This model is sometimes referred to as the Ostwald-de Waele relationship model. The Power Law model is perhaps the most commonly used of the three, and is used to capture the behavior of Dilatant and Pseudoplastic fluids. These three models are perhaps the three most commonly used, and together capture almost the entire range of non-Newtonian behavior. We will discuss the three major models: the Power Law model, the Bingham Plastic model, and the Herschel-Bulkley model. Numerous models exist to capture the real behavior of non-Newtonian fluids. How to Model Non-Newtonian Fluids Mathematically A Bingham Pseudoplastic fluid has a yield stress, but also decreases in viscosity as it shears at higher rates. Small amounts of force applied to the fluid will not deform the fluid, but once enough force is applied, the fluid can deform and flow like any fluid without a yield stress. Toothpaste and peanut butter are examples of fluids with a yield stress. The Bingham Plastic and Bingham Pseudoplastic fluids both have a yield stress associated with them. Oobleck (the mixture of cornstarch and water) and paint are examples of Dilatant and Pseudoplastic fluids, respectively. A Pseudoplastic fluid starts shearing as soon as any force is applied to it, then decreases in viscosity as it shears at a higher rate. A Dilatant fluid begins to shear immediately, then thickens as it shears at a higher rate. For each type of fluid, the plotted curve describes the force required to shear the fluid at a given rate.įigure 1, above, shows the general behavior of each type of non-Newtonian fluid. Time-dependent viscosity is a fascinating field of study, though as it falls outside the scope of most engineering applications, we will ignore this subset of fluid types.Ī figure many readers may be familiar with is shown in Figure 1 below, plotting shear stress (τ) against shear rate (γ) for the types of non-Newtonian fluids mentioned above. Non-Newtonian fluids even include those whose viscosity depends on the shear rate history of the fluid, meaning the viscosity changes as the fluid is deformed at a constant rate. Types of non-Newtonian fluids include dilatants, pseudoplastics, Bingham plastics, and Bingham pseudoplastics. A Newtonian fluid on the other hand, is a fluid where the viscosity is constant across any rate of deformation. If viscosity is defined as the resistance a fluid has to deformation, then a non-Newtonian fluid is one whose resistance to deformation depends on the speed at which that deformation is occurring. For engineers though, it is important to understand the science and math behind non-Newtonian fluids in order to accurately model how they will behave in a pipe network.Īs we discuss non-Newtonian fluids here, we will cover three major topics: what it means for a fluid to be non-Newtonian, how non-Newtonian fluids are modeled mathematically, and how AFT software models non-Newtonian fluids.Ī non-Newtonian fluid is a fluid whose viscosity is dependent on the instantaneous shear rate of the fluid. The Discovery Channel show Mythbusters even showed Adam Savage walking across a tub of cornstarch and water.įor young students, knowing that the liquid acts like a solid when impacted is enough to satisfy their curiosity. Mixing cornstarch and water to create a liquid that acts as a solid is an experiment which has captured the attention of children (and adults) for generations. Non-Newtonian fluids are something almost every elementary school student is familiar with.
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