Thixotropic Fluids

In thixotropic flow, viscosity decreases continuously with time when flow is applied to a sample that has been previously at rest. Viscosity is recovered when the flow is discontinued.

Thixotropic effects are found in many industrial processes such as the processing of metals, minerals, paper and pulp, polymer, food, pharmaceuticals, and ceramics, or when using products such as coatings and paints, gels, inks, drilling muds, or concrete. Thixotropic fluids have an underlying microstructure that reversibly breaks down under shear flow and rebuilds when the flow ceases.

Simcenter STAR-CCM+ uses two structure-based scalar models to calculate the thixotropic response of materials to flow. These models use a parameter $λ$ to represent the degree of structure. The kinetic equations describe the evolution of $λ$ with time and shear conditions. These kinetic equations determine buildup or breakdown of the suspension microstructure from the flow shear. In the limit of very high shear rates, the microstructure in a thixotropic suspension goes to zero (that is, $λ = 0$ ), which represents a state of complete microstructural breakdown. When flow stops, the microstructure rebuilds through processes such as Brownian motion.

Generic Kinetic Model

The general form of this evolutionary equation can be given as:

Figure 1. EQUATION_DISPLAY

\frac{\partial^{} λ}{\partial t^{}} + v \cdot \nabla λ = - k_{1} {\dot{γ}}^{a} λ^{b} + k_{2} {\dot{γ}}^{c} {(1 - λ)}^{d}

(728)

where:

$k_{1}$ and $k_{2}$ are the kinetic rate constants for breakdown and buildup of structure.
The exponenets $a$ , $b$ , $c$ , and $d$ are model parameters.

Irreversible Structural Breakdown Model

In this model, the governing equation for structure parameter $λ$ can be written as:

Figure 2. EQUATION_DISPLAY

\frac{\partial^{} λ}{\partial t^{}} + v \cdot \nabla λ = - k {\dot{γ}}^{e} {(λ - λ_{s s})}^{f}

(729)

where:

$k$ is the kinetic constant.
The exponents $e$ and $f$ are model parameters.
$λ_{s s}$ is the steady state value of the structure parameter.

Notice this equation can be used when the breakdown of structure is partially or fully irreversible.

Apparent Viscosity

The viscosity of a thixotropic fluid is modified by the structure parameter $λ$ through the thixotropic factor, which accounts for time-dependent effects. The apparent viscosity of a thixotropic fluid is defined according to:

Figure 3. EQUATION_DISPLAY

μ_{a} (\dot{γ}, t) = κ μ

(730)

where $μ$ is the dynamic viscosity of the structured fluid (when $λ = 1$ ). The dynamic viscosity $μ$ can be constant or depend on the shear rate. Any of the shear-rate dependent viscosity functions of Eqn. (699) to Eqn. (701) can be applied. $κ$ is the thixotropic factor, which is defined according to a power law relation:

κ = λ^{n}

where the exponent $n$ is a model parameter.

Constitutive Equation

The stress tensor is calculated as:

T = 2 μ_{a} D

where $D$ is the rate-of-deformation tensor.