Understanding Rheological Models in Food Science
Rheological models are mathematical equations that describe how food materials respond to applied forces (stress, strain, shear). When we squeeze, stir, pump, or chew a food, we are applying forces on it. The food either flows (like honey), resists (like dough), or breaks (like biscuits). Rheological models are equations that capture this behavior in numbers.
- Stress: Force applied per unit area (e.g., pressing ketchup out of a bottle).
- Strain: Deformation the food undergoes (e.g., stretching of dough).
- Shear: Relative motion between layers of the food (e.g., stirring honey with a spoon).
Examples Tomato ketchup does not flow easily until shake or squeeze the bottle. A Bingham plastic model describes this by saying it has a “yield stress” that must be overcome before it starts flowing. Bread dough stretches when pulled. This is because dough has both elastic (spring-like) and viscous (flow-like) properties, which can be modeled using the Maxwell model.
Rheological models help engineers simplify complex food behaviors into equations, predict how food will flow or deform in new situations, and control industrial processes to get the desired quality (Whether it’s ketchup that pours just right, yogurt that holds its body, or chocolate that flows smoothly in production).
- Simplify: We don’t need to test ketchup under every possible stirring speed. If we fit ketchup data to the Power Law model, we only need two parameters: consistency (K) and flow index (n). These two values can describe its entire flow curve.
- Predict: Once we know the model, we can predict how the food will behave under new conditions. Example: A chocolate manufacturer can predict if chocolate will flow smoothly in narrow pipes during coating, just by knowing its Casson model parameters. (The Casson model is a rheological model that describes the flow of suspensions containing dispersed particles, especially when the fluid shows a yield stress and shear-thinning behavior. It is standard model used by the chocolate industry to describe flow during pumping, coating, and enrobing (coating a food product with a thin, even layer of chocolate)
- Control: Food industries adjust formulations and processes to control flow behavior. Example: Ice cream manufacturers add stabilizers (gums) to ensure it doesn’t melt too quickly but still scoops smoothly.
Understanding Rheological Models in Food Science
Why So Many Models?
When we talk about food, we are not dealing with one single type of material. Foods can behave like simple liquids, thick pastes, soft solids, or even a mixture of all three at the same time. Because of this wide diversity, no single rheological model can describe the behavior of all foods. Engineers and scientists use different mathematical models depending on how a particular food reacts to applied forces.
Everyday examples:
- Milk flows like water: When you pour milk, it flows freely at a constant speed. Its viscosity (resistance to flow) does not change whether you stir it fast or slow. Such foods are described by the Newtonian model, which is the simplest flow model.
- Ketchup needs shaking before it flows: We’ve all had the experience of turning a ketchup bottle upside down and nothing comes out until we hit or squeeze it. This happens because ketchup has a yield stress—a minimum force that must be applied before it starts flowing. This kind of behavior is captured by the Bingham plastic model.
- Bread dough is springy yet sticky: When you pull dough, it stretches like a rubber band (elastic), but at the same time it also flows slowly (viscous). This combined behavior is called viscoelasticity. To describe such foods, scientists use viscoelastic models like the Maxwell or Kelvin–Voigt models. They are spring–dashpot models (spring = elasticity, dashpot = viscosity).
Understanding Rheological Models in Food Science
In Maxwell model, spring and a dashpot connected in series. Under a sudden force (stress), the spring stretches immediately (elastic response), and then the dashpot flows slowly (viscous response). This model is good at describing stress relaxation (stress decreases with time when a material is held at constant strain). To see how stress relaxation works in practice, let’s look at bread dough.
Imagine stretching bread dough to a fixed length and then just hold it there (no more pulling). At the beginning, the dough pushes back strongly (resisting the stretch). But if you keep holding it at the same length, after some time the force you feel reduces; the dough slowly “relaxes” its stress. This decrease in resistance (stress) over time, while strain (stretch) is constant, is called stress relaxation. Maxwell model cannot explain creep (slow deformation under constant stress) very well.
In Kelvin–Voigt Model, a spring and a dashpot are connected in parallel. When stress is applied, the spring resists instant deformation while the dashpot slows down the strain. This model is good at describing creep behavior (time-dependent deformation under constant stress). This can be better understood with the example of a cheese block.
Imagine you put a block of cheese on the table and hang a small weight on it. The cheese does not suddenly stretch a lot (because the spring part resists the force). But if you keep the weight there, the cheese will slowly sag and stretch more and more with time (this is the dashpot effect, called creep). Now, if you remove the weight, the cheese will partly return back to its original shape (because of the spring).
So, the Kelvin–Voigt model explains why foods like cheese or dough don’t instantly deform but instead slowly change shape under load, and then bounce back a little when the load is gone. When stress is removed, the spring pulls the material back.
In nutshell, both Maxwell and Kelvin–Voigt models help us understand the time-dependent behavior of foods. While the Maxwell model is best suited for explaining stress relaxation (as in bread dough), the Kelvin–Voigt model is better for describing creep (as in cheese). In reality, foods often show both behaviors together, which is why some more advanced models are sometimes used by food rheologists.
Understanding Rheological Models in Food Science
Some of the most commonly used rheological models to describe food behavior are given below.
1. Newtonian & Non-Newtonian Flow Models
- Newtonian Model: Milk, water, oils (constant viscosity).
- Power Law (Ostwald–de Waele Model): Tomato paste, fruit purees, sauces (shear thinning or thickening).
- Herschel–Bulkley Model: Ketchup, mayonnaise, mustard (yield stress + shear thinning).
- Bingham Plastic Model: Ketchup, toothpaste, margarine (flow only after yield stress).
- Casson Model: Chocolate, cocoa suspensions (used in chocolate industry).
2. Viscoelastic Models (spring–dashpot combinations)
- Maxwell Model: As explained above, it is useful in studying stress relaxation in dough, cheese.
- Kelvin–Voigt Model: Creep in cheese, gels.
- Standard Linear Solid Model (Zener Model): Better description of both creep & stress relaxation (used for bread dough, gels).
- Burger’s Model (Maxwell + Kelvin–Voigt): Describes creep and recovery in starch gels, dairy gels, pasta dough.
In short: Newtonian is used for simple fluids, Power Law for shear-dependent fluids, Herschel–Bulkley and Bingham for yield-stress foods, and Casson specifically for chocolate. No single model fits all foods. In the viscoelastic category: Maxwell is ideal for describing stress relaxation, Kelvin–Voigt for creep, Zener for capturing both (a balanced model), and Burger’s is the most realistic for complex food textures.
Test your knowledge with a fun quiz on food rheology: Food Rheology Quiz
