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Van der Waals Equation01:10

Van der Waals Equation

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The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
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An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
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The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
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Chemical-potential-based lattice Boltzmann method for nonideal fluids.

Binghai Wen1,2, Xuan Zhou1, Bing He1

  • 1Guangxi Key Lab of Multi-source Information Mining & Security, Guangxi Normal University, Guilin 541004, China.

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|July 16, 2017
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Summary

This study introduces a novel chemical-potential-based multiphase lattice Boltzmann model for thermodynamic modeling. The new model offers improved computational efficiency and accurately simulates phase transitions and wettability.

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Area of Science:

  • Thermodynamics
  • Computational Physics
  • Fluid Dynamics

Background:

  • Chemical potential is crucial for thermodynamic modeling of complex systems, including phase transitions and chemical reactions.
  • Existing pressure-tensor-based models can be computationally intensive.

Purpose of the Study:

  • To develop a more efficient multiphase lattice Boltzmann model using chemical potential.
  • To investigate the thermodynamic consistency and Galilean invariance of the new model.
  • To explore the application of chemical potential in modeling surface wettability.

Main Methods:

  • Developed a chemical-potential-based multiphase lattice Boltzmann model.
  • Derived chemical potentials from free-energy density for common equations of state.
  • Implemented an effective chemical-potential boundary condition to study surface wettability.

Main Results:

  • The new model avoids complex calculations of pressure tensor and its divergence, enhancing computational efficiency.
  • Theoretical analysis and numerical simulations confirm the model's adherence to thermodynamics and Galilean invariance.
  • The model successfully simulates surface wettability, with tunable contact angles via surface chemical potential.

Conclusions:

  • The chemical-potential-based multiphase lattice Boltzmann model provides an efficient and thermodynamically consistent approach for complex fluid simulations.
  • This model offers a versatile tool for studying phase transitions and interfacial phenomena, including surface wettability.