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Dimensionless Groups by Entropic Similarity: I - Diffusion, Chemical Reaction and Dispersion Processes.

Robert K Niven1

  • 1School of Engineering and Information Technology, The University of New South Wales, Canberra, ACT 2600, Australia.

Entropy (Basel, Switzerland)
|May 16, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces entropic similarity, a new category of dimensionless groups based on entropy production and transport. This approach offers a novel perspective for analyzing irreversible processes across science and engineering.

Keywords:
chemical reactiondiffusiondimensional analysisdispersionentropic similarity

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Area of Science:

  • Thermodynamics
  • Fluid Mechanics
  • Chemical Engineering
  • Environmental Engineering

Background:

  • Dimensional analysis and similarity arguments are crucial tools in science and engineering.
  • Existing dimensionless groups are classified into geometric, kinematic, and dynamic similarity.
  • These methods analyze systems based on ratios of lengths, velocities, and forces, respectively.

Purpose of the Study:

  • To propose and define a new category of dimensionless groups: entropic similarity.
  • To analyze irreversible processes directly through entropy production and transport phenomena.
  • To expand the application of dimensional analysis to new and existing scientific and engineering problems.

Main Methods:

  • Defined entropic similarity based on ratios of entropy production terms, entropy flow rates, or information flow rates.
  • Derived entropic groups for diffusion, chemical reaction, and dispersion processes.
  • Re-interpreted traditional dimensionless groups, such as the Reynolds number, using entropic similarity.

Main Results:

  • Demonstrated that entropic similarity can recover many traditional dimensionless groups with new interpretations.
  • Identified novel dimensionless groups through the entropic similarity framework.
  • Showcased the applicability of entropic groups to various diffusion, reaction, and dispersion processes.

Conclusions:

  • Entropic similarity provides a powerful alternative and complementary approach to traditional dimensional analysis.
  • This framework offers a more direct analysis of systems governed by the second law of thermodynamics.
  • The proposed entropic groups significantly enhance the scope of dimensional analysis for scientific and engineering problem-solving.