Crossing the bottleneck of rain formation

• DOI: 10.48550/arxiv.1411.7882
• Publication Date: 2014-01-01
• Authors: Martin Rohloff; Tobias Lapp; Jürgen Vollmer
• Keywords: Supersaturation; Péclet number

The demixing of a binary fluid mixture, under gravity, is two stage process. Initially droplets, or in general aggregates, grow diffusively by collecting supersaturation from the bulk phase. Subsequently, when droplets have grown to size, where their Peclet number order unity, buoyancy substantially enhances droplet growth. dynamics approaches finite-time singularity are removed system precipitation. growth regimes separated bottleneck minimal Here, we present low-dimensional model addressing time span required cross bottleneck, and hence determine time, Δt, initial rainfall. Our prediction faithfully captures dependence Δt on ramp rate volume fraction, ξ, density, interfacial tension, mass diffusion coefficient, density contrast coexisting phases, viscosity agreement observations demonstrated for methanol/hexane isobutoxyethanol/water mixtures determined vast range rates, temperatures. very good quantitative demonstrates that it sufficient consider (i) diffusive accretion relaxes supersaturation, (ii) collisions sedimenting droplets. An analytical solution resulting provides description material constants. Extensions will admit other settings addressed.