Influence of the gas-phase Lewis number and thermocapillary stress on motion of a slowly evaporating droplet in Stokes flow

Abstract

The influence of thermocapillary stresses on motion of a slowly evaporating single-component droplet in Stokes flow is investigated analytically for the situation where the environment does not have a temperature gradient in the far field. The conservation equations are solved in the liquid and gas phases and coupled at the gas–liquid interface by applying conditions for conservation of mass, species, momentum and energy. It is found that thermocapillary stresses may influence droplet motion by changing the the interface velocity, and that the gas-phase Lewis number of the evaporating component determines whether Marangoni effects increase or decrease droplet drag. If the Lewis number is less than unity, then thermal Marangoni effects increase droplet drag, while if the Lewis number is greater than unity, then thermal Marangoni effects decrease droplet drag. This is related to the sign of the temperature gradient along the droplet surface that is induced by convection. It is found that conditions may exist where a vaporizing droplet in a microgravity environment will exhibit continuous translational motion driven by thermocapillary effects.