Introduction to Viscosity

Viscosity is a fundamental property of fluids that quantifies their resistance to flow or deformation. It describes the internal friction between fluid layers as they move past one another. In simpler terms, viscosity determines how "thick" or "thin" a fluid is.

The scientific study of viscosity dates back to the 19th century, with significant contributions from scientists like Isaac Newton, Jean Léonard Marie Poiseuille, and George Gabriel Stokes. Today, viscosity measurements are crucial in industries ranging from petroleum to food processing, and in scientific fields from meteorology to biomedical engineering.

Types of Viscosity

1. Dynamic Viscosity (Absolute Viscosity)

Dynamic viscosity (μ) measures a fluid's resistance to shear flow when an external force is applied. The SI unit is Pascal-seconds (Pa·s), with the CGS unit being poise (P). Water at 20°C has a dynamic viscosity of about 0.001 Pa·s or 1 centipoise (cP).

2. Kinematic Viscosity

Kinematic viscosity (ν) is the ratio of dynamic viscosity to fluid density (ν = μ/ρ). It's measured in m²/s in SI units or stokes (St) in CGS units. This measurement is particularly useful when inertial forces are significant.

The Physics Behind Viscosity

Viscosity arises from intermolecular forces and momentum transfer between fluid layers. In liquids, viscosity primarily results from molecular cohesion, while in gases, it's mainly due to molecular momentum transfer.

Newton's Law of Viscosity

For laminar flow between two parallel plates where one plate moves relative to the other, the shear stress (τ) is proportional to the velocity gradient (du/dy):

Fluids that obey this linear relationship are called Newtonian fluids (e.g., water, air). Non-Newtonian fluids exhibit more complex behavior.

Temperature Dependence

Viscosity is highly temperature-dependent:

• Liquids: Viscosity decreases with temperature (molecules have more energy to overcome cohesive forces)
• Gases: Viscosity increases with temperature (more frequent molecular collisions transfer more momentum)

The temperature dependence can be modeled by:

Measurement Techniques

1. Capillary Viscometers

Based on Poiseuille's law, these measure the time for a fixed volume of fluid to flow through a capillary tube:

2. Rotational Viscometers

These measure the torque required to rotate a spindle in the fluid at a given speed. The viscosity is calculated from the relationship between torque and angular velocity.

3. Falling Sphere Viscometers

Based on Stokes' law, these measure the terminal velocity of a sphere falling through the fluid:

Practical Applications

Industrial Applications

• Petroleum Industry: Determining optimal pipeline transport conditions
• Food Processing: Controlling texture and mouthfeel of products
• Paint Manufacturing: Ensuring proper coverage and leveling
• Pharmaceuticals: Formulating drug delivery systems

Scientific Research

• Meteorology: Modeling atmospheric circulation
• Oceanography: Studying ocean currents
• Geophysics: Understanding magma flow
• Biomechanics: Analyzing blood flow

Common Fluid Viscosities

Using This Viscosity Calculator

Our viscosity calculator implements several standard viscosity calculation methods:

1. Dynamic Viscosity Calculation: Compute from shear stress and shear rate
2. Kinematic Viscosity Conversion: Convert between dynamic and kinematic viscosity using fluid density
3. Temperature Corrections: Adjust viscosity values for different temperatures using known coefficients
4. Mixture Viscosity: Estimate viscosity of fluid mixtures using appropriate models

The calculator is particularly useful for engineers, scientists, and students who need quick viscosity calculations without manual computation errors.

Advanced Topics

Non-Newtonian Fluids

Many real-world fluids don't obey Newton's law of viscosity. Their viscosity changes with applied stress or strain rate:

• Shear-thinning: Viscosity decreases with increasing shear rate (e.g., ketchup)
• Shear-thickening: Viscosity increases with increasing shear rate (e.g., cornstarch in water)
• Bingham plastics: Require a minimum yield stress to flow (e.g., toothpaste)
• Thixotropic: Viscosity decreases over time under constant shear

Microscopic Theory

From kinetic theory, viscosity in gases can be expressed as:

For liquids, viscosity is better described by Eyring's theory of activated flow, where molecules must overcome energy barriers to move relative to each other.