Shapes and dynamics of miscible liquid/liquid interfaces in horizontal capillary tubes

Abstract

We report optical observations of the dissolution behaviour of glycerol/water, soybean oil/hexane, and isobutyric acid (IBA)/water binary mixtures within horizontal capillary tubes. Tubes with diameters as small as 0.2mm were initially filled with one component of the binary mixture (solute) and then immersed into a solvent-filled thermostatic bath. Both ends of the tubes were open, and no pressure difference was applied between the ends. In the case of glycerol/water and soybean oil/hexane mixtures, we managed to isolate the dissolution (the interfacial mass transfer) from the hydrodynamic motion. Two phase boundaries moving from the ends into the middle section of the tube with the speeds v∼D(1/3)t(-2/3)d(2) (D,t and d are the coefficient of diffusion, time and the diameter of the tube, respectively) were observed. The boundaries slowly smeared but their smearing occurred considerably slower than their motion. The motion of the phase boundaries cannot be explained by the dependency of the diffusion coefficient on concentration, and should be explained by the effect of barodiffusion. The shapes of the solute/solvent boundaries are defined by the balance between gravity and surface tension effects. The contact line moved together with the bulk interface: no visible solute remained on the walls after the interface passage. Changes in temperature and in the ratio between gravity and capillary forces altered the apparent contact angles. The IBA/water system had different behaviour. Below the critical (consolute) point, no dissolution was observed: IBA and water behaved like two immiscible liquids, with the IBA phase being displaced from the tube by capillary pressure (the spontaneous imbibition process). Above the critical point, two IBA/water interfaces could be identified, however the interfaces did not penetrate much into the tube.

On the phase-field modelling of a miscible liquid/liquid boundary

“…The profiles This can be seen in figures 1d,e, where the dissolution from smaller tubes happen faster. Such a dependence contradicts to the experimental observations [1], where the dissolution in smaller tubes occurred slower.…”

“…Ref. [1] clearly point out that the evolution of the solute/solvent 90 mixture in the tube is much more complex, and could not be reduced to the 1D process.…”

“…It is also known that this simple approach is not valid for the case of large concentration gradients, in particular, for the description of diffusion at a liquid/liquid (solute/solvent) boundary. This, in 5 particular, was illustrated by the recent experiments, where mixing of liquid solute and liquid solvent was investigated [1]. The settings of the experiments were rather simple: a long capillary, initially boundaries were seen at the sides of the capillary for very long time periods.…”

“…Next, these simulations were repeated for the more sophisticated geometry, that included two big blocks, initially filled with the solvent, connected by the solute-filled tube. Such a geometry should be a closer reproduction of the experiment [1], and, in addition, such a geometry would 120 allow us to introduce the flows (as otherwise the velocity boundary conditions at the capillary ends are difficult to define). The solutal convection is driven by gravity and by the dependence of the mixture density on concentration.…”

“…In this work, following the experimental work [1], we restrict our analysis to isothermal systems. It should be mentioned though that phase transformations may frequently involve release or absorption of some latent heats.…”