Casson Model Explained: Two Numbers for Chocolate Flow

Two chocolates can look equally thick in a bowl yet behave differently when pumped or spread into a thin shell. The Casson model helps describe that difference with two fitted numbers: yield value and plastic viscosity. It is a useful model for many molten chocolates, rather than a law that every recipe follows exactly.

For a maker, its main lesson is practical: record how a batch behaves under consistent conditions before deciding whether to change the ingredients, processing, or temperature.

What Makes Chocolate Non-Newtonian?

Molten chocolate contains solid particles—such as sugar, nonfat cocoa material, and milk solids—dispersed in a continuous fat phase that includes cocoa butter. Its apparent viscosity commonly decreases as shear rate increases. In other words, the resistance measured during gentle movement can differ from that measured during faster deformation.

Chocolate is often modeled as a material with yield stress. Calling it a Bingham plastic and then applying the Casson equation mixes up two different mathematical models. Above its yield threshold, an ideal Bingham model has a linear stress–shear-rate relationship; the Casson relationship is curved on those ordinary axes. Both have been investigated for chocolate, along with models such as Herschel–Bulkley. Afoakwa and colleagues’ model comparison discusses these alternatives.

Particle contacts, adhesion, packing, and friction help explain the resistance to flow. A fitted Casson yield value should not be mistaken for a direct measurement of one particular molecular bond or of the force needed to pull chocolate off a spatula.

Reading the Casson Equation Correctly

For the flowing branch of the model:

√τ = √τ₀ + √(η_ca × γ̇)

The quantities are:

• τ: shear stress, measured in pascals (Pa), or force per unit area.
• τ₀: fitted Casson yield value, also in Pa.
• η_ca: Casson plastic viscosity, in Pa·s.
• γ̇: shear rate, in inverse seconds (s⁻¹).

Plot the square root of stress against the square root of shear rate, and the equation gives a straight line. The intercept is √τ₀ and the slope is √η_ca. Square those two fitted values to recover the Casson parameters. On an ordinary stress-versus-shear-rate plot, the model is not a straight line with constant slope η_ca.

Plastic viscosity is also not the actual viscosity at every speed once flow begins. The apparent viscosity at a particular shear rate is τ divided by γ̇; in this model it approaches η_ca as shear rate becomes very large.

As an arithmetic illustration, suppose a fitted model has τ₀ = 4 Pa and η_ca = 1 Pa·s. At 1 s⁻¹ it predicts stress of 9 Pa and apparent viscosity of 9 Pa·s. At 100 s⁻¹ it predicts 144 Pa and 1.44 Pa·s. These are invented model parameters for explaining the equation, not measurements or recommended chocolate specifications.

Measurement Conditions Belong Beside the Numbers

A Casson result is incomplete without the test temperature, sample preparation, instrument geometry, shear history, and fitting range. The extrapolated yield value is especially sensitive to the method and data being fitted.

A current NETZSCH application study measures two chocolates at 40°C, after melting and homogenizing them, with controlled pre-shear and upward and downward shear-rate ramps. It fits Casson curves over 5–50 s⁻¹. That is an example of a defined laboratory procedure, not evidence that simply warming any chocolate to 40°C produces a standardized result.

An international inter-laboratory trial published in 2000 found much better agreement from direct shear-stress measurements than from the calculated Casson parameters. It helped lead to the revised IOCCC method. Casson analysis remains in use, as the NETZSCH example shows, but there is no universal promise that it describes every craft chocolate within a few percent.

A laboratory measurement of fully molten chocolate also does not directly describe a tempering bowl containing cocoa butter crystals. Treat the two situations separately.

Fat and Particle Size Work Together

Adding cocoa butter generally makes a chocolate suspension more fluid by reducing the concentration of solid particles relative to the continuous fat phase. The amount needed depends on the original recipe and the intended application. There is no universal progression in which 28% fat means paste, 32% means workable, and 36% means ideal enrobing chocolate.

In Afoakwa and colleagues’ dark-chocolate experiment, the researchers varied fat, lecithin, and particle-size distribution. All three affected the rheological measurements and interacted with one another. Fat had the largest effect on variability in that experiment. Increasing particle size reduced several measures of resistance to flow, but the size effect depended on the other ingredients.

Finer grinding often increases surface area and changes how much fat is needed for acceptable flow. However, a narrow distribution is not automatically better than a broad one. A 2020 model-chocolate study found that suitable mixtures of fine and coarse particles could pack more efficiently and lower viscosity. Its result depended on the size ratio, mixture proportions, and solids concentration.

This is why one average particle size—or a largest-particle estimate from a grindometer—cannot specify the whole flow behavior. Nor does “couverture” identify one universal fat percentage or one fluidity suitable for every job.

Lecithin and PGPR Are Different Formulation Tools

Lecithin can reduce viscosity, but it does not reliably lower yield value in every recipe or at every dose. A 2024 study of an industrial 48% cocoa chocolate began with a formula already containing 0.3% lecithin and 0.2% PGPR. Further lecithin additions reduced plastic viscosity until approximately 0.5–0.6% total lecithin, after which it leveled off; fitted yield stress increased over the tested lecithin range.

That finding is a useful warning against a universal U-shaped dose curve or a fixed “ten times better than cocoa butter” substitution rule. It is not a recommendation to reproduce that dose in a different chocolate.

PGPR can reduce yield stress strongly, as the same study found, but it is not interchangeable with lecithin. Choose food-grade ingredients suitable for the product and follow the supplier’s formulation guidance and applicable rules. A research concentration or a slider’s maximum is not a universal legal limit.

Keep track of total emulsifier already present, not just the addition. For percentage calculations, 0.3% of a final 1,000 g formula is 3 g. Adding 3 g to an existing 1,000 g batch instead makes a 1,003 g batch; the new addition is approximately 0.299% of the result. The recipe formulation guide explains ingredient accounting.

Moisture, Conching, and Temperature Need Their Own Checks

Moisture: Small accidental water additions can thicken melted chocolate and produce clumps. Keep utensils and molds dry and account for water-bearing additions. The amount that causes trouble depends on the chocolate and mixing conditions; there is no universal droplet size or 0.1% failure threshold. Chocolate formulated with enough liquid can become a sauce or ganache, which is a different product. King Arthur’s water-and-chocolate demonstration illustrates this distinction.

Conching: Conching can improve flow through physical changes as well as moisture removal. A 2019 experiment using a simplified chocolate formulation identified aggregate breakdown and changes in particle interactions during mechanical mixing and staged dispersant addition. More elapsed time alone does not guarantee a continuing decrease in yield value. Follow the machine’s operating instructions and compare samples at a consistent temperature; do not assume “run lid-off longer” diagnoses every thick batch.

Fat additions: When testing additional cocoa butter, weigh the change and assess both the processing behavior and the finished bar. Five grams added to an existing kilogram is approximately 0.498% of the new batch. It is not a guaranteed sensory improvement. Ingredient-addition order depends on the process: Cacao Barry’s manufacturing overview describes adding cocoa butter after hours of conching to adjust fluidity, so adding all of it at the start is not universally preferable.

Temperature and crystals: A chocolate that thickens during tempering may be overcrystallized. Callebaut explains that crystal content can increase even at the intended working temperature. Use the product’s tempering guidance; a laboratory flow test at 40°C is not a depositing-temperature recommendation.

Use the Model to Compare Batches

For practical comparisons, hold the recipe and handling conditions steady, then change one factor at a time. Record ingredient amounts, processing history, sample temperature, and what happened during the same pouring or molding task. This can identify useful differences without pretending that a spoon test measures τ₀ or η_ca.

A waxy mouthfeel, a bar stuck in its mold, or chocolate dragging in a tempering machine does not identify one Casson parameter as the cause. Check crystallization and handling as well as formulation. The viscosity troubleshooting guide covers related checks, while flavor chemistry concerns another part of the finished eating experience.