Thixotropy Simulator: Time-Dependent Viscosity & Structural Kinetics

simulator intermediate ~10 min
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λ_eq = 0.001 — nearly fully broken structure at γ̇ = 100/s

At a shear rate of 100/s with k_b = 0.5 and k_r = 0.05, the equilibrium structure parameter is 0.001 — the microstructure is almost completely destroyed, leaving viscosity near its minimum value.

Formula

dλ/dt = k_r × (1 − λ) − k_b × γ̇ × λ
η(λ) = η_∞ + (η₀ − η_∞) × λ
λ_eq = k_r / (k_r + k_b × γ̇)

Viscosity That Remembers

Shake a bottle of ketchup and it pours freely; set it down and it thickens back to a gel within seconds. This time-dependent flow behavior — thixotropy — arises because the material possesses an internal microstructure (particle networks, droplet clusters, or polymer entanglements) that breaks down under shear and rebuilds at rest. Unlike simple shear-thinning, thixotropy carries a memory of deformation history, making it one of the most challenging phenomena in rheology to model accurately.

Structural Kinetics

The most intuitive modeling framework uses a structure parameter λ (ranging from 0 to 1) to track the fraction of intact microstructure. Shearing breaks structure at a rate proportional to both shear rate and current structure level, while thermal Brownian motion drives recovery. The competition between these two processes determines the transient and equilibrium viscosity. This simulation solves the kinetic equation in real time and visualizes λ evolving as you toggle shear on and off.

Hysteresis Loops

A classic experimental signature of thixotropy is the hysteresis loop: ramp shear rate up, then back down, and plot stress versus shear rate. The down-curve falls below the up-curve because the microstructure was progressively destroyed during the ramp-up and has not yet recovered during the ramp-down. The area enclosed by the loop quantifies the degree of thixotropy and depends on the ramp rate relative to the breakdown and recovery time scales.

Formulation Science

Thixotropy is deliberately engineered into consumer and industrial products. Paint formulators add associative thickeners that build structure at rest (preventing sagging) but break down under brush shear (enabling smooth application). Drilling engineers tune bentonite clay concentrations to achieve rapid gelation (suspending cuttings) with low plastic viscosity (minimizing pumping power). Understanding and controlling thixotropic kinetics is the key to balancing opposing performance requirements in complex fluids.

FAQ

What is thixotropy?

Thixotropy is the time-dependent decrease in viscosity under constant shear, followed by gradual recovery when shearing stops. Unlike simple shear-thinning (which is instantaneous), thixotropy involves actual microstructural breakdown and rebuilding over time. Common thixotropic materials include paints, ketchup, yogurt, and drilling muds.

How is thixotropy different from shear-thinning?

Shear-thinning is an instantaneous, reversible drop in viscosity with increasing shear rate. Thixotropy adds a time dimension: at a fixed shear rate, viscosity continues to decrease as structure breaks down, and it takes time to recover at rest. A hysteresis loop in a shear-rate ramp test is the hallmark of thixotropy.

What is the structure parameter lambda?

Lambda (λ) is a scalar between 0 and 1 representing the fraction of intact microstructure. λ = 1 means fully structured (maximum viscosity), λ = 0 means completely broken down (minimum viscosity). Its evolution follows a kinetic equation balancing breakdown (proportional to shear rate) and recovery (a rest-driven process).

Why does thixotropy matter in industry?

Paint must be thin enough to brush (broken structure) yet thick enough not to drip (recovering structure). Drilling mud must flow during circulation but gel at rest to suspend cuttings. Ketchup must flow when shaken but stay on a plate. Thixotropy controls all these behaviors, and proper modeling prevents costly formulation failures.

Sources

Embed

<iframe src="https://homo-deus.com/lab/rheology/thixotropy/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub