# Computational Modeling of Small-Scale Flow of Thixotropic Yield-stress Materials

## Palavras-chave:

Thixotropy, Fluidity, Capillary, Finite Element Method, Avalanche and Construction times## Resumo

Computational modeling of flow of thixotropic yield-stress materials is challenging, because it requires

an accurate model which should be able to describe the break and buildup of the material microstructure. Tradi-

tionally, thixotropic flows have been modeled by using very empirical equations which have a very restricted range

of feasibility. Alternatively, in the present work, it is used a novel fluidity-based constitutive model that involves no

postulated functions or parameters. Instead of using empirical parameters, this model involves measurable material

functions whose parameters are obtained from data of standard experiments. Likewise it is more appropriate to

describe the behavior of thixotropic material flows. In addition, the model assumes a one-to-one correspondence

between the fluidity (i.e., the reciprocal of viscosity) and the microscopic state.

A numerical model of thixotropic yield-stress materials flowing through a capillary with a constriction is

presented here. The complex flow is governed by the continuity and momentum equations coupled with two

additional equations. One is a scalar evolution equation of fluidity while the other is a tensorial equation. The

latter relates stress and strain rate. The system of equations was solved by using the Galerkin and Petrov-Galerkin

/ Finite Element Method.

The results show how fluidity , which represents the internal microstructure level, and velocity of thixotropic

yield-stress liquids change inside the capillary. Both velocity and fluidity are a function of the flow behavior index,

the yield stress and two material properties associated with different thixotropic characteristic-time scales: the

avalanche time and the construction time.