8.5 Viscosity
7 min read•august 21, 2024
Viscosity is a fundamental property of fluids that describes their resistance to flow. It plays a crucial role in fluid dynamics, affecting everything from in our bodies to the movement of tectonic plates beneath Earth's surface.
At the microscopic level, viscosity arises from molecular interactions and collisions. Understanding these origins helps connect statistical mechanics to macroscopic fluid properties, providing insights into how molecular structure influences flow characteristics in various systems.
Definition of viscosity
- Viscosity characterizes a fluid's resistance to deformation under applied stress
- Plays a crucial role in fluid dynamics and statistical mechanics by describing internal friction within fluids
- Quantifies how easily a fluid flows and its ability to maintain its shape under external forces
Fluid resistance to flow
Top images from around the web for Fluid resistance to flow
Experiment #4: Energy Loss in Pipes – Applied Fluid Mechanics Lab Manual View original
Is this image relevant?
Viscosity and Laminar Flow; Poiseuille’s Law | Physics View original
Is this image relevant?
Viscosity and Laminar Flow; Poiseuille’s Law | Physics View original
Is this image relevant?
Experiment #4: Energy Loss in Pipes – Applied Fluid Mechanics Lab Manual View original
Is this image relevant?
Viscosity and Laminar Flow; Poiseuille’s Law | Physics View original
Is this image relevant?
1 of 3
Top images from around the web for Fluid resistance to flow
Experiment #4: Energy Loss in Pipes – Applied Fluid Mechanics Lab Manual View original
Is this image relevant?
Viscosity and Laminar Flow; Poiseuille’s Law | Physics View original
Is this image relevant?
Viscosity and Laminar Flow; Poiseuille’s Law | Physics View original
Is this image relevant?
Experiment #4: Energy Loss in Pipes – Applied Fluid Mechanics Lab Manual View original
Is this image relevant?
Viscosity and Laminar Flow; Poiseuille’s Law | Physics View original
Is this image relevant?
1 of 3
- Measures the internal friction of a fluid as it moves or is deformed
- Determines the amount of force required to cause fluid motion
- Influenced by factors such as temperature, pressure, and molecular structure
- Higher viscosity fluids (honey) require more force to flow than lower viscosity fluids (water)
Shear stress vs strain rate
- Viscosity defined as the ratio of shear stress to strain rate in a fluid
- Shear stress represents the force per unit area applied parallel to the fluid's surface
- Strain rate measures the rate of deformation of fluid layers relative to each other
- Relationship expressed mathematically as , where η is viscosity, τ is shear stress, and γ̇ is strain rate
- Linear relationship between shear stress and strain rate characterizes
Microscopic origins
- Viscosity emerges from molecular-level interactions and movements within fluids
- Understanding microscopic origins crucial for connecting statistical mechanics to macroscopic fluid properties
- Provides insights into how molecular structure and behavior influence fluid flow characteristics
Molecular interactions
- Intermolecular forces (van der Waals, hydrogen bonding) contribute to viscosity
- Stronger molecular interactions result in higher viscosity
- Molecular size and shape affect the strength of these interactions
- Polar molecules (water) tend to have higher viscosities due to stronger intermolecular forces
- Non-polar molecules (hydrocarbons) generally exhibit lower viscosities
Mean free path
- Average distance a molecule travels between collisions with other molecules
- Inversely related to viscosity: shorter leads to higher viscosity
- Affected by temperature, pressure, and molecular size
- In gases, mean free path decreases with increasing pressure, leading to higher viscosity
- Liquids have much shorter mean free paths compared to gases, contributing to their higher viscosities
Kinetic theory of viscosity
- Applies principles of statistical mechanics to explain viscosity at the molecular level
- Provides a framework for understanding how molecular motion and collisions contribute to fluid friction
- Connects microscopic particle behavior to macroscopic fluid properties
Maxwell-Boltzmann distribution
- Describes the statistical distribution of molecular velocities in a fluid
- Key component in understanding energy and in fluids
- Probability density function given by
- Determines the range of molecular speeds contributing to viscosity
- Affected by temperature: higher temperatures lead to broader velocity distributions
Momentum transfer
- Viscosity arises from the transfer of momentum between fluid layers
- Faster-moving molecules collide with slower ones, exchanging momentum
- Rate of momentum transfer determines the magnitude of viscosity
- In gases, momentum transfer occurs through molecular collisions
- In liquids, momentum transfer involves both collisions and intermolecular forces
Temperature dependence
- Viscosity varies significantly with temperature for both liquids and gases
- Understanding temperature dependence crucial for predicting fluid behavior in various applications
- Reveals insights into molecular structure and interactions within fluids
Liquids vs gases
- Liquids generally decrease in viscosity as temperature increases
- Weakening of intermolecular forces in liquids at higher temperatures reduces resistance to flow
- Gases exhibit opposite behavior: viscosity increases with temperature
- Increased molecular motion in gases at higher temperatures leads to more frequent collisions and momentum transfer
- Crossover point exists where some substances transition from liquid-like to gas-like viscosity behavior
Arrhenius equation
- Describes for many liquids
- Mathematical form: , where η is viscosity, A is a pre-exponential factor, E_a is activation energy, R is the gas constant, and T is temperature
- Activation energy represents the energy barrier molecules must overcome to move past each other
- Higher activation energy indicates stronger temperature dependence of viscosity
- Used to predict viscosity changes in industrial processes and material design
Viscosity measurement techniques
- Accurate measurement of viscosity essential for characterizing fluid properties
- Various methods developed to accommodate different fluid types and viscosity ranges
- Understanding measurement techniques crucial for interpreting experimental data in statistical mechanics
Capillary viscometers
- Measure viscosity based on fluid flow through a narrow tube
- Utilize Poiseuille's law to relate flow rate to viscosity
- Suitable for Newtonian fluids with low to medium viscosities
- Types include Ostwald, Ubbelohde, and Cannon-Fenske viscometers
- Measure , which can be converted to by multiplying with fluid density
Rotational viscometers
- Determine viscosity by measuring torque required to rotate an object in a fluid
- Suitable for both Newtonian and
- Can measure a wide range of viscosities, from very low to extremely high
- Types include concentric cylinder, cone and plate, and parallel plate viscometers
- Allow for continuous measurement and shear rate control, useful for studying complex fluids
Types of viscosity
- Different viscosity measures used to characterize fluid behavior under various conditions
- Understanding various viscosity types essential for accurately describing fluid properties in different applications
- Enables proper selection of viscosity measure for specific fluid systems and flow conditions
Dynamic vs kinematic viscosity
- Dynamic viscosity (absolute viscosity) measures fluid's resistance to shearing flows
- Defined as the ratio of shear stress to shear rate, units typically Pascal-seconds (Pa·s)
- Kinematic viscosity represents the ratio of dynamic viscosity to fluid density
- Measured in units of square meters per second (m²/s) or Stokes (St)
- Relationship: kinematic viscosity = dynamic viscosity / density
- Kinematic viscosity often used in fluid dynamics calculations involving gravity or inertial forces
Apparent viscosity
- Describes the effective viscosity of non-Newtonian fluids
- Changes with shear rate or stress, unlike constant viscosity of Newtonian fluids
- Calculated as the ratio of shear stress to shear rate at a specific point
- Useful for characterizing complex fluids (polymers, suspensions, emulsions)
- Allows for comparison of non-Newtonian fluids to Newtonian fluids at specific flow conditions
Non-Newtonian fluids
- Fluids whose viscosity changes with applied stress or shear rate
- Exhibit complex flow behaviors not described by simple Newtonian model
- Understanding non-Newtonian behavior crucial for many industrial and biological applications
- Requires advanced statistical mechanical models to describe molecular-level origins
Shear-thinning fluids
- Decrease in viscosity as shear rate increases
- Common examples include ketchup, paint, and blood
- Molecular explanation involves alignment or disentanglement of polymer chains
- Power-law model often used to describe behavior: , where K is consistency index and n is flow behavior index
- Exhibit improved flow properties in high-shear applications (spraying, pumping)
Shear-thickening fluids
- Increase in viscosity as shear rate increases
- Examples include cornstarch in water and some ceramic suspensions
- Molecular mechanism involves formation of hydroclusters or jamming of particles
- Can be modeled using modified power-law equations or more complex constitutive models
- Used in impact-resistant materials and smart fluids for various applications
Viscosity in statistical mechanics
- Connects microscopic molecular behavior to macroscopic fluid properties
- Utilizes principles of statistical physics to derive viscosity from fundamental interactions
- Provides theoretical framework for understanding and predicting viscosity in complex systems
Chapman-Enskog theory
- Extends kinetic theory to derive transport coefficients, including viscosity
- Based on solving the Boltzmann equation using perturbation methods
- Provides expressions for viscosity in terms of molecular properties and interaction potentials
- Accurate for dilute gases but requires modifications for dense fluids and liquids
- Incorporates higher-order corrections to account for molecular collisions and energy transfer
Correlation functions
- Describe statistical relationships between molecular positions and velocities over time
- link transport coefficients to time correlation functions
- Viscosity expressed as integral of stress autocorrelation function
- Enable calculation of viscosity from molecular dynamics simulations
- Provide insights into molecular-level mechanisms contributing to viscosity
Applications in physics
- Viscosity plays crucial role in various branches of physics and engineering
- Understanding viscosity essential for predicting and controlling fluid behavior in diverse systems
- Applications range from microscopic to macroscopic scales, spanning multiple disciplines
Fluid dynamics
- Viscosity fundamental to describing fluid motion and energy dissipation
- Navier-Stokes equations incorporate viscosity terms to model fluid flow
- Reynolds number, which includes viscosity, determines flow regime (laminar vs turbulent)
- Viscous effects crucial in boundary layer formation and separation
- Important in designing efficient fluid systems (pipelines, aircraft, turbines)
Boundary layer theory
- Describes fluid behavior near solid surfaces where viscous effects dominate
- Developed by Ludwig Prandtl to explain fluid-solid interactions
- Boundary layer thickness depends on fluid viscosity and flow conditions
- Crucial for understanding drag, heat transfer, and mass transfer in fluid systems
- Applications include aerodynamics, meteorology, and oceanography
Viscosity in everyday life
- Viscosity impacts numerous aspects of daily experiences and technologies
- Understanding viscosity crucial for optimizing products and processes in various industries
- Influences diverse fields from engineering to food science
Lubrication
- Viscosity key property in selecting and formulating lubricants
- Determines oil's ability to form protective film between moving surfaces
- Viscosity index measures how viscosity changes with temperature
- Multigrade oils designed to maintain optimal viscosity across temperature ranges
- Crucial for reducing friction and wear in engines, machinery, and bearings
Food science applications
- Viscosity affects texture, mouthfeel, and processing of food products
- Used to control consistency of sauces, dressings, and dairy products
- Thickeners and stabilizers modify food viscosity for desired properties
- Rheological measurements help predict food behavior during processing and consumption
- Important in developing new food formulations and improving existing products
Key Terms to Review (27)
Apparent viscosity: Apparent viscosity refers to the measure of a fluid's resistance to flow, considering its behavior under specific flow conditions, especially when the fluid exhibits non-Newtonian characteristics. This term highlights how the viscosity of a fluid can change with factors like shear rate, temperature, and pressure, making it crucial for understanding fluid dynamics in various applications, such as in industrial processes and biological systems.
Arrhenius Equation: The Arrhenius Equation is a formula that shows the relationship between the rate of a chemical reaction and temperature. It expresses how the rate constant of a reaction increases exponentially with temperature, providing insight into the effect of temperature on reaction kinetics. This equation is vital for understanding viscosity, as it helps explain how temperature changes influence the flow and resistance of liquids.
Bingham Plastics: Bingham plastics are materials that behave like a solid until a certain yield stress is exceeded, at which point they flow like a fluid. This unique behavior is characterized by a viscosity that is not constant; it changes depending on the stress applied, making it crucial for understanding how these materials can be processed and utilized in various applications, particularly in industries involving complex fluid dynamics.
Blood flow: Blood flow refers to the movement of blood through the circulatory system, driven by the heart's pumping action and influenced by various physiological factors. It is essential for delivering oxygen and nutrients to tissues while removing waste products. Understanding blood flow involves examining how viscosity and other properties affect circulation in the body.
Capillary Viscometry: Capillary viscometry is a technique used to measure the viscosity of a fluid by observing the time it takes for the fluid to flow through a capillary tube under the influence of gravity. This method relies on the relationship between the flow rate and the viscosity, allowing for precise determination of how resistant a fluid is to flow. The technique is particularly useful for characterizing fluids that have low to moderate viscosities and provides insights into their molecular interactions and behavior.
Centipoise: Centipoise is a unit of measurement for dynamic viscosity, representing the internal resistance of a fluid to flow. One centipoise is defined as one-hundredth of a poise, which is a measurement derived from the SI unit for viscosity. This term is commonly used in various scientific fields, particularly in physics and engineering, to quantify the thickness or stickiness of fluids.
Chapman-Enskog Theory: The Chapman-Enskog theory is a mathematical framework used to derive transport properties, such as viscosity, thermal conductivity, and diffusion coefficients, from the kinetic theory of gases. It connects the microscopic behavior of gas molecules to macroscopic phenomena by providing a systematic approach to calculate these transport coefficients based on molecular interactions and velocities. This theory is crucial in understanding how gases behave under various conditions and how they facilitate the movement of momentum, energy, and particles.
Dynamic viscosity: Dynamic viscosity is a measure of a fluid's resistance to flow when an external force is applied. It quantifies how much force is needed to move one layer of fluid over another, providing insights into the fluid's internal friction. This property plays a crucial role in determining how fluids behave under various conditions, influencing everything from industrial processes to natural phenomena.
Green-kubo relations: Green-Kubo relations are mathematical expressions that relate the transport coefficients of a system to time integrals of correlation functions of current fluctuations. These relations provide a theoretical framework to connect microscopic dynamics to macroscopic transport properties, such as viscosity, thermal conductivity, and diffusion. By establishing this connection, Green-Kubo relations enable the calculation of transport coefficients from equilibrium properties of a system.
Kinematic viscosity: Kinematic viscosity is a measure of a fluid's internal resistance to flow under the influence of gravity, defined as the ratio of dynamic viscosity to fluid density. It plays a crucial role in characterizing how fluids behave when they move, influencing factors like flow rates and turbulence in various contexts.
Lubrication: Lubrication refers to the process of reducing friction between surfaces in mutual contact, which ultimately minimizes the wear and tear of those surfaces. In the context of viscosity, lubrication is crucial for understanding how different fluids behave under shear stress and how they can effectively reduce the resistance to motion. The properties of a lubricant, such as its viscosity, greatly influence its effectiveness in minimizing friction and energy loss in mechanical systems.
Maxwell-Boltzmann distribution: The Maxwell-Boltzmann distribution describes the statistical distribution of speeds of particles in a gas that is in thermal equilibrium. This distribution provides insights into the behavior of gas molecules and connects directly to concepts such as temperature, energy, and molecular interactions.
Mean Free Path: Mean free path is the average distance a particle travels between collisions with other particles in a gas or fluid. This concept is crucial for understanding how particles interact in various states of matter, influencing properties like pressure and temperature, as well as phenomena such as viscosity and diffusion.
Momentum transfer: Momentum transfer refers to the process by which momentum is exchanged between particles or systems during interactions, such as collisions or fluid motion. This concept is essential in understanding how forces influence the motion of particles, especially in relation to the viscosity of fluids and the behavior of materials under stress.
Newton's Law of Viscosity: Newton's Law of Viscosity describes the relationship between the shear stress and the shear rate of a fluid, stating that the shear stress is directly proportional to the shear rate. This principle helps explain how fluids flow and resist deformation, making it crucial in understanding fluid behavior in various transport processes.
Newtonian Fluids: Newtonian fluids are a class of fluids that maintain a constant viscosity regardless of the applied shear rate. This means that the flow behavior of these fluids is linear, and they follow Newton's law of viscosity, which states that the shear stress between fluid layers is directly proportional to the shear rate. Common examples include water, air, and most simple oils, making them essential in various applications across different fields.
Non-newtonian fluids: Non-newtonian fluids are substances whose viscosity changes when under stress or shear rate, unlike Newtonian fluids which maintain a constant viscosity regardless of the applied forces. This unique behavior means that non-newtonian fluids can exhibit properties such as thickening or thinning depending on how quickly or slowly they are stirred, making them essential in various applications, from industrial processes to everyday products like paints and food items.
Pascal-second: The pascal-second is a unit of dynamic viscosity in the International System of Units (SI), defined as the ratio of shear stress to shear rate. It connects the concepts of force, area, and velocity, making it essential for understanding fluid behavior under different conditions, such as temperature and pressure. This unit helps quantify how resistant a fluid is to flow, which is crucial in applications ranging from engineering to natural sciences.
Poiseuille's Equation: Poiseuille's Equation describes the flow rate of a viscous fluid through a cylindrical pipe. It highlights the relationship between the pressure drop, the viscosity of the fluid, the length and radius of the pipe, and the flow rate, establishing a crucial link between viscosity and fluid dynamics.
Pressure Dependence of Viscosity: The pressure dependence of viscosity refers to how the viscosity of a fluid changes with variations in pressure. Generally, as pressure increases, the viscosity of liquids tends to rise due to the enhanced interactions between molecules, leading to greater resistance to flow. This phenomenon is crucial for understanding fluid behavior in various applications, including industrial processes and natural phenomena.
Rotational viscometry: Rotational viscometry is a technique used to measure the viscosity of a fluid by applying a controlled rotational force to a spindle or rotor submerged in the fluid. This method provides insights into the flow behavior and properties of non-Newtonian fluids, allowing for a better understanding of how they respond under varying shear rates. The results from rotational viscometry are essential for applications in industries such as food, cosmetics, and pharmaceuticals, where viscosity plays a critical role in product formulation and performance.
Shear Thinning: Shear thinning is a non-Newtonian fluid behavior where the viscosity of a fluid decreases with an increase in shear rate. This means that when you stir or apply force to the fluid, it becomes easier to move and flow. This property is crucial in various applications, including industrial processes and biological systems, as it allows for easier manipulation of materials under stress.
Shear-thickening fluids: Shear-thickening fluids are non-Newtonian fluids that exhibit an increase in viscosity with an increase in shear rate. This means that when these fluids are subjected to stress or force, they become thicker and resist flow more than when at rest. This behavior contrasts with Newtonian fluids, where viscosity remains constant regardless of the applied shear rate, highlighting unique characteristics in their flow behavior and applications.
Shear-thinning fluids: Shear-thinning fluids, also known as pseudoplastic fluids, are liquids whose viscosity decreases with an increase in shear rate. This behavior is crucial in various applications, such as in paint and certain food products, where easy flow is desired when stirred or pumped. Understanding the properties of shear-thinning fluids helps in analyzing how they respond under different stress conditions.
Stokes' Law: Stokes' Law describes the motion of a small spherical particle through a viscous fluid, stating that the force of viscosity acting on the particle is directly proportional to its radius, the velocity of its movement, and the viscosity of the fluid. This law is essential in understanding how particles behave in fluids, especially in terms of sedimentation and drag forces, which are critical for various applications in physics and engineering.
Temperature Dependence of Viscosity: Temperature dependence of viscosity refers to how the viscosity of a fluid changes with temperature. Generally, as temperature increases, the viscosity of liquids decreases because the increased kinetic energy allows molecules to move more freely. Conversely, for gases, viscosity tends to increase with temperature due to enhanced molecular motion leading to more frequent collisions between gas molecules.
Thixotropy: Thixotropy refers to the property of certain non-Newtonian fluids that become less viscous over time when subjected to shear stress, allowing them to flow more easily. This behavior is significant because it illustrates how some materials can change their viscosity based on the application of force, which is crucial in many applications, including paints, gels, and biological fluids.