Water droplets evaporating on horizontal semi-infinite solids at room temperature

Abstract

A global approach to the evaporating droplets on solid substrates in stagnant air is presented. The focus is on simplifying the fundamental physics and mathematics involved in order to develop a sound engineering method for determining droplet temperatures and evaporation rates of sessile water droplets on semi-infinite substrates. A mathematically based factor, γ, is introduced to describe the droplet shape, where γ takes the value of 1 for flat (pan cake shaped) droplets and 2 for half sphere shaped droplets, and a representative value in the range of 1–2 between these extremes. It is shown that droplets on thermally insulating substrates gets colder and evaporates at about half the rate of similar droplets on high thermal conductivity substrates. Heat radiation dominates the evaporation rate for insulating substrates while substrate thermal conductivities above 1 W/m K do not significantly increase the evaporation rate. The theoretical findings were verified by recording temperature and drying time of droplets evaporating on semi-infinite substrates of XPS foam, PMMA and stainless steel at 24 °C and about 30% relative humidity. The convective water vapour flow from the cold droplets was directed upwards due to the lower molar mass of the water vapour. For the 10–13 mm radius droplets studied in the present work, the average convective radius to ambient air was about 15 mm ± 5 mm larger than the droplet radius. It was largest for droplets on stainless steel and smallest for droplets on the XPS-foam.