### 物理代写|流体力学代写Fluid Mechanics代考|CIVL3612

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## 物理代写|流体力学代写Fluid Mechanics代考|The concept of equilibrium in the domain of interfaces

Phase separations can be observed at thermodynamic equilibrium at rest. For example, an interface between a liquid and a gas can present itself as being at equilibrium. We then consider its capillary tension, as well as the equilibrium of the liquid in the presence of its vapor. Similarly, thermodynamic equilibrium is a reference for solid-liquid systems, as well as for solid phases when they are multiple. The presence of stresses that are external to the system, of a mechanical or thermal nature, can lead to lesser or greater deviations from the equilibrium. The concepts of a local state and local equilibrium are used to study these systems, which are the domain of thermodynamics of irreversible processes (Defay and Prigogine 1946; Defay 1949; Prigogine and Defay 1949; Defay et al. 1972). However, there are systems with interfaces – which we will call generalized interfaces – that offer no reference to the equilibrium state. This is the case with thin flames or shock waves, for instance, which can be localized as discontinuity surfaces at a macroscopic level. However, these interfaces can also be studied when not in thermodynamic equilibrium by starting with the concept of a local equilibrium. Although these situations do not necessarily require interface laws, it is satisfying to observe the similarity in the analysis and writing between these and the case of phase separation interfaces that are out of equilibrium.

## 物理代写|流体力学代写Fluid Mechanics代考|Generalized interfaces

Zones with a high gradient allow the appearance of surfaces, even without a phase change.

Figure 1.4(a) shows a thermal drop that is of the same nature as the liquid that contains it, but at a much lower temperature and therefore at a higher density, which explains its downward motion.

Figure 1.4(b) shows a stained shock in front of a satellite during its re-entry into the atmosphere.

Figure 1.4(c) shows an observation of a premixed flame under low pressure. The surface above it is the very thin reaction zone and, the surface below it is an isotherm in the unburned mixture. At normal pressure, both of these surfaces and the zone that separates them can be combined into a single interface, which makes up the flame.

Miscible liquids, brought into contact in their pure states, produce interfaces whose thickness increases over time with the mutual diffusion of the fluids. The experimental study of these interfaces reveals the existence of an effective surface tension. While it is certainly lower than the capillary tension between immiscible liquids, it is non-negligible. Such surface tension probably also exists in pure fluids subject to high thermal gradients. This would certainly explain the shape of a thermal drop. Calculations carried out on supercritical fluids show that similar phenomena are possible during the propagation of a thermal field.

Thus, high density gradients are not the only ones that can generate capillary tensions – concentration and thermal gradients can also produce effective surface tensions. The second gradient theory is certainly a means of explaining these behaviors.

With respect to shock and deflagration waves, characteristics other than surface tension are also manifested. Surface stretching rates are elements that must be considered. In turbulent combustion, certain flame models bring the volume fractions of interfacial areas into play.

Mathematical tools are required to study interfaces and interfacial zones. Modeling these systems often requires simplifying hypotheses.

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## MATLAB代写

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