The concept of a Deborah number is widely used in the study of viscoelastic materials to represent the ratio of a material relaxation time to the time scale 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 nonmonotonic stress jumps that are often observed in more complex time-varying systems. Many of these nonintuitive 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 the 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 time scale. Since long transient 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 time scale of experiment/observation to the thixotropic time scale. Collating the mutation number and the Mnemosyne number, we can construct a general two-dimensional map that helps understand thixotropic behavior. We quantify these ideas using several of the simplest canonical thixotropic models available in the literature.

中文翻译：

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Mnemosyne 数和记忆流变学

Deborah 数的概念广泛用于粘弹性材料的研究，以表示材料弛豫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，这种结构无助于量化在更复杂的时变系统中经常观察到的长瞬变和非单调应力跳跃的重要性。许多这些非直观的影响统称为触变性。但是，没有专有名词与在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是九位缪斯的母亲和记忆女神。因此，我们建议将 Mnemosyne 数定义为触变时间尺度和施加的变形率的无量纲乘积。因此，Mnemosyne 数是与触变时间尺度相比流动强度的量度。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，它将实验/观察的时间尺度与触变时间尺度进行比较。整理突变数和 Mnemosyne 数，我们可以构建一个有助于理解触变行为的通用二维图。