Generalized Einstein Equation for Ceramics Suspension Rheology

Area of Science:

• Rheology
• Materials Science
• Physical Chemistry

Background:

• Traditional models for suspension rheology often struggle with concentrated systems.
• Empirical models lack physical consistency and introduce arbitrary constants.
• A need exists for a robust, physically grounded model for suspension viscosity.

Purpose of the Study:

• Introduce the Generalized Einstein-type Equation Rheological Gaussian Model (E²RG).
• Extend Einstein-type rheology to concentrated suspensions.
• Provide accurate relative viscosity predictions across the entire packing interval.

Main Methods:

• Developed E²RG by modulating the Einstein expression with a Gaussian error function correction.
• Avoided empirical exponents on particle concentration.
• Utilized model parameter physical meaning for intrinsic verifiability and self-consistency checks.

Main Results:

• E²RG accurately predicts relative viscosity from φ = 0 to φ_max.
• The model provides a smooth, physically consistent transition from ideal to nonideal regimes.
• E²RG parameters reflect particle interaction intensity, not free-fitting constants.

Conclusions:

• E²RG offers a conceptually transparent and versatile tool for suspension rheology.
• The model aligns with the Central Limit Theorem and jamming framework.
• E²RG provides a physically coherent interpretation of flow cessation without viscosity divergence.