Upstream motion of oil droplets in co-axial Ouzo flow due to Marangoni forces

TL;DR

The paper addresses how Marangoni stresses in a multi-component Ouzo-type coaxial flow can reverse droplet motion, enabling upstream migration. It combines experiments, axisymmetric simulations, and a semi-analytical model to identify nucleation zones and hovering equilibria, showing droplets can hover at fixed positions or move upstream depending on $Q_{ ext{jet}}$ and $R_{ ext{drop}}$. A force-balance framework yields two limiting expressions for the critical jet flow rate and maps regions of stable hovering, linking interfacial-tension gradients to droplet dynamics. The findings have practical implications for droplet manipulation in microfluidics and multiphase processing, and highlight the role of interfacial physics in multi-component flows.

Abstract

To explore the physicochemical hydrodynamics of phase-separating ternary liquids (Ouzo-type), a binary oil-ethanol mixture is introduced into a co-flowing stream of water. Oil droplets nucleate at the interface between the two liquids, leading to a larger oil droplet interacting with the ethanol-rich jet. Although buoyancy forces and hydrodynamic drag forces push the droplet in downstream direction, we observe an upstream motion. Using computational fluid dynamics simulations of a simplified model system, we identify the nucleation zone for oil droplets and uncover Marangoni forces to be responsible for the upstream motion of the droplet. A semi-analytical model allows us to identify the key parameters governing this effect. A general conclusion is that Marangoni stresses can reverse the motion of droplets through channels, where the surrounding liquid is a multi-component mixture. The insights from this work are not only relevant for channel flow, but more generally, for the physicochemical hydrodynamics of multiphase, multi-component systems.

Figures (9)

• Figure 1: Coaxial flow cell. The outer square capillary is clamped between two aluminum blocks using EPDM rubber (yellow) to create a seal. The inner circular capillary is centered using a circular EPDM rubber ring that is placed halfway on the inner capillary, allowing for the sheath flow to pass through at the edges of the outer capillary.
• Figure 2: Ternary diagram of the Ouzo system in terms of mass fraction, as predicted by UNIFAC constantinescu2016further. The solid black line denotes the binodal, and the dark green lines denote tie lines. The change in composition in the radial direction inside the flow is indicated with the magenta arrows, starting at a mixture of $\qty{12}{\percent}$ transanethole and $\qty{88}{\percent}$ ethanol by weight.
• Figure 3: Image sequence showing the creation, growth and upstream motion of an oil droplet. On the left, a detailed view of the Rayleigh-Plateau-like instability (I) and the chain of droplets downstream of a large droplet (II) are shown. Once a droplet has formed, it grows while it moves downstream until it starts hovering (III), moves upstream (IV), gets deformed into an oblate shape and undergoes a rotational instability (V) that eventually transitions into a radial translational motion (VI). The maximum axial velocity of the droplet in upstream direction is $\qty{1.83}{\milli\metre\per\second}$. Sheath flow: 175 of pure water; Jet flow: 5 of 88:12 ethanol to transanethole, weight ratio. The bottom and the top of the images correspond to a downstream position of $z_{\mathrm{bottom}}=\qty{6.085}{\milli\metre}$ and $z_{\mathrm{top}}=\qty{7.238}{\milli\metre}$, respectively. The frames shown in this figure correspond to supplementary movie 1.
• Figure 4: Bubble size-dependent motion reversal of a $\mathrm{CO_2}$ bubble in an ethanol jet in water. The ethanol jet is super-saturated with $\mathrm{CO_2}$ and contains smaller bubbles (downstream motion indicated by dashed arrows) that coalesce with the large bubble. (I): bubble moves downstream. (II): bubble starts to hover at constant z-position. (III): bubble starts to move upstream. Throughout this process, the bubble grows due to coalesence with smaller bubbles and because of the flow of liquid supersaturated with $\mathrm{CO_2}$ along the bubble surface. The flow rates are $\qty{200}{\micro\litre\per\minute}$ (water) and $\qty{23}{\micro\litre\per\minute}$ (ethanol). The bottom and the top of the images correspond to a downstream position of $z_{\mathrm{bottom}}=\qty{1.069}{\milli\metre}$ and $z_{\mathrm{top}}=\qty{1.834}{\milli\metre}$, respectively. The frames shown in this figure correspond to supplementary movie 2.
• Figure 5: Quasi-stationary solution for the single-phase system under the experimental conditions. (a) Composition and jet development, with gravity acting from top to bottom. At the left, the ethanol mass fraction ($wt\%$) is shown, at the right the regions prone to nucleation (green) based on the binodal curve from Fig. \ref{['fig:binodal_exp']} are indicated. At the nozzle, an ethanol-transanethole mixture enters through the inflow boundary, while water flows in at the outer boundary. (b) Regions prone to nucleation due to Ouzo effect (right) and ethanol $wt\%$ (left) within an area between 6mm and 7mm away from the nozzle. (c) Ethanol $wt\%$ (left) and velocity magnitude (right) close to the nozzle.