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A note about convected time derivatives for flows of complex fluids.
Howard A Stone1, Michael J Shelley2,3, Evgeniy Boyko4
1Department of Mechanical and Aerospace Engineering, Princeton University, New Jersey 08544, USA. hastone@princeton.edu.
Soft Matter
|July 5, 2023
Summary
This study directly derives time derivatives for complex fluid flow continuum models using line element kinematics. This approach clarifies microstructural conformation tensor evolution and derivative interpretations in fluid dynamics.
Area of Science:
- Fluid Dynamics
- Continuum Mechanics
- Rheology
Background:
- Continuum descriptions of complex fluids often employ various time derivatives.
- The physical interpretation and derivation of these derivatives can be challenging.
- Understanding microstructural evolution is key to modeling complex fluid behavior.
Purpose of the Study:
- To provide a direct, principle-based derivation of time derivatives for continuum fluid flow.
- To elucidate the physical meaning of different time derivatives.
- To establish a clear link between kinematics and microstructural evolution.
Main Methods:
- Utilizing the kinematics of line elements within the flow field.
- Applying fundamental principles of continuum mechanics.
- Analyzing the evolution of the microstructural conformation tensor.
Main Results:
- A direct derivation of commonly used time derivatives in complex fluid dynamics.
- A clear physical interpretation for each derived derivative.
- Demonstration of how line element kinematics naturally leads to these derivatives and explains microstructural evolution.
Conclusions:
- The kinematics of line elements offers a rigorous foundation for continuum fluid flow derivatives.
- This method simplifies the understanding of microstructural tensor evolution.
- Provides a unified framework for analyzing complex fluid behavior.
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