Clouds and Aerosols

Microphysics, growth, and radiative effects of atmospheric clouds and aerosols.

Conceptual context

Clouds and aerosols contain enormous populations of small particles interacting with air, water vapor, and radiation. Although one droplet seems negligible, its size determines whether it remains suspended, grows, evaporates, scatters light, or falls. The central question is how $r$ controls $v_s$. The answer links fluid dynamics, microphysics, and atmospheric optics. A particle does not fall in a vacuum: its motion results from the balance among effective weight, buoyancy, and viscous resistance. Consequently, a modest size change can transform a nearly suspended particle into one that separates appreciably from the surrounding air.

🟢 Essential level

A small droplet or particle does not accelerate forever while falling. Its speed first rises, but air resistance increases until an almost constant $v_s$ is reached.

For very small spherical particles, this speed is highly sensitive to $r$. As size grows, effective weight increases with volume, while viscous drag follows a different size dependence. Therefore, slightly larger particles settle much faster. $\rho_{p}$, $\rho_{a}$ and $g$ also matter, along with the dynamic viscosity of the air. Inside a cloud, $r$ may change through condensation or evaporation, controlled by water vapor excess and a diffusion growth coefficient, so the same particle can spend part of its life growing and part of it falling. Growth and settling are therefore coupled: a droplet that grows may shift from following weak air motions to separating gravitationally from them, marking the start of the physical process that eventually leads to precipitation reaching the ground during a storm or ordinary rain.

🔵 Formal level

Basic formulas

For a small sphere in the viscous regime, $v_s$ follows from balancing effective weight and Stokes drag:

Stokes terminal settling velocity

The relation shows that $v_s$ grows with the square of $r$, increases with the difference between $\rho_{p}$ and $\rho_{a}$, increases with $g$, and decreases as $\mu$ rises. The formula assumes terminal motion, an isolated sphere, and a small particle Reynolds number.

Real student questions

Why does a droplet not fall with constant acceleration? Because air drag rises until it balances effective weight.

Does a denser particle always fall faster? At equal size and in the same regime, larger $\rho_{p}$ usually increases $v_s$, but shape and drag regime also matter.

Why is squared size used in condensational growth? Vapor diffusion naturally makes the characteristic surface variable evolve almost linearly.

Is $\tau$ the same as transmittance? No. The former measures integrated opacity; the latter is the transmitted fraction.

Final synthesis

$r$ organizes much of cloud and aerosol physics. It controls $v_s$, conditions growth, and modifies $\tau$. The essential skill is to use each relation within its regime, interpret signs correctly, and recognize when the quadratic graph no longer represents reality.