Non-trivial rheological exponents in sheared yield stress fluids

Area of Science:

• Soft matter physics
• Rheology
• Materials science

Background:

• Athermal rheology of soft materials exhibits complex behaviors at low driving rates.
• Understanding the physical origins of non-trivial exponents is crucial for material characterization.

Purpose of the Study:

• To investigate the role of self-consistent mechanical noise in athermal rheology.
• To analyze deviations from standard Herschel-Bulkley predictions.
• To propose experimental validation methods.

Main Methods:

• Analytical study of a mean-field model incorporating stress diffusion.
• Numerical simulations on a mesoscopic lattice model.
• Explicit implementation of long-range elastic responses.

Main Results:

• A mechanical noise mechanism, arising from localized plastic deformation, is proposed.
• Dependence of shear modulus and relaxation time on shear rate modifies the predicted exponent (1/2).
• The findings are robust against structural disorder and partial stress relaxation.

Conclusions:

• The proposed scenario explains non-trivial exponents in soft material rheology.
• The model provides a framework for understanding complex flow behaviors.
• Rheological experiments can be designed to test these predictions.