A continuum hydrodynamic model is presented for one-component liquid-gas flows on nonisothermal solid substrates. Numerical simulations are carried out for evaporative droplets moving on substrates with thermal gradients. For droplets in one-component fluids on heated/cooled substrates, the free liquid-gas interfaces are nearly isothermal. Consequently, a thermal singularity occurs at the contact line while the Marangoni effect due to interfacial temperature variation is suppressed. Through evaporation/condensation near the contact line, the thermal singularity makes the contact angle increase with the increasing substrate temperature. Due to this effect, droplets will move toward the cold end on substrates with thermal gradients. The droplet migration velocity is found to be proportional to the change of substrate temperature across the droplet. It follows that for two droplets of different sizes on a substrate with temperature gradient, the larger droplet moves faster and will catch up with the smaller droplet ahead. As soon as they touch, they coalesce rapidly into an even larger droplet that will move even faster.
- capillary and thermocapillary flows
- evaporation and condensation of liquids
- heat flow in multiphase systems