Week 2 Module: Rheology I: Flow Behaviour

Research question#

Honey pours the instant you tilt the jar. Doubanjiang (豆瓣酱, fermented broad bean and chilli paste — the base of mapo tofu sauce) sits in the jar under gravity and does not move until you drag a spoon through it. Both are thick pastes. Why does one have a threshold and the other doesn’t, and how do we describe that threshold quantitatively rather than just naming it?

Specimen doubanjiang, fermented broad bean & chilli paste

Where this sits#

Second module of Stage 1, Measuring Edible Matter. Module 1 established that texture properties are measurable; this module gives the first real governing equations — the flow models that the Virtual Rheometer instrument implements, and that Module 10 revisits when fitting models to noisy data.

The models#

Three nested models describe how shear stress τ relates to shear rate γ̇ for a fluid:

τ (shear stress, Pa)

the force per unit area you apply to make the fluid move.

γ̇ (shear rate, s⁻¹)

how fast adjacent layers of the fluid slide past each other.

η (viscosity, Pa·s)

the single stress-to-rate ratio that fully describes a Newtonian fluid — constant at every γ̇.

K (consistency index, Pa·sⁿ)

a scale factor for stress; not directly comparable between fluids with different n.

n (flow behaviour index, dimensionless)

n < 1 is shear-thinning (apparent viscosity drops as you stir harder — most food pastes); n > 1 is shear-thickening (rare in food, common in some starch-water slurries at high concentration); n = 1 recovers the Newtonian case.

τ₀ (yield stress, Pa)

the stress that must be exceeded before any flow starts at all. Doubanjiang's resistance to gravity is exactly τ₀ > (stress gravity applies at rest).

Honey is well described as Newtonian (n = 1, τ₀ = 0): its apparent viscosity is the same whether you stir gently or vigorously. Doubanjiang is better described by the Herschel-Bulkley model: a suspension of bean and chilli solids in a viscous liquid phase forms a weak, jammed solid-like network at rest (giving τ₀ > 0), which breaks down and flows, shear-thinning, once τ₀ is exceeded.

Flow models

3

Yield stress

τ₀ (Pa)

n < 1

shear-thinning

What you measure and analyse#

In the Virtual Rheometer, you set a specimen (doubanjiang, honey, or a dumpling dough with a stronger yield stress), sweep shear rate, and read off the resulting flow curve. You then fit each of the three models to the curve and compare the residual sum of squares — the wrong model (e.g. Newtonian fitted to doubanjiang) visibly fails to track the curve at low shear rate, where the yield-stress plateau appears.

Activity#

Before opening the instrument, sketch by hand what you expect the flow curve (τ vs γ̇) to look like for doubanjiang, honey, and a dumpling dough, on the same axes. Then use the Virtual Rheometer to check your sketch against the fitted curves. Where your sketch disagrees with the fit, say which physical intuition was wrong — most students initially expect a yield stress to show up as a curved line through the origin rather than as a non-zero stress at γ̇ = 0.

References#

• Steffe, J.F. (1996). Rheological Methods in Food Process Engineering, 2nd ed. Freeman Press.
• Walstra, P. (2003). Physical Chemistry of Foods. Marcel Dekker.