Modélisation d'un écoulement Marangoni dans une goutte en équilibre avec sa vapeur

Modeling of a Marangoni flow inside a droplet in equilibrium with its vapor

¹ Commissariat à l'Energie Atomique / LETI - DSIS, Grenoble
² Laboratoire des Ecoulements Géophysiques et Industriels, Institut National Polytechnique de Grenoble
³ Laboratoire des Matériaux et du Génie Physique, Institut National Polytechnique de Grenoble
⁴ CEA/LETI - DSIS

Abstract

Inducing a convective motion inside a liquid without using any mechanical contact is a convenient and efficient way for the mixing of liquids in biotechnology, where the volumes to be treated are very small. We analyze a system constituted by a water droplet surrounded by its vapor in which a Marangoni convection has been set up. The aim of this work is to calculate the velocity field inside the droplet assuming it is at equilibrium with its vapor. Fluids are supposed incompressible and the geometry 2D axisymmetric. Non primitive variables (ω-ψ-φ) are used in the equation govering the motion of the fluid. Numerical simulations show the influence on the droplet velocity field : (i) of the vaporization-condensation mass transfer. (ii) of the presence of vapor between the droplet and the cold source and (iii) of the convection inside the liquid.