3. Rheological Behavior of Fluids

Summary

This script explores the complex behavior of non-Newtonian fluids, contrasting them with Newtonian fluids through various experiments. It delves into the concept of rheology, the study of deformation in response to force, and highlights how non-Newtonian materials, such as high polymer solutions, exhibit unique properties like memory, nonlinearity, and yield stress. The video demonstrates how these fluids can bounce like solids, support weight, and display shear thinning or thickening behavior, challenging traditional fluid dynamics models and showcasing their practical implications in industries like food processing and manufacturing.

Takeaways

• 🔍 Rheology is the study of the relationship between force and deformation in continuous media, with a focus on fluids in this script.
• 🌊 The concept of an inviscid fluid is introduced, where there are no shear stresses and pressure is isotropic.
• 📚 The Navier-Stokes equation is derived from the stress-deformation relation for Newtonian fluids, which are independent of the observer.
• 🚫 Traditional models are inadequate for materials with large molecules, such as high polymer solutions, which exhibit non-Newtonian behavior.
• 🔨 The script demonstrates a high polymer solution's ability to support a shearing stress up to a critical yield value, highlighting non-Newtonian characteristics.
• 🔄 The memory fluid model is presented as a more general model that accounts for the history of deformation, showing nonlinear stress functions.
• 🧪 Experiments are conducted to show that stress in viscoelastic materials depends on the history of deformation, with examples like honey and high polymer solutions.
• 📉 The script explains how nonlinearity in non-Newtonian fluids affects both shear and normal stresses, leading to unique flow behaviors.
• 📈 Pseudoplastic or shear-thinning behavior and dilatant or shear-thickening behavior are described, showing how viscosity changes with flow rate.
• 🌀 Non-Newtonian fluids can exhibit normal stress differences, leading to phenomena like climbing up a rotating shaft, different from Newtonian fluids.
• 🛠️ The script concludes with complex flow experiments, such as extrusion and rotational flow, to illustrate the unique characteristics of non-Newtonian fluids.

Q & A

What is rheology in the context of this script?

Rheology, in the broadest sense, is the study of the relationship between force and deformation in continuous media. In this script, the focus is specifically on fluids.

What is the basic assumption behind the stress-deformation relation in the model of an inviscid fluid?

In the model of an inviscid fluid, the basic assumption behind the stress-deformation relation is that there are no shear stresses, or equivalently, that the pressure is isotropic.

What is the significance of the Navier's Stokes equation in the context of fluid dynamics?

Navier's Stokes equation is significant as it is derived from the stress-deformation relation for a Newtonian fluid and the momentum equations. It helps in understanding the motion of viscous fluid substances.

What is a Newtonian fluid and how does it behave?

A Newtonian fluid is a fluid in which the shear stress is linearly related to the rate of shear strain. It has no shear stresses with no relative motion, and the pressure is isotropic. However, in relative motion, the stresses are linear functions of the instantaneous velocity gradients.

Why are traditional models inadequate for materials containing large molecules?

Traditional models are inadequate for materials containing large molecules because they do not account for the complex behavior of these materials, such as their ability to bounce like an elastic solid or to hold their shape like mayonnaise, which are not explained by simple Newtonian models.

What is a memory fluid and how does it differ from a Newtonian fluid?

A memory fluid is a more general model of fluid behavior where the history of deformation is significant. Unlike Newtonian fluids, the stress in a memory fluid is a nonlinear function of the history of the deformation gradient. This means that the stress depends not only on the current state but also on the past states of deformation.

What is the yield value in the context of materials like clay suspension?

The yield value is a critical stress value that a material can support up to a point without flowing. Materials like clay suspension do not flow until a certain yield value is exceeded, indicating a transition from a solid-like to a fluid-like state.

What is viscoelastic behavior and how does it relate to the stress history?

Viscoelastic behavior refers to the properties of materials that exhibit both viscous and elastic characteristics. It relates to the stress history in that the material's response to stress depends on the duration and history of the applied stress, showing a memory effect that influences its flow and deformation.

What is the phenomenon of shear thinning and how does it differ from shear thickening?

Shear thinning, or pseudoplastic behavior, is when the viscosity of a fluid decreases with increasing shear rate. In contrast, shear thickening, or dilatant behavior, is when the viscosity increases with increasing shear rate. These behaviors are indicative of non-Newtonian fluids that do not follow the simple linear relationship between shear stress and shear rate.

How do normal stresses affect the behavior of non-Newtonian fluids in flow?

Normal stresses in non-Newtonian fluids can lead to phenomena such as the climbing of fluid up a rotating shaft or the unequal distribution of stress across different parts of a flow system. These effects are due to the nonlinearity in the stress-deformation relation, which is a characteristic of non-Newtonian fluids.

What is the significance of the velocity profile in the flow of non-Newtonian fluids through tubes?

The velocity profile in the flow of non-Newtonian fluids through tubes can be very different from the parabolic profile typical of Newtonian fluids. This is because the flow rate and velocity field are governed by a viscosity function that can vary with the shear rate, leading to complex flow patterns and behaviors.