Viscosity is a fundamental property of fluids that quantifies their resistance to flow. It plays a crucial role in numerous scientific and engineering applications, from oil and gas extraction to the design of biomedical devices.
Historical Context
The concept of viscosity can be traced back to Sir Isaac Newton, who in the 17th century described it in his work on fluids. The study of viscosity was further developed in the 19th century by prominent scientists such as George Gabriel Stokes.
Types of Viscosity
Dynamic (Absolute) Viscosity
Dynamic viscosity, often represented by the symbol \( \eta \) (or \( \mu \)), measures the internal resistance of a fluid to flow when an external force is applied.
Kinematic Viscosity
Kinematic viscosity, denoted by \( \nu \), is the ratio of dynamic viscosity to fluid density, providing a measure of how a fluid flows under gravity.
Key Events and Developments
- 1668: Isaac Newton’s first formulation of viscosity.
- 1845: George Gabriel Stokes published his work on the drag experienced by spherical objects in a viscous medium.
- 1929: The introduction of the Ubbelohde viscometer, improving the accuracy of viscosity measurements.
Mathematical Models
Newton’s Law of Viscosity
Newton’s Law of Viscosity states that the shear stress \( \tau \) between adjacent fluid layers is proportional to the rate of change of velocity with respect to the distance between the layers:
Where:
- \( \tau \) = shear stress (Pa)
- \( \eta \) = dynamic viscosity (Pa·s)
- \( \frac{du}{dy} \) = velocity gradient (s\(^{-1}\))
Non-Newtonian Fluids
For non-Newtonian fluids, the relationship between shear stress and velocity gradient is not linear. Such fluids can be characterized by more complex models, like the Power Law:
Where:
- \( K \) = consistency index
- \( n \) = flow behavior index
Charts and Diagrams
graph TB
A[Fluid Resistance] --> B[Newtonian Fluids]
A --> C[Non-Newtonian Fluids]
B --> D[Constant Viscosity]
C --> E[Variable Viscosity]
E --> F[Dilatant (Shear-Thickening)]
E --> G[Pseudoplastic (Shear-Thinning)]
E --> H[Thixotropic]
E --> I[Rheopectic]
Importance and Applicability
Viscosity is crucial in various fields, including:
- Automotive: Engine oils must have appropriate viscosity for efficient lubrication.
- Pharmaceuticals: The viscosity of syrups and injectables affects their administration and absorption.
- Food Industry: Viscosity impacts the texture and mouthfeel of products like sauces and yogurt.
Examples
- Water: Low viscosity (approx. 1 mPa·s at 20°C)
- Honey: High viscosity (approx. 10,000 mPa·s at 20°C)
Considerations
- Temperature Dependence: Viscosity typically decreases with an increase in temperature.
- Pressure Dependence: For most liquids, viscosity increases with pressure.
Related Terms
- Rheology: The study of the flow and deformation of matter.
- Shear Stress: The force per unit area exerted by a fluid against a surface.
- Viscometer: An instrument used to measure the viscosity of a fluid.
Comparisons
- Newtonian vs. Non-Newtonian Fluids: Newtonian fluids have a constant viscosity, whereas non-Newtonian fluids have variable viscosity depending on applied stress.
Interesting Facts
- Blood Viscosity: The viscosity of human blood can change under different physiological conditions.
- Glasses: Some substances like pitch and glass are technically very high-viscosity fluids that flow extremely slowly over time.
Inspirational Stories
The study of viscosity has led to significant technological advancements, such as improved engine lubricants that have increased the efficiency and lifespan of car engines.
Famous Quotes
- “Viscosity is the quality that distinguishes a liquid from a solid.” - Anonymous
Proverbs and Clichés
- Smooth as Honey: Reflecting the high viscosity of honey, indicating something that flows well despite being thick.
Expressions, Jargon, and Slang
- “Thixotropy” in everyday language refers to a substance becoming more fluid when shaken or stirred.
FAQs
How is viscosity measured?
Why does oil viscosity change with temperature?
What is the difference between shear-thinning and shear-thickening fluids?
References
- Newton, I. (1668). “Philosophiae Naturalis Principia Mathematica.”
- Stokes, G. G. (1845). “On the Effect of the Internal Friction of Fluids on the Motion of Pendulums.”
- Wikipedia: Viscosity. (https://en.wikipedia.org/wiki/Viscosity)
- Encyclopedia Britannica: Viscosity.
Summary
Viscosity is a crucial concept in fluid mechanics that affects various scientific and industrial processes. Understanding its principles, types, and applications allows for the optimized design and functionality of systems ranging from household products to complex engineering systems.
