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Equation of State01:07

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The equation of state is an equation that relates physical quantities, such as pressure, volume, temperature, and the number of moles, of a thermodynamics system with each other. The equation relating physical quantities with each other can be a simple mathematical expression or too complicated to express in mathematical form. In either case, a relationship between physical quantities exists. If the equation of state cannot be expressed in a mathematical form, then experimental data and...
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Viscosity measures the resistance a fluid offers to flow and deformation. It results from internal friction between layers of fluid moving relative to one another. Dynamic viscosity, denoted by the Greek letter mu (μ), quantifies the force needed to move one fluid layer over another. For Newtonian fluids like water and air, the relationship between the shearing stress and the rate of shearing strain is linear, meaning their viscosity remains constant regardless of the applied stress.
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For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
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Physically based equation of state for Mie ν-6 fluids.

Anja Reimer1, Thijs van Westen1, Joachim Gross1

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We developed a physically based equation of state for Mie fluids, achieving accuracy comparable to empirical models. This new model offers broader applicability and better descriptions of fluid properties, especially in metastable regions.

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Area of Science:

  • Thermodynamics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Accurate equations of state are crucial for predicting fluid behavior.
  • Empirical models for Mie fluids often lack broad applicability and physical grounding.
  • Existing theoretical models may not fully capture thermodynamic properties across all relevant densities and temperatures.

Purpose of the Study:

  • To develop a physically based equation of state for Mie ν-6 fluids.
  • To achieve accuracy comparable to state-of-the-art empirical models.
  • To extend the applicability of equations of state to a wider range of Mie exponents and fluid states.

Main Methods:

  • Developed a physically based equation of state within the uv-theory framework.
  • Incorporated the third virial coefficient (B3) for improved low-density description.
  • Interpolated between Weeks-Chandler-Andersen (WCA) perturbation theory at high densities and a modified WCA theory at low densities.
  • Derived a new algebraic equation for the third virial coefficient of Mie fluids.

Main Results:

  • The new equation of state accurately describes Mie ν-6 fluids (9 ≤ ν ≤ 48).
  • Model performance for the Lennard-Jones fluid (ν = 12) matches leading empirical equations of state.
  • The model is applicable to densities up to ρ*(T*)⪅1.1+0.12T* and temperatures T* > 0.3.
  • Accurate prediction of thermodynamic properties and phase equilibria validated against molecular simulation data.

Conclusions:

  • The physically based equation of state offers a robust alternative to empirical models for Mie fluids.
  • The model provides superior description of metastable and unstable regions, beneficial for density functional theory applications.
  • The theoretical foundation allows for potential extensions to complex systems like non-spherical fluids and mixtures.