Casson Model Explained: Why Chocolate Needs Two Numbers to Describe Its Flow

Liquid chocolate is a non-Newtonian fluid whose flow is described by the Casson model using two numbers: yield value (the minimum stress to start flow) and plastic viscosity (the resistance once moving). Pour it into a mold at 40 degrees Celsius and it drags, slumps, and holds a slight peak before it settles — behavior that is both the maker’s tool and the maker’s headache. Understanding why requires a short trip into fluid mechanics, where a single equation developed for printer’s ink in 1959 ended up governing almost every chocolate bar on the planet.

This is a science-explainer with practical handles. If you have ever thinned a too-thick batch with cocoa butter, added a pinch of lecithin at the end of a conche, or wondered why a dry day gives you smoother chocolate than a humid one, you have already been working the Casson model by feel.

Chocolate Is a Non-Newtonian Fluid, Not a Thin Liquid

Chocolate is a non-Newtonian fluid, which means its viscosity depends on how hard you push it. Water is Newtonian — stir it faster and it does not get thicker or thinner, it just moves. Chocolate does not play that game.

Specifically, chocolate is classified as a Bingham plastic: it refuses to flow at all until a minimum stress is applied, and then it flows with a viscosity that changes with shear rate. That refusal-to-flow-at-first is why a bar of just-tempered chocolate holds its glossy dome on a spatula for a second before releasing. It is not “thick” in the honey sense. It is structurally stuck.

The reason is the suspension. Liquid chocolate is a dense slurry of solid particles — sugar crystals, cocoa solids, sometimes milk powder — dispersed in a continuous phase of melted cocoa butter. Those particles are touching, lightly bonded, and electrostatically sticky. Before the fluid can flow, those bonds have to break.

The Casson Equation Describes Chocolate in Two Numbers

The Casson model captures chocolate’s flow behavior with a simple square-root relationship:

√τ = √τ₀ + √(η_ca × γ̇)

Here τ is the shear stress applied (how hard you are pushing), τ₀ is the Casson yield value (the minimum push required to start flow), η_ca is the Casson plastic viscosity (the resistance once it is flowing), and γ̇ is the shear rate (how fast you are making it move). Plot shear stress against shear rate and chocolate traces a curve that intercepts the y-axis at a non-zero value — that intercept is τ₀, and the slope past it is governed by η_ca.

In plain English: chocolate needs two numbers to describe it, not one. A thick-tasting bar might actually have low plastic viscosity but sky-high yield value — it fights you at the start of every pour, then runs fine once moving. A runny-feeling chocolate might have almost no yield but high viscosity in motion — it releases easily from a ladle but drags in a moldline.

Industrial labs measure both numbers at 40 degrees Celsius using a rotational rheometer, a standard fixed by Beckett’s Industrial Chocolate Manufacture. That temperature matters. Fat crystallization states change viscosity wildly, and 40 degrees Celsius guarantees cocoa butter is fully liquid, so the measurement captures the suspension — not accidental tempering.

Yield Value Is the Stickiness Number, and It Is Sensitive

The Casson yield value τ₀ is the minimum stress needed to start chocolate flowing, and it is the most temperamental number in a chocolate maker’s life. Four levers move it — lecithin, moisture, particle size, and fat — and they do not move it equally or predictably.

Lecithin is the big one. Soy lecithin at 0.3 to 0.5 percent dramatically lowers yield value by coating sugar crystals and breaking the particle-to-particle bonds that resist flow. It is roughly ten times more efficient than cocoa butter by weight for viscosity reduction, according to Dandelion’s formulation notes. But lecithin is non-linear: push above 0.5 to 0.6 percent and yield value actually starts to increase again — a critical finding documented in Beckett Industrial. More is not better. There is a U-shaped dose response, and passing the bottom of the U costs you.

Moisture is the silent killer. Even 0.1 to 0.5 percent water in a batch dramatically increases yield value, because water dissolves the surface of sugar crystals and glues them together into sticky clumps. This is why conched chocolate aims for under 0.5 percent final moisture, why humid storage ruins liquid chocolate, and why the first drops of water hitting a melter can “seize” a whole bowl. Water is the enemy of flow.

Particle size couples strangely with yield value. Smaller particles mean more total surface area, which means more sugar faces for water and lecithin to interact with and more particle-to-particle contacts to break. A more thoroughly refined chocolate is not automatically smoother to pour. That is one reason particle size distribution — not just mean particle size — matters; a tight 10 to 20 micron distribution often pours better than a mean of 15 microns with a wide spread.

Fat lowers yield value because more continuous phase means particles are farther apart and easier to separate. But fat is expensive in calories, flavor, and formulation — so makers hunt for the minimum fat that gives acceptable flow, then use lecithin to trim the rest.

Plastic Viscosity Is the “Once Moving” Number, Controlled Mostly by Fat

The Casson plastic viscosity η_ca governs how hard chocolate fights you once it is already flowing, and it is mostly a story about total fat, particle size, and temperature. Unlike yield value, plastic viscosity is relatively well-behaved — it responds in fairly linear ways to the levers that move it.

Total fat content is the dominant lever. Chocolate at 28 percent fat is a stubborn paste; at 32 percent fat it is a workable liquid; at 36 percent fat it enrobes beautifully. Every extra gram of cocoa butter lubricates the slurry and drops η_ca. This is why couverture, the chocolate made for enrobing, typically runs 38 percent or more fat — the low viscosity matters more than cost.

Particle size raises plastic viscosity in the same way it raises yield value — more particles per unit volume, more drag. A chocolate refined to 18 microns will flow noticeably thicker than the same formula at 25 microns, all else equal.

Temperature matters because cocoa butter’s viscosity drops as it warms. Industrial chocolate is dosed and molded in the 32 to 45 degree Celsius window, and every degree up makes it thinner. But temperature is a short-term lever — you cannot ship warm chocolate.

The practical consequence is that when a bar feels waxy, heavy, or slow to melt in the mouth, plastic viscosity is often the culprit — and the fix is usually more fat, coarser particle size, or both.

Craft Makers Apply the Casson Model Without a Rheometer

Most craft chocolate makers never measure τ₀ or η_ca directly — a lab rheometer starts at around $15,000 — but they steer both numbers constantly using four tools: conche time, cocoa butter, lecithin, and moisture management.

Conching is the slowest and most transformative viscosity lever. Long conching drops yield value sharply, primarily by driving off moisture (from approximately 1.5 to 2 percent pre-conche to under 0.5 percent post-conche) and by distributing fat more completely around every particle. The rheological takeaway is simple: if your chocolate has ragged flow, run the melanger longer with the lid off. Hours in the conche are hours of yield-value reduction.

Cocoa butter is the brute-force lever. A 5 g/kg addition — just 0.5 percent — noticeably drops plastic viscosity and gives the bar a richer release in the mouth. Adding cocoa butter at the start of a melanger run integrates better than a late addition; the fat has time to coat every newly-created particle surface. Use it when the bar tastes “short” or feels dry, not just when it pours thick.

Lecithin is the precision lever. Doses in the 0.01 to 0.05 percent range already show measurable viscosity drops; 0.3 to 0.5 percent is the industrial sweet spot. Remember the U-curve — the recipe formulation guide lays out the dose math alongside PGPR, which attacks yield value specifically and is effective down to under 0.5 percent.

Moisture discipline is the cheapest lever. Drying beans properly, storing nibs below 65 percent relative humidity, keeping melangers and molds bone-dry, and never adding water-bearing ingredients (fresh fruit, unstabilized extracts) mid-process. When a batch turns thick mid-run for no obvious reason, the first suspect is always water. Our viscosity troubleshooting guide walks the full decision tree — and moisture is the first question it asks.

The Casson Model Has Limits, and Modern Chocolate Is Pushing Them

The Casson equation was published by N. Casson in 1959 for printer’s ink, and it has governed chocolate rheology ever since because it fits cleanly at the shear rates real chocolate experiences during pumping, molding, and enrobing — roughly 5 to 50 inverse seconds. Outside that window, the model frays.

At very high shear rates — the kind you see in industrial depositing nozzles or high-speed enrobers — chocolate shear-thins more aggressively than Casson predicts, and producers often fit to the Windhab or Herschel-Bulkley model instead. At very low fat content (under approximately 28 percent for dark chocolate), the suspension is so crowded that particle jamming dominates and Casson under-predicts the true yield. And for very fine-ground chocolate (below 10 microns), surface-area effects push yield value into regions where simple two-parameter fits break down.

For any craft bean-to-bar maker operating in the normal cocoa-butter and particle-size ranges, none of this matters in practice. The Casson model will describe your chocolate within a few percent, and the four levers above — conche, fat, lecithin, moisture — are the only handles you have anyway. The equation is a useful way of organizing intuition, not a prediction engine you run every batch.

What the model really buys you is the realization that chocolate’s flow is two distinct problems — the stickiness at rest and the drag in motion — with overlapping but not identical fixes. Once you see the two numbers, you stop chasing “thickness” as one thing. A bar that will not release from a mold has a yield-value problem. A bar that drags in the tempering machine has a viscosity problem. The lever you reach for should match the number you are moving.

For more on the flavor compounds that emerge during processing, or the crystal polymorphism that makes tempered chocolate behave differently from untempered, those guides connect the rheology story to the bigger picture of what makes chocolate work.