The fate of an aerosol particle—its transport through the air, its deposition onto surfaces, and its residence time in the atmosphere—is governed by a complex interplay of forces. A particle’s response to these forces is overwhelmingly dependent on its size, which determines whether its behavior is dominated by inertia, diffusion, or other phenomena. This section deconstructs the key size-dependent dynamic properties and transport mechanisms that define aerosol behavior.

4.1 Motion of Large Particles (Inertial Regime)

For larger particles, motion is primarily governed by the balance between external forces (like gravity) and the fluid’s resistance, or drag force (Fd). The drag force is a function of the particle’s projected area (Ap), the fluid density (ρf), and the relative velocity (u), and is defined as:

Fd = CD * Ap * (ρf * u^2 / 2) (Eq. 12)

The drag coefficient (CD) is not constant; it depends on the flow regime, which is characterized by the dimensionless Reynolds number (Re):

Re = u * Dp * ρf / μ (Eq. 13)

where μ is the fluid viscosity. The relationship between Re, CD, and the resulting terminal settling velocity under gravity is summarized in the table below.

A critical property related to a particle’s inertia is its relaxation time (τg), given by τg = ρp * Dp^2 * Cc / (18 * μ) (Eq. 3.6), where Cc is the slip correction factor. This value represents the time required for a particle to adjust its velocity in response to a change in external forces. Physically, it is a direct measure of a particle’s inertia; a particle projected into still air will travel a “stop-distance” equal to its initial velocity multiplied by its relaxation time.

4.2 Motion of Small Particles (Diffusive Regime)

For small particles, the random, incessant bombardment by gas molecules becomes the dominant mechanism of motion. This phenomenon, known as Brownian motion, causes particles to diffuse through the gas in a manner analogous to molecular diffusion. The intensity of this motion is quantified by the Brownian diffusion coefficient (D):

D = Cc * k * T / (3 * π * μ * Dp) (Eq. 15)

where k is the Boltzmann constant and T is the absolute temperature. The mean square displacement (<Δx²>) of a particle in a given time t is directly proportional to this coefficient: <Δx²> = 2Dt (Eq. 16).

The relative importance of gravitational settling versus Brownian motion is strongly size-dependent. The plot of fundamental aerosol properties in Figure 3 shows that the gravitational settling velocity (vt) decreases with particle size, while the average Brownian displacement (Δx) increases. For particles in air at standard conditions, these two effects are of a comparable magnitude at a diameter of approximately 0.5 μm. Below this size, diffusion dominates transport, while above it, gravitational settling is more significant.

4.3 Electrical Properties and Behavior

If a particle carries an electrical charge, it will experience a force in the presence of an electric field. This allows for its manipulation and is the basis for many measurement techniques. The terminal electrophoretic velocity (ve) a charged particle attains in an electric field (E) is given by:

ve = np * e * E * Cc / (3 * π * μ * Dp) (Eq. 20)

where np is the number of elementary charges (e) on the particle. The particle’s electrical mobility (Be) is its velocity in a unit-strength electric field (Be = ve / E). This predictable relationship between size, charge, and velocity in an electric field is the foundational principle of electrical mobility analyzers, as will be detailed in Section 6.4.

Particles in the atmosphere acquire charge through two primary mechanisms:

1. Diffusion Charging: Dominant for particles smaller than ~0.2 μm, this process occurs due to random thermal collisions between particles and gaseous ions.
2. Field Charging: This mechanism involves ions drifting along electric field lines until they collide with and transfer charge to a particle.

When an aerosol is exposed to a high concentration of both positive and negative ions (bipolar ions) for a sufficient duration, it reaches an equilibrium charge distribution. The charge distribution in this state, shown in Figure 5, is stable and predictable, with the number of positively and negatively charged ions being roughly equal.

4.4 Brownian Coagulation

Brownian coagulation is a fundamental process where random collisions between particles cause them to stick together, forming larger aggregates. This process continuously reduces the total particle number concentration and shifts the size distribution towards larger sizes, while the total particle volume (or mass) is conserved.

For an initially monodisperse aerosol (all particles of the same size), the rate of decrease in number concentration (N) over time (t) is given by:

dN/dt = -K₀ * N^2 (Eq. 21)

where K₀ is the coagulation coefficient. Integrating this equation shows that the concentration at time t is:

N = N₀ / (1 + 0.5 * K₀ * N₀ * t) (Eq. 22)

The characteristic time for coagulation, or the time it takes for the number concentration to be halved, is 2 / (K₀ * N₀). The Brownian coagulation coefficient varies with particle size, exhibiting distinct maxima for particles smaller than 0.1 μm, particularly in the ultrafine range as shown in Figure 6.

4.5 Additional Physical Phenomena

• Kelvin Effect: The vapor pressure over a droplet’s curved surface is higher than that over a flat surface of the same liquid. This effect, described by Pd / P∞ = exp(4 * M * σ / (R * T * ρl * Dp)) (Eq. 3.8), becomes increasingly significant as the droplet diameter decreases. It dictates whether a small droplet will grow via condensation or shrink via evaporation in an environment with a given vapor saturation ratio.
• Phoretic Phenomena: These phenomena describe particle motion induced by gradients in the surrounding gas.
  • Thermophoresis: Particle motion driven by a temperature gradient, with particles moving from hotter to colder regions.
  • Photophoresis: A special case of thermophoresis where a particle is non-uniformly heated by absorbing light, causing it to move.
  • Diffusiophoresis: Particle motion driven by a gradient in the concentration of vapor molecules, with particles moving from higher to lower concentration.

The physical dynamics of particles set the stage for understanding their interaction with electromagnetic radiation, a key property with profound atmospheric and measurement implications.