Rheologies

Rheologies, in plural, refers to the diverse subfields, theories, and models that describe how materials deform and flow under applied forces. Rheology is the science that relates stress to the rate of deformation in substances ranging from liquids to soft solids. It encompasses Newtonian fluids, whose viscosity remains constant, and non-Newtonian fluids, whose apparent viscosity changes with shear rate or time, as well as viscoelastic solids that exhibit both viscous and elastic responses.

Key concepts in rheologies include viscosity, elastic moduli, yield stress, thixotropy, and viscoelastic relaxation. Materials may exhibit shear-thinning or shear-thickening behavior, time-dependent recovery, and complex responses under oscillatory loading. Constitutive models provide mathematical descriptions of these behaviors. Classical models include Newtonian fluids, Bingham plastics and Herschel-Bulkley yield-stress fluids, and power-law (Ostwald-de Waele) descriptions. Other common models are Carreau and Casson for non-Newtonian viscosity, along with viscoelastic representations such as Maxwell, Kelvin-Voigt, and the Standard Linear Solid model, plus more advanced fractional or multi-mode formulations.

Measurement and instrumentation are central to rheologies. A rheometer or viscometer assesses flow and deformation properties. Tests range from steady shear experiments to determine viscosity versus shear rate, to capillary or extrusion rheometry for high-shear conditions, and to oscillatory rheometry that yields storage and loss moduli (G’ and G’’) across frequencies.

Applications span polymer processing, food and cosmetic formulation, paints and coatings, geotechnical and geological materials, petroleum and drilling fluids, and biomedical materials. The term rheologies acknowledges the plural, recognizing specialized subfields such as polymer rheology, food rheology, georheology, and bio-rheology, each focusing on material-specific behavior and modeling approaches.