Effective modelling of the Rayleigh-Bénard convection of concentrated emulsions with finite-size droplets

Abstract

We present mesoscale numerical simulations of Rayleigh-Bénard convection in a two-dimensional concentrated emulsion, confined between two parallel walls, heated from below and cooled from above, under the effect of buoyancy forces. The systems under study comprise finite-size droplets, whose concentration Φ0 is varied, ranging from the dilute limit up to the point where the emulsion starts to be packed and exhibits non-Newtonian rheology. We focus on the characterisation of the convective heat transfer properties close to the transition from conductive to convective states. The convective flow is confined and heterogeneous, which causes the emulsion to exhibit concentration heterogeneities in space φ0(y), depending on the location in the wall-to-wall direction (y). With the aim of assessing quantitatively the heat transfer efficiency of such heterogeneous systems, we resort to a side-by-side comparison between the concentrated emulsion system and a single-phase (SP) system, whose local viscosity η SP (y) is suitably constructed from the shear rheology of the emulsion. Such comparison highlights that a suitable degree Λ of coarse-graining needs to be introduced in the local viscosity η SP Λ (y), in order for the single-phase system to attain the same heat transfer efficiency of the emulsion. Specifically, it is shown that a quantitative matching between the two systems is possible whenever the coarse-graining is performed over a scale of the order of the droplet size.