrational model and a related question concerning the location of the gas–liquid dynamical crossover are discussed. [ABSTRACT FROM AUTHOR]

• This work presents a novel perspective on viscosity and a new interpretation using the thermodynamic dimension (D T) idea. • A general viscosity equation is developed utilizing standard and well-established statistical thermodynamic relations. • The derived viscosity equation is reasonably accurate and comparable to recent, precise viscosity equations. • This perspective makes it simple to understand the dual behavior of viscosity in dense fluids and provides a straightforward explanation for the viscosity minimum. • It can be shown that variations in the intermolecular potential u (r, T) of the fluid particles, which can be deduced from the fluid EoS using standard thermodynamic concepts, are responsible for the link between a fluid's viscosity equation and its EoS. This work presents a different perspective on viscosity and a new interpretation of it by treating the fluid as a fractal lattice incorporating temporary molecular clusters (t-clusters) and using the thermodynamic dimension (D T) idea. The D T connects fluid viscosity to its EoS by computing the effective intermolecular potential, U (r, T), which may be found via thermodynamic relations from the fluid equation of state (EoS). Finally, a general viscosity equation is developed utilizing standard and well-established statistical thermodynamic relations. The approach is applied to nitrogen fluid as a case study because of the fluid's extensiveness data in the literature. Less than 2 % is the absolute average deviation percent (AAD%) for viscosity prediction in the range of 65 K to 1000 K for pressures less than 2000 MPa. It is simple to code the viscosity equation that is obtained. [ABSTRACT FROM AUTHOR]

By considering Frenkel's point of view regarding the concept of relaxation time, every molecule of a fluid possesses an effective space. We name this permissible and accessible space of each molecule of fluid as the molecular cage (MC). All motions of the molecule, including translational, rotational, and vibrational motions, take place within this space. In this paper, by using the new concept of the thermodynamic dimension (D T) and the generalized Debye model for the isochoric heat capacity (C V) of matter in different states, we want to indicate at high pressures the MCs confine the internal molecular vibrations. By calculation of C V of supercritical fluid (SCF), the restriction of molecular vibrations is detected. To investigate the effect of molecular cages, we have studied C V of diatomic SCFs including nitrogen, oxygen, and carbon monoxide. [ABSTRACT FROM AUTHOR]

Using the Maxwell-Boltzmann distribution function and considering Frenkel's theory of liquids; a substance is approached as a fractal lattice. We introduce a new concept that we call it thermodynamic dimension D T to generalize both Einstein and Debye models, so that both models are a special case of the general model (D T = 3). The thermodynamic dimension D T of a fluid is a dimensionless quantity whose value can be a number between zero and three (0 ≤ D T ≤ 3). In a wide range of temperature and pressure comparison of calculated results with experimental data for isochoric heat capacities in dense region show good agreement in the studied fluids. Based on the obtained results, we illustrate existence of the principle of the corresponding states for simple fluids. Finally, in addition to introducing a new condition (D T = 1/2) to plotting the Frenkel line, we predict solid-like features for around of the critical point. [ABSTRACT FROM AUTHOR]