连续介质力学中混合物的变分理论
Variational Theory of Mixtures in Continuum Mechanics
摘要：
在连续介质力学中，混合物的运动方程是通过使用汉密尔顿扩展原理推导出来的，该原理将混合物视为不同连续介质的集合。假定内能是各组分密度、熵和连续空间梯度的函数。我们首先写出没有化学反应或扩散的无粘可混溶流体混合物的每一组分的运动方程。我们的工作导致在一个普遍的热力学形式的运动方程，其中相互作用项受本构关系，难以解释物理，不发生。对于密度、熵和空间梯度的内能函数，得到了描述组分质心运动的方程。将结果推广到耗散混合物，得到了能量方程。推导了代表热力学第二定律的Clausius-Duhem不等式的一种形式。在可压缩混合物的特殊情况下，方程再现了经典的结果。远离临界条件，流体混合物中不同相之间的界面是具有强密度梯度和熵梯度的层。解释了这种界面的表面张力。
英文摘要：
In continuum mechanics, the equations of motion for mixtures are derived through the use of Hamilton's extended principle which regards the mixture as a collection of distinct continua. The internal energy is assumed to be a function of densities, entropies and successive spatial gradients of each constituent. We first write the equations of motion for each constituent of an inviscid miscible mixture of fluids without chemical reactions or diffusion. Our work leads to the equations of motion in an universal thermodynamic form in which interaction terms subject to constitutive laws, difficult to interpret physically, do not occur. For an internal energy function of densities, entropies and spatial gradients, an equation describing the barycentric motion of the constituents is obtained. The result is extended for dissipative mixtures and an equation of energy is obtained. A form of Clausius-Duhem's inequality which represents the second law of thermodynamics is deduced. In the particular case of compressible mixtures, the equations reproduce the classical results. Far from critical conditions, the interfaces between different phases in a mixture of fluids are layers with strong gradients of density and entropy. The surface tension of such interfaces is interpreted.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
