Collision-coalescence

Growth of liquid cloud droplets by collisions followed by merging. Differences in droplet fall speeds and collection efficiency affect the process. Increasing droplet number at fixed liquid-water content can reduce typical sizes and delay drizzle, but cloud mixing and water-content adjustments prevent a universal precipitation response.

If a spherical collector falls with $u_R=k_{R}R$ through constant liquid-water content $L$ and efficiency $E$, neglecting condensation and small-droplet fall speed, then $\dot{R}={\alpha }_{R}R$ with ${\alpha }_R=k_{R}LE/(4{\rho }_l)$. A uniform updraft gives $h(t)=Ut-(k_R{R}_0/{\alpha }_R)(e^{{\alpha }_{R}t}-1)$. The formula is valid only while the assumed cloud conditions hold.

A gravitational collision kernel multiplies geometric encounter area, relative fall speed, collection efficiency and coalescence efficiency. Its units are volume per time. The number of encounters also depends on the droplet size distribution. Hydrodynamic deflection, breakup and turbulence change the simple settling picture. Condensational growth alone tends to reduce relative size differences, so a precipitation-growth calculation must explain how efficient collectors arise.