The Mnemosyne number and the rheology of remembrance

Abstract

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.

Microscale Flows of Thixotropic Liquids

“…When the residence time is much larger than the liquid characteristic time, the material has enough time to recover its equilibrium state at every point and the viscosity is only a function of the local deformation rate. This is the same behavior discussed by Jamali and McKinley [68], which show that pronounced thixotropic and hysteretic effects occur at intermediate values of the mutation number (reciprocal of the thixotropy number used here).…”

“…This is the inverse of the Mutation number M u, defined by Mours and Winter [67] and discussed in detail by Jamali and McKinley [68].…”

“…The results clearly show that the need to consider time-dependent effects on an accurate flow model depends not only on the ratio of the characteristic time of the liquid to the residence time of the flow, characterized here by the thixotropy number Λ, but also to the strength of the flow, represented here by the dimensionless wall stress. The dependence of the thixotropic behavior both on the strength and the duration of the shearing history was discussed in detail by Jamali and McKinley [68]. They constructed a general two-dimensional map of thixotropic behavior.…”

A rheologist's guideline to data-driven recovery of complex fluids' parameters from constitutive models

“…As noted in Larson's reviews, 11,12 thixotropy is far from a mere continuous decrease of viscosity with time (which is also seen for viscoelastic materials) and has to do with the material's memory of the entire ow history. 13,14 Generally, one popular and effective way of modeling thixotropic behavior is through the introduction of a quantitative measure to the material's microstructure. The extent of microstructure breakdown or formation can be approximated through a competition between shearing forces that break down the structure and the natural structuration of the material.…”

Response: Naoko Saito, Finding as Founding: Rejoinder to René Arcilla’s Review, Naoko Saito, Associate Professor of Education at Kyoto University, Japan. Kyoto University, Yoshidahonmachi, Sakyo-ku, Kyoto 606-8501

“…Data-driven methods are powerful approaches for addressing the aforementioned challenges in rheology. Indeed, such methods have enhanced rheological studies such as constitutive modeling, flow predictions of complex fluids, and model selection [22,23]. Some applications have successfully identified constitutive relations of complex fluids or governing equations to predict the dynamics of fluids with knowledge of rheology.…”