Motivation and Examples Sample Clauses

Motivation and Examples. 6 1.3.2 The Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Mathematical Formulation 11 2.1 Regularized Formulations 11
Sample 1
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Motivation and Examples. Xxxxxxx fluids now enjoy a great amount of attention in the study of visco-plastic materials. The flow of Xxxxxxx materials occurs in various fields of modern research, ranging from geology, geophysics to medicine and many other industrial applications. The Xxxxxxx model is used, among others, for describing the flow of oil bearing materials, slurries, mud and magma as well as certain powder mixtures. A material often associated with Xxxxxxx fluids is ketchup. The vico-plasticity can be observed when turning an opened ketchup bottle upside down. The content will likely remain inside the bottle since the shear stress induced by the earth’s gravity is less than the yield stress of the material. To force a flow, the bottle needs to be shaken sufficiently strong so that the stress on the material exceeds the yield stress. This results in the (former rigid) medium to become an incompressible fluid and the content pours out of the bottle [71]. Another material associated with Xxxxxxx fluids is toothpaste; a certain minimal amount of force needs to be applied to the tube before the toothpaste pours out of the tube [73]. Xxxxxxx fluids are addressed in various fields of scientific literature. Numerical simulations of Xxxxxxx fluid flows are used for analyzing the flow of mud-rich debris and and its deposits [101] and for routing the flow of channel- ized debris. Magnetorheologial fluids are field-controllable materials whose rheological properties can be altered by applying magnetic fields [49]. These materials are used for example for shock-absorbers and artificial joints and the Xxxxxxx model can be used for describing the flow of these fluids [60]. Mud flow is an example of Xxxxxxx flow, making the model interesting for applica- tions involving geology. For example in [56], Xxxxxxx fluids are used for modeling and predicting landslides. Xxxxxxx fluids are of interest to the oil industry; the model is used for analyzing start-up flows of waxy crude oils in pipelines [98, 99]. Xxxxxxx fluids may, under certain circumstances, be used for simulating the flow of blood, especially under a high concentration of white blood cells or blood solutes. We will discuss the Xxxxxxx model for blood flow problems in more detail in Chapter 7. See also [47] for applications of Xxxxxxx fluids involving problems in hemodynamics. It should be mentioned that the examples listed here are just a small subset of ap- plications and Xxxxxxx fluids in many more situations of interest. See ...
Sample 1

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