Nonlinear fluid dynamics description of non-Newtonian fluids
Nonlinear fluid dynamics description of non-Newtonian fluids
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非牛顿流体的非线性流体动力学描述
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
H. Brand
中科院分区：
文献类型：
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作者：
H. Pleiner;Mario Liu;H. Brand
讨论了粘弹性介质的非线性流体动力学方程。我们从最近推导的完全流体动力学的永久弹性，利用（欧拉）应变张量的非线性描述。毫无疑问，应变张量动力学中的可逆二次非线性属于“低对流”类型。取代（经常被忽视）的应变扩散的应变作为一个最小的成分的松弛，广义流体动力学描述的粘弹性。这可以用来得到应力张量的非线性动力学方程（有时称为本构方程），其变量为幂级数。该方程的形式，特别是非线性对流项的形式不是通用的，而是取决于各种材料参数。与现有的唯象模型的比较。特别是，我们将讨论如何适应这些特设模型的流体动力学描述和各种非牛顿的贡献来自哪里。
Nonlinear hydrodynamic equations for visco-elastic media are discussed. We start from the recently derived fully hydrodynamic nonlinear description of permanent elasticity that utilizes the (Eulerian) strain tensor. The reversible quadratic nonlinearities in the strain tensor dynamics are of the “lower convected” type, unambiguously. Replacing the (often neglected) strain diffusion by a relaxation of the strain as a minimal ingredient, a generalized hydrodynamic description of viscoelasticity is obtained. This can be used to get a nonlinear dynamic equation for the stress tensor (sometimes called constitutive equation) in terms of a power series in the variables. The form of this equation and in particular the form of the nonlinear convective term is not universal but depends on various material parameters. A comparison with existing phenomenological models is given. In particular we discuss how these ad-hoc models fit into the hydrodynamic description and where the various non-Newtonian contributions are coming from.