Researchers distinguish between orderly flow and chaotic flow as the laminar flow and the turbulent flow. The fluid mechanics can also be distinguish between a single phase flow and multiphase flow flow made more than one phase or single distinguishable material. The last boundary as all the boundaries in fluid mechanics isn't sharp because fluid can go through a phase change condensation or evaporation in the middle or during the flow and switch from a single phase flow to a multi phase flow.
Moreover, flow with two phases or materials can be treated as a single phase for example, air with dust particle. After it was made clear that the boundaries of fluid mechanics aren't sharp, the study must make arbitrary boundaries between fields. Or, when a general model is need because more parameters are effecting the situation.
It is this author's personal experience that the knowledge and ability to know in what area the situation lay is one of the main problems. For example, engineers in software company analyzed a flow of a complete still liquid assuming a complex turbulent flow model.
Such absurd analysis are common among engineers who do not know which model can be applied. Thus, one of the main goals of this book is to explain what model should be applied. Before dealing with the boundaries, the simplified private cases must be explained. Thank you. Your request has been sent. You should be hearing from a site administrator shortly.
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Corn starch and water mixture suspension is a good example with which low and high De number effects can be shown. The Newtonian fluids show a linear relation. Fluids which do not follow the linear law between stress an the deformation rate are called non-newtonian and they are the subject of rheology. A dilatant shear-thickening fluid increases resistance with increasing applied stress. Alternately, a pseudoplastic shear-thinning fluid decreases resistance with increasing stress.
If the thinning effect is very strong, the fluid is termed plastic. The limiting case of a plastic substance is one which requires a finite yield stress before it begins to flow. The linear-flow Bingham plastic idealization is shown in the figure, but the flow behavior after yield may also be nonlinear.
Examples of a yielding fluid are toothpaste and ketchup, which will not flow out of the tube until a finite stress is applied by squeezing. Some fluids show decreasing thixotropic or increasing resistance rheopectic in time for the same deformation rate. For example, pudding is a rheopectic fluid and some paints are thixotropic. The molecules are not fixed in a lattice but move about freely relative to each other. Thus fluid density, or mass per unit volume, has no precise meaning because the number of molecules occupying a given volume continually changes.
This effect becomes unimportant if the unit volume is large compared with, say, the cube of the molecular spacing, when the number of molecules within the volume will remain nearly constant in spite of the enormous interchange of particles across the boundaries. Over this value, the medium can be accepted as continuum , such that the variations in space and time can be accepted to be smooth and differential equations can be written to describe the fluid motion. In a fluid at rest, the tangential viscous forces are absent and the only force between adjacent surfaces is normal to the surface.
In a resting fluid there is only a normal stress pressure. In other words, force caused by the pressure on a surface is normal to that surface.
Surface tension phenomena occur at the interface of one liquid and another liquid, gas or a solid wall. The cohesive forces between molecules down into a liquid are shared with all neighboring atoms. Those on the surface have no neighboring atoms above, and exhibit stronger attractive forces upon their nearest neighbors on the surface.
This enhancement of the intermolecular attractive forces at the surface is called surface tension. If the interface is curved, a mechanical balance shows that there is a pressure difference across the interface, the pressure being higher on the concave side,. Surface tension coefficient is not a property of the liquid alone, but a property of the liquid's interface with another medium.
According to the above equation, in the soap bubble or in the droplet, inner pressure is higher than outer pressure. This can also be shown by a force balance. In the droplet, the force balance in the vertical direction reads. Note that owing to the two interfaces in the soap bubble force due to surface tension is as double as that in the droplet. The contact angle is the angle between the liquid-solid and gas-liquid interfaces.
It is calculated such that angle remains in the liquid. It is dependent on the adhesion forces between the liquid molecules and the solid wall. These forces are sensitive to the actual physicochemical conditions of the solid-liquid interface. Evaporation occurs at the liquid gas interface.
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