Turbulent Pipe Flow of Thixotropic Fluids

TL;DR

This study uses direct numerical simulations to explore the complex interplay between microstructure, rheology, and turbulence in thixotropic fluids flowing through pipes, revealing that their behavior can be approximated by generalized Newtonian models across various kinetics.

Contribution

It introduces a stochastic modeling approach for thixotropic turbulence, demonstrating the validity of generalized Newtonian analogues for different thixotropic kinetics.

Findings

Intermediate thixotropic kinetics are governed by a path integral of the fading memory kernel.

Effective viscosity closure matches fully thixotropic model within 2.4% error at b1=1.

Purely viscous analogues persist across all thixotropic timescales.

Abstract

Complex materials with internal microstructure such as suspensions and emulsions exhibit time-dependent rheology characterized by viscoelasticity and thixotropy. In many large-scale applications such as turbulent pipe flow, the elastic response occurs on a much shorter timescale than the thixotropy, hence these flows are purely thixotropic. The fundamental dynamics of thixotropic turbulence is poorly understood, particularly the interplay between microstructural state, rheology, and turbulence structure. To address this gap, we conduct direct numerical simulations (DNS) of fully developed turbulent pipe flow of a model thixotropic (Moore) fluid over a range of thixoviscous numbers $\Lambda$ from slow ($\Lambda\ll 1$) to fast ($\Lambda\gg 1$) thixotropic kinetics relative to the eddy turnover time. Analysis of DNS results in the Lagrangian frame shows that, as expected, in the limits of slow and fast kinetics, these time-dependent flows behave as time-independent purely viscous (generalized Newtonian) analogues. For intermediate kinetics ($\Lambda\sim 1$), the rheology is governed by a \emph{path integral} of the thixotropic fading memory kernel over the distribution of Lagrangian shear history, the latter of which is modelled via a simple stochastic model for the radially non-stationary pipe flow. DNS computations based on this effective viscosity closure exhibit excellent agreement (within 2.4\% error) with the fully thixotropic model for $\Lambda=1$, indicating that the purely viscous (generalized Newtonian) analogue persists for arbitrary values of $\Lambda\in[0,\infty^+)$ and across nonlinear rheology models. These results uncover the feedback mechanisms between microstructure, rheology, and turbulence and offer fundamental insights into the structure of thixotropic turbulence.