The Mnemosyne number and the rheology of remembrance

The concept of a Deborah number is widely used in study viscoelastic materials and to represent the ratio material relaxation time timescale observation, demarcate transitions between predominantly viscous or elastic responses. However, this construct does not help quantify importance long transients non-monotonic stress jumps that are often observed more complex time-varying systems. Many these non-intuitive effects lumped collectively under term thixotropy; however, no proper nouns associated with key phenomena such materials. Thixotropy arises from ability structured fluid remember its prior deformation history, so it natural name dimensionless group representing behavior respect remember. In Greek mythology, Mnemosyne was mother nine Muses goddess memory. We thus propose definition as product thixotropic scale imposed rate deformation. measure flow strength compared timescale. Since responses endemic materials, one also needs consider duration flow. relevant can be represented terms mutation which compares experiment/observation Collating number, we general two-dimensional map behavior, ideas using canonical models.