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Cloud droplets grow via vapor condensation and collisional aggregation. Upon reaching approximately $\approx 100~{\rm \mu m}$, their inertia allows them to capture smaller droplets during descent, initiating rain. Here, we show that raindrop formation is not primarily governed by gravity or thermal diffusion, but by a critical range of drop sizes ($3-30~{\rm \mu m}$) where collisions are largely ineffective and controlled by van der Waals and electrostatic interactions. We identify four pathways to rain. The coalescence pathway, which is slow, involves the broadening of the drop size distribution across the $3-30~{\rm \mu m}$ low-efficiency gap through collisions, until enough large individual droplets achieving efficient collisions have formed. The mixing pathway, which is faster, requires mixing at the cloud top with drop-free, cold, humid air to create locally supersaturated conditions that grow droplets above the low-efficiency gap. The electrostatic pathway bypasses the gap through a static vertical field creating attractive interactions between droplets. The turbulence pathway relies on air turbulence to bring the droplets together at an increased rate, but we show that this pathway is unlikely. For all dynamical mechanisms, we demonstrate that the initiation time for rainfall occurs at the crossover between the broadening of the drop size distribution and the emergence of individual droplets large enough to trigger the onset of the rainfall cascade.

Rain drops form in clouds by collision of submillimetric droplets falling under gravity: larger drops fall faster than smaller ones and collect them on their path. The puzzling stability of fogs and non-precipitating warm clouds with respect to this avalanching mechanism has been a longstanding problem. How to explain that droplets of diameter around $10~{\rm \mu m}$ have a low probability of collision, inhibiting the cascade towards larger and larger drops? Here we review the dynamical mechanisms that have been proposed in the literature and quantitatively investigate the frequency of drop collisions induced by Brownian diffusion, electrostatics and gravity, using an open-source Monte-Carlo code that takes all of them into account. Inertia dominates over aerodynamic forces for large drops, when the Stokes number is larger than $1$. Thermal diffusion dominates over aerodynamic forces for small drops, when the P\'eclet number is smaller than $1$. We show that there exists a range of size (typically $1-10~{\rm \mu m}$ for water drops in air) for which neither inertia nor Brownian diffusion are significant, leading to a gap in the collision rate. The effect is particularly important, due to the lubrication film forming between the drops immediately before collision, and secondarily to the long-range aerodynamic interaction. Two different mechanisms regularise the divergence of the lubrication force at vanishing gap: the transition to a noncontinuum regime in the lubrication film, when the gap is comparable to the mean free path of air, and the induction of a flow inside the drops due to shear at their surfaces. In the gap between inertia-dominated and diffusion-dominated regimes, dipole-dipole electrostatic interactions becomes the major effect controlling the efficiency of drop collisions., Comment: 21 pages, 13 figures. Code available at https://gitlab.com/fpoydenot/dropletmicrophysics