Viscosity & Rheology Simulator

The core concept is the relationship between shear stress ($\tau$) and shear rate ($\dot{\gamma}$). For Newtonian fluids, this is a simple linear law defined by a constant viscosity ($\mu$).

Here, $\tau$ is the shear stress [Pa], $\mu$ is the dynamic viscosity [Pa·s], and $\dot{\gamma}$ is the shear rate [1/s]. This is the baseline behavior of fluids like water and air.

Non-Newtonian models introduce a variable "apparent viscosity" ($\eta(\dot{\gamma})$). A common and powerful model is the generalized Newtonian fluid formulation, where the stress is still proportional to shear rate, but the proportionality factor changes with flow conditions.

The function $\eta(\dot{\gamma})$ defines the rheology. For example, the Power Law model is $\eta = K \dot{\gamma}^{\,n-1}$, where $K$ is consistency and $n$ is the flow index. If $n \lt 1$, the fluid thins with shear (shear-thinning); if $n \gt 1$, it thickens (shear-thickening).

Food Processing: Designing pumps and pipes for products like yogurt, mayonnaise, or chocolate requires precise rheology models. A shear-thinning fluid like ketchup needs different handling than a Newtonian fluid like cooking oil to ensure consistent filling and packaging.

Polymer Processing & 3D Printing: Molten plastics are strongly shear-thinning. Accurate rheology data is critical for simulating injection molding or extrusion processes to predict flow into molds and ensure part quality without defects.

Drilling Mud in Oil & Gas: Drilling muds are often modeled as Bingham plastics. They must have a yield stress to suspend rock cuttings when circulation stops, but flow easily when pumped. CAE simulations of wellbore hydraulics rely on these models for safety and efficiency.

Biomedical Flows: Blood is a complex non-Newtonian fluid, exhibiting shear-thinning behavior. Understanding its rheology is vital for simulating blood flow in arteries, designing heart assist devices, and developing diagnostic equipment.

When you start using this tool, there are a few common pitfalls to watch out for. The first is thinking that the power-law exponent 'n' alone tells you everything about the fluid's properties. It's true that n<1 indicates shear-thinning, but that only means there's "a tendency for viscosity to decrease as shear rate increases." Real materials, like polymer melts, often deviate from the power law at extremely low or high shear rates. Try comparing n=0.3 and n=0.8 in the tool. The trends are similar, but the way viscosity drops is completely different, right? In practice, it's rare for a single model to fit all measured data points; sometimes you need to switch models for different shear rate regimes.

The second point is the interpretation of the Reynolds number. The tool calculates it assuming pipe flow, but this value is only a "guideline." For instance, a Reynolds number exceeding 2300 doesn't guarantee turbulent flow. It varies greatly with channel geometry and inlet conditions. Use it as preliminary information for choosing CFD meshing or analysis methods, nothing more.

Finally, avoid simplistically equating Bingham fluids with ketchup. While ketchup does have a yield stress, it also has strong time-dependent (thixotropic) behavior. The tool's Bingham model is a highly idealized model that "behaves like a Newtonian fluid once it starts flowing." The real thing is more complex; it can solidify again after being stirred and left to stand. The tool teaches you the entry point to the concept of "yield stress." Keep in mind that actual product design often requires more complex models.