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The concept of dimension is important because every mathematical equation linking physical quantities must be dimensionally consistent, implying that mathematical equations must meet the following two rules. The first rule is that, in an equation, the expressions on each side of the equal sign must have the same dimensions. This is fairly intuitive since we can only add or subtract quantities of the same type (dimension). The second rule states that, in an equation, the arguments of any of the...
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Mesoscale perspective on the Tolman length.

Matteo Lulli1, Luca Biferale2, Giacomo Falcucci3,4

  • 1Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China.

Physical Review. E
|February 23, 2022
PubMed
Summary
This summary is machine-generated.

The multiphase Shan-Chen lattice Boltzmann method accurately calculates curvature-dependent surface tension and the Tolman length for hydrostatic droplets and bubbles. This hydrodynamic mesoscale approach offers a new way to study critical phenomena and cavitation.

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Area of Science:

  • Computational physics and fluid dynamics
  • Thermodynamics and statistical mechanics
  • Mesoscale simulations

Background:

  • Surface tension's curvature dependence is crucial for understanding fluid interfaces.
  • The Tolman length characterizes this dependence but is challenging to compute.
  • Existing methods like Molecular Dynamics and Density Functional Theory are computationally intensive.

Purpose of the Study:

  • To demonstrate the multiphase Shan-Chen lattice Boltzmann method (LBM) for computing curvature-dependent surface tension.
  • To accurately determine the Tolman length using LBM simulations.
  • To explore the universality and critical behavior of the Tolman length.

Main Methods:

  • Three-dimensional hydrostatic droplet and bubble simulations using the multiphase Shan-Chen lattice Boltzmann method (LBM).
  • Precise computation of surface tension (σ) at the surface of tension (R_s).
  • Determination of the Tolman length (δ) from the first-order correction coefficient.

Main Results:

  • LBM successfully yields curvature-dependent surface tension (σ).
  • Accurate computation and determination of the Tolman length (δ) were achieved.
  • The Tolman length exhibits universality across different equations of state and follows power-law scaling near the critical temperature.

Conclusions:

  • The multiphase Shan-Chen LBM provides a computationally efficient mesoscale framework for studying interfacial phenomena.
  • This method enables effective investigation of the Tolman length's role in cavitation and other applications.
  • Results are reproducible via the "idea.deploy" framework, promoting further research.