Marangoni flotation of liquid droplets

Abstract

Flotation of liquid droplets on pool surfaces, in the presence of temperature differences, is studied experimentally and numerically. Coalescence or sinking of the droplet is prevented by the thermal Marangoni motion, owing to the surface tension imbalance at the pool surface. The mechanism is the same as that investigated in previous works on coalescence and wetting prevention in the presence of temperature differences. If the droplet is colder than the liquid surface, the flow is directed radially towards the drop; this radial flow field drags the ambient air under the drop, thus creating an air film and avoiding a direct contact between the droplet and the pool molecules. The surface velocities are measured visually with a CCD camera to image the motion of tracers floating on the pool surface; the surface temperature distributions along the pool and the droplet surfaces are measured by an infrared thermocamera. The experimental results are correlated by numerical results obtained under the assumption of spherical drop and axisymmetric flow regime. Different liquids are considered and the influence of evaporation is discussed, showing a good agreement between the experiments and the numerical simulations.

Thermal delay of drop coalescence

“…These studies demonstrate that above a critical temperature difference, coalescence is precluded by Marangoni stresses driving recirculating flows inside the drops that enhance the intervening lubrication pressure (as in figure 1) -a physical picture supported by the numerical simulations of Monti, Savino & Cicala (1996) and Monti & Savino (1997). Savino, Paterna & Lappa (2003) confirmed that coalescence of drops floating on a liquid bath could be delayed by a temperature difference between drop and bath, and the sustenance of the intervening air film by the associated thermocapillary flows. Neitzel & Dell'Aversana (2002) and Lappa (2005) have reviewed studies of different aspects of non-coalescence.…”

“…Our study suggests that a similar formulation can be applied to the case of drop flotation (Savino et al 2003) and also to the case of impinging drops (Dell'Aversana et al 1996) provided the drop weight is replaced by the applied load. The onset of the coalescence cascade should be delayed but otherwise largely unaffected by an initial temperature difference between the mother droplet and the bath.…”

“…Figure 2(b,c) suggest that the geometry of the flow is non-trivial due to the bath curvature induced locally by the drop's weight. Previous studies (Dell'Aversana et al 1997;Neitzel & Dell'Aversana 2002;Savino et al 2003) have pointed out that in these conditions the underside of the drop may deform such that the height of the gap is not constant. We avoid such geometrical complexities by treating the gap as a cylindrical disk with height h(t) and radius R d , where R d = R 2 /l c is the effective contact radius (Mahadevan & Pomeau 1999), and l c = √ σ /ρ o g is the capillary length of the oil; an approximation one expects to be valid provided Bo = ρ o gR 2 /σ < 1.…”

“…A mathematical framework to study related advection-diffusion problems has been developed in the context of mixing by Ottino, Ranz & Macosko (1979) and Ranz (1979), and recently applied by Meunier & Villermaux (2003) to describe scalar mixing in an axisymmetric vortex flow. In the following, we apply this method to the case of thermal homogenization within the drop, assuming that a roughly symmetric process is also taking place in the bath (Savino et al 2003). We assume that the velocity field is expressible in terms of the Hill's spherical vortex (Batchelor 1967, p. 237).…”

“…While it has been established that the influence of thermocapillary flows in the lubricating air layer will resist coalescence between two drops with a temperature difference above some critical value (Neitzel & Dell'Aversana 2002;Savino et al 2003), no theoretical model has provided a rationale for this critical temperature difference. Moreover, previous studies have neither characterized nor rationalized the dependence of the residence time of a floating droplet (denoted τ r henceforth) on the temperature difference between drop and bath.…”