Geological Fluid Dynamics: Sub-surface Flow and Reactions


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Important fluids, like water as well as most gases, behave—to good approximation—as a Newtonian fluid under normal conditions on Earth.

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By contrast, stirring a non-Newtonian fluid can leave a "hole" behind. This will gradually fill up over time—this behaviour is seen in materials such as pudding, oobleck , or sand although sand isn't strictly a fluid. Alternatively, stirring a non-Newtonian fluid can cause the viscosity to decrease, so the fluid appears "thinner" this is seen in non-drip paints. There are many types of non-Newtonian fluids, as they are defined to be something that fails to obey a particular property—for example, most fluids with long molecular chains can react in a non-Newtonian manner.

The constant of proportionality between the viscous stress tensor and the velocity gradient is known as the viscosity. A simple equation to describe incompressible Newtonian fluid behaviour is. For a Newtonian fluid, the viscosity, by definition, depends only on temperature and pressure , not on the forces acting upon it. If the fluid is incompressible the equation governing the viscous stress in Cartesian coordinates is. If the fluid is not incompressible the general form for the viscous stress in a Newtonian fluid is.

If a fluid does not obey this relation, it is termed a non-Newtonian fluid , of which there are several types. Non-Newtonian fluids can be either plastic, Bingham plastic, pseudoplastic, dilatant, thixotropic, rheopectic, viscoelastic. In some applications another rough broad division among fluids is made: ideal and non-ideal fluids. An Ideal fluid is non-viscous and offers no resistance whatsoever to a shearing force. An ideal fluid really does not exist, but in some calculations, the assumption is justifiable.

One example of this is the flow far from solid surfaces. In many cases the viscous effects are concentrated near the solid boundaries such as in boundary layers while in regions of the flow field far away from the boundaries the viscous effects can be neglected and the fluid there is treated as it were inviscid ideal flow. The equation reduced in this form is called the Euler equation. From Wikipedia, the free encyclopedia. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources.


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