Brownian Motion: Definition and History

Definition and History

• Brownian motion is the random movement of particles suspended in a fluid (liquid or gas) resulting from collisions with the surrounding fluid molecules.
• Named after Scottish botanist Robert Brown, who first observed the phenomenon in 1827.

Causes of Brownian Motion

• Thermal energy: particles in a fluid are in constant random motion due to thermal energy.
• Collisions: particles collide with surrounding fluid molecules, causing them to change direction and speed.

Characteristics

• Random and irregular movement: particles move in unpredictable paths.
• No net movement: overall movement is zero, as particles are equally likely to move in any direction.
• Increased temperature: increases the velocity and frequency of particle movements.

Importance and Applications

• Confirmation of kinetic molecular theory: Brownian motion provides evidence for the existence of molecules and their motion.
• Particle sizing and analysis: used in fields like chemistry, biology, and materials science to analyze particle size and distribution.
• Random walk models: used in fields like finance, economics, and computer science to model random processes.

Mathematical Modeling

• Langevin equation: a stochastic differential equation that models the movement of a particle in a fluid.
• Wiener process: a mathematical model used to describe the random movement of particles in Brownian motion.

Observations and Measurements

• Microscopy: used to observe and record particle movements.
• Scattering techniques: used to measure particle size and distribution, such as dynamic light scattering (DLS).

Definition and History

• Brownian motion is the random movement of particles suspended in a fluid (liquid or gas) resulting from collisions with surrounding fluid molecules.
• Named after Scottish botanist Robert Brown, who first observed the phenomenon in 1827.

Causes of Brownian Motion

• Thermal energy causes particles in a fluid to be in constant random motion.
• Collisions between particles and surrounding fluid molecules cause them to change direction and speed.

Characteristics

• Particles move in unpredictable paths due to Brownian motion.
• There is no net movement of particles, as they are equally likely to move in any direction.
• Increased temperature increases the velocity and frequency of particle movements.

Importance and Applications

• Brownian motion confirms the existence of molecules and their motion, supporting the kinetic molecular theory.
• Particle sizing and analysis are used in fields like chemistry, biology, and materials science to analyze particle size and distribution.
• Random walk models, inspired by Brownian motion, are used in fields like finance, economics, and computer science to model random processes.

Mathematical Modeling

• The Langevin equation is a stochastic differential equation that models the movement of a particle in a fluid.
• The Wiener process is a mathematical model used to describe the random movement of particles in Brownian motion.

Observations and Measurements

• Microscopy is used to observe and record particle movements.
• Scattering techniques, such as dynamic light scattering (DLS), are used to measure particle size and distribution.