Fluids

Physically a fluid is defined as a substance which deforms continuously under the application of a shear stress. The term fluid generally includes both the liquid and gas phases. Some substances can be both fluid and solid. Viscoelastic fluids appear to behave similar to a solid when a sudden force is applied. Also substances with a very high viscosity such as pitch appear to behave like a solid. Here fluids are characterized via the constitutive properties. It is a common property of fluids that they exhibit elasticity in their response to compression. Fluids do not possess natural reference configurations and that is why it is more convenient to develop the pertinent equations in the spatial form. Fluids show lack of resistance to permanent deformation, resisting only relative rates of deformation in a dissipative, frictional manner. These properties are typically a function of their inability to support a shear stress in static equilibrium. Some models are examined in detail: elastic fluids (along with water wave theories), thermoelastic fluids, the ideal gas and some real gases, heat-conducting viscous fluids, Newtonian fluids, Stokesian fluids, generalized Newtonian fluids, viscoplastic and viscoelastic fluids, models of turbulence.