记忆同步数与记忆流变学
The Mnemosyne Number and the Rheology of Remembrance
摘要：
Deborah数的概念被广泛用于粘弹性材料的研究，并表示材料松弛时间与观察时间尺度的比率，并划分主要粘性或弹性材料响应之间的过渡。然而，这种结构并不能帮助量化的重要性，长瞬变和非单调应力跳变，经常观察到更复杂的时变系统。许多这些非直观的影响集中在术语触变性;然而，没有专有名词与这些材料中观察到的关键现象相关联。触变性源于复杂结构流体记忆其先前变形历史的能力，因此很自然地将代表这种行为的无量纲组命名为记忆能力。在希腊神话中，Mnemosyne是九位缪斯的母亲，也是记忆女神。因此，我们提出了Mnemosyne数的定义为触变时间尺度和变形的施加速率的无量纲产品。因此，Mnemosyne数是与触变时间尺度相比的流动强度的量度。由于长瞬态响应是触变材料特有的，因此还需要考虑流动的持续时间。该持续时间的相关无量纲测量可以用突变数表示，该突变数将实验/观察的时间尺度与触变时间尺度进行比较。整理的突变数和Mnemosyne数，我们构建了一个一般的触变行为的二维地图，并量化这些想法使用典型的触变模型。
英文摘要：
The concept of a Deborah number is widely used in study of viscoelastic materials and to represent the ratio of a material relaxation time to the timescale of observation, and to demarcate transitions between predominantly viscous or elastic material responses. However, this construct does not help quantify the importance of long transients and non-monotonic stress jumps that are often observed in more complex time-varying systems. Many of these non-intuitive effects are lumped collectively under the term thixotropy; however, no proper nouns are associated with the key phenomena observed in such materials. Thixotropy arises from the ability of a complex structured fluid to remember its prior deformation history, so it is natural to name the dimensionless group representing such behavior with respect to the ability to remember. In Greek mythology, Mnemosyne was mother of the nine Muses and the goddess of memory. We thus propose the definition of a Mnemosyne number as the dimensionless product of the thixotropic time scale and the imposed rate of deformation. The Mnemosyne number is thus a measure of the flow strength compared to the thixotropic timescale. Since long transients responses are endemic to thixotropic materials, one also needs to consider the duration of flow. The relevant dimensionless measure of this duration can be represented in terms of a mutation number which compares the timescale of experiment/observation to the thixotropic timescale. Collating the mutation number and the Mnemosyne number, we construct a general two-dimensional map of thixotropic behavior, and quantify these ideas using canonical thixotropic models.
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