Viscosity models for mixtures

The shear viscosity of a fluid is a material property that describes the friction between internal neighboring fluid surfaces flowing with different fluid velocities. This friction is the effect of (linear) momentum exchange caused by molecules with sufficient energy to move between these fluid sheets due to fluctuations in their motion. The viscosity is not a material constant, but a material property that depends on temperature, pressure, fluid mixture composition, local velocity variations. This functional relationship is described by a mathematical viscosity model called a constitutive equation which is usually far more complex than the defining equation of shear viscosity. One such complicating feature is the relation between the viscosity model for a pure fluid and the model for a fluid mixture which is called mixing rules. When scientists and engineers use new arguments or theories to develop a new viscosity model, instead of improving the reigning model, it may lead to the first model in a new class of models. This article will display one or two representative models for different classes of viscosity models, and these classes are:Elementary kinetic theory and simple empirical models - viscosity for dilute gas with nearly spherical molecules Power series - simplest approach after dilute gas Equation of state analogy between PVT and TP Corresponding state model - scaling a variable with its value at the critical point Friction force theory - internal sliding surface analogy to a sliding box on an inclined surface Multi- and one-parameter version of friction force theory Transition state analogy - molecular energy needed to squeeze into a vacancy analogous to molecules locking into each other in a chemical reaction Free volume theory - molecular energy needed to jump into a vacant position in the neighboring surface Significant structure theory - based on Eyring's concept of liquid as a blend of solid-like and gas-like behavior / features

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