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

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.