Frost Propagation on Breath Figures

The formation of frost on surfaces is ubiquitous in cold and humid environments. The various mechanisms that take place during frost formation are still under active scrutiny, both from a fundamental point of view and for their applications to frost control. Frost propagates through condensation figures by means of the solidification of droplets and the formation of inter-droplet ice bridges. Many studies on this topic, involving superhydrophobic surfaces, soft substrates, liquid-infused surfaces, or drops arranged in arrays have been published in recent years. We take a novel experimental approach using infrared microscopy to follow the propagation of the frosted area. Starting from a first nucleation event, a frost front propagates radially at a constant speed for a given experiment. The droplet size distribution was varied systematically and we found that the front speed is a non-monotonous function of droplet size with a maximum speed of 70 µm.s^-1, for a characteristic drop radius of 300 µm. The dynamics are governed by three timescales: the freezing time of individual droplets, their cooling time, and the inter-droplet bridge formation time. We present a mean-field model that without any free parameters is in very good agreement with both experimental and numerical data.