The behavior of aerosol particles is governed by a range of physical forces and properties that are highly dependent on particle size.

Particle Motion in a Fluid

The motion of a particle in a fluid is determined by the sum of forces acting upon it, including drag, gravity, and electrical forces.

• Drag Force: A particle moving relative to a fluid experiences a drag force that depends on the fluid viscosity (μ), the particle’s projected area, and the Reynolds Number (Re), which characterizes the flow regime.
• Terminal Settling Velocity (vt): Under gravity, a particle accelerates until the drag force balances the gravitational force, at which point it reaches a constant terminal settling velocity. This velocity is directly proportional to the square of the particle diameter in the Stokes regime (Re < 1).
• Slip Coefficient (Cc): For particles with diameters approaching the mean free path of gas molecules, the air can no longer be treated as a continuous medium. The slip correction factor, Cc, accounts for this effect. Cc increases as particle size or gas pressure decreases, leading to a higher settling velocity than predicted by Stokes’ law alone.
• Relaxation Time (τg): This property characterizes the time required for a particle to adjust its velocity in response to a change in external forces. It is a measure of particle inertia; a particle projected into a fluid will travel a “stop-distance” equal to its initial velocity multiplied by τg.

Brownian Motion and Diffusion

Small particles are subject to random, incessant bombardment by gas molecules, resulting in erratic movement known as Brownian motion.

• Diffusion Coefficient (D): This coefficient quantifies the rate of particle diffusion and is inversely proportional to particle diameter (Dp).
• Brownian Displacement: The average displacement of a particle due to Brownian motion increases with time. For particles around 0.5 µm, the displacement due to Brownian motion in one second is comparable to the distance traveled due to gravitational settling.

Electrical Properties and Charging

Aerosol particles can carry an electrical charge, which subjects them to an electrical force in the presence of an electric field.

• Charging Mechanisms:
  • Diffusion Charging: Arises from random thermal collisions between particles and gaseous ions. This is the dominant mechanism for particles smaller than ~0.2 µm.
  • Field Charging: Occurs when ions drift along electric field lines and collide with particles.
• Electrical Mobility (Be): Defined as the terminal velocity of a charged particle in an electric field of unit strength. It is a key property used in sizing techniques.
• Equilibrium Charge: In the presence of bipolar ions (both positive and negative), particles will reach an equilibrium charge distribution where the number of positively and negatively charged particles is approximately equal.

Coagulation

Brownian coagulation is the process by which particles collide due to their random thermal motion, leading to a continuous decrease in number concentration and an increase in average particle size, while the total particle volume remains constant. The rate of coagulation is described by a coagulation coefficient (K), which is a function of particle size. The characteristic time, or half-life, for coagulation is inversely proportional to the initial number concentration (N₀) and the coagulation coefficient. The coefficient is highest for particles in the 0.01 µm to 0.1 µm range.

Other Phenomena

• Kelvin Effect: The vapor pressure over a curved droplet surface is higher than that over a flat surface. This effect becomes more pronounced as droplet diameter decreases, determining whether a small droplet will grow or evaporate based on the ambient saturation ratio.
• Phoretic Phenomena: Particle motion can be induced by gradients in the surrounding medium.
  • Thermophoresis: Particle motion from a high-temperature region to a low-temperature region.
  • Photophoresis: Motion induced by non-uniform heating of a particle by light absorption.
  • Diffusiophoresis: Motion caused by a concentration gradient of vapor molecules.