Symmetry relations in viscoplastic drag laws

Area of Science:

• Fluid Mechanics
• Rheology
• Nonlinear Dynamics

Background:

• Lorentz reciprocity is key for linear viscous fluid resistance formulas.
• Nonlinear viscoplastic fluids present complex flow behaviors.
• Onsager relations are fundamental in describing reciprocal relationships in transport phenomena.

Purpose of the Study:

• To extend the concept of resistance formula symmetry to nonlinear viscoplastic fluids.
• To investigate the applicability of Edelen's nonlinear generalization of Onsager relations.
• To explore implications for strongly dissipative rheological systems.

Main Methods:

• Utilizing Edelen's nonlinear generalization of Onsager relations.
• Applying the concept of dissipation potential for constitutive equations.
• Analyzing flow domains with strong interior and boundary dissipation.

Main Results:

• Demonstrated symmetry in resistance formulae for a broad range of nonlinear viscoplastic fluids.
• Established a nonlinear generalization of Stokes resistance formulae.
• Showcased implications for strongly dissipative traction-velocity responses.

Conclusions:

• The symmetry principles extend beyond linear systems to nonlinear viscoplastic fluid dynamics.
• Findings are applicable to nonlinear Darcy flow and effective slip in textured surfaces.
• The study provides a theoretical framework for analyzing complex fluid flows with strong dissipation.