The Mnemosyne Number and the Rheology of Remembrance

TL;DR

This paper introduces the Mnemosyne number, a new dimensionless parameter to quantify thixotropic memory effects in complex fluids, and develops a two-dimensional map of thixotropic behavior based on this and the mutation number.

Contribution

It proposes the Mnemosyne number as a novel measure of memory in thixotropic materials and constructs a two-dimensional behavior map using this and the mutation number.

Findings

The Mnemosyne number effectively characterizes thixotropic memory effects.

A two-dimensional map of thixotropic behavior is developed.

Canonical models validate the proposed framework.

Abstract

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.