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

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.

💡 Research Summary

The paper investigates a counter‑intuitive phenomenon observed in a coaxial “Ouzo” flow: oil droplets, which should be carried downstream by buoyancy and drag, actually migrate upstream. The authors combine three complementary approaches—experiments, computational fluid dynamics (CFD) simulations, and a semi‑analytical model—to uncover the underlying physics and identify the governing parameters.

Experimental setup
A vertical coaxial microfluidic cell is used. A binary mixture of trans‑anethole (oil) and ethanol (12 % oil, 88 % ethanol by weight) is injected through a 30 µm inner capillary, forming a central jet. A sheath flow of pure water surrounds the jet in a square outer capillary (2 mm × 2 mm). Because water diffuses inward while ethanol and oil diffuse outward, a radial concentration gradient develops. At a certain radius the ternary composition enters the two‑phase region of the water‑ethanol‑oil phase diagram, causing spontaneous nucleation of nanometer‑scale oil droplets (the classic “Ouzo effect”). These nanodroplets are observed as a dark mist surrounding the jet.

Droplet formation and upstream motion
Further downstream (z > 6 mm) the jet becomes unstable in a Rayleigh‑Plateau‑like manner, shedding larger droplets whose diameter is comparable to the jet width. Immediately after shedding, the droplet’s axial velocity is lower than the local centerline velocity of the surrounding continuous phase, so the droplet lags behind the jet. As the droplet grows, it experiences a strong interfacial tension gradient: the ethanol concentration is higher on the upstream side, lowering the surface tension there (σ = σ₀ − κc). This creates a Marangoni stress τ_M = ∇σ that pulls fluid along the droplet surface from low‑σ (high‑ethanol) to high‑σ (low‑ethanol) regions, generating a net force directed upstream. When this Marangoni force exceeds the combined drag and buoyancy forces, the droplet reverses its motion and travels upstream while continuing to grow. At larger sizes the droplet deforms into an oblate shape, develops a rotational instability, and eventually follows a meandering upstream trajectory.

Numerical simulations
To isolate the essential mechanisms, the authors perform axisymmetric CFD of the Navier‑Stokes equations coupled with a convection‑diffusion equation for ethanol concentration. The surface tension is modeled as σ(c) = σ₀ − κc, with κ > 0. Simulations reproduce the nucleation zone near the jet interface, the emergence of a Marangoni‑driven upstream force, and the subsequent droplet deformation and instability. Quantitatively, the Marangoni force per unit length, F_M ≈ 2πR ∂σ/∂z, is shown to dominate over the viscous drag, F_D ≈ 6πμU, for the experimentally relevant parameters.

Semi‑analytical model
Treating the droplet as a sphere (or spheroid) of radius R, the balance between Marangoni propulsion and Stokes drag yields an expression for the critical concentration gradient needed for upstream motion:
Δc_crit ≈ (9 μ U)/(κ R).
Using measured values of μ (water‑ethanol viscosity), κ (determined from independent tensiometry), and R (≈ 50–100 µm), the predicted Δc_crit matches the gradients inferred from the experiments, confirming that Marangoni stresses are the primary driver.

Auxiliary gas‑bubble experiment
To demonstrate the generality of the mechanism, the authors replace the oil‑ethanol mixture with pure ethanol saturated with CO₂. Large CO₂ bubbles nucleated in the ethanol jet exhibit the same sequence: downstream motion, hovering, and upstream migration as they grow by coalescence with smaller bubbles and by absorbing dissolved CO₂. This shows that the reversal does not rely on the specific oil‑water interfacial chemistry but on any system where a concentration‑induced surface‑tension gradient can develop.

Key governing parameters

1. Axial concentration gradient ∂c/∂z (set by diffusion and flow rates).
2. Surface‑tension sensitivity κ (∂σ/∂c).
3. Droplet (or bubble) radius R.
4. Continuous‑phase viscosity μ.
5. Density difference Δρ (buoyancy).

When the product κ R ∂c/∂z is large enough to overcome viscous drag and buoyancy, upstream motion occurs.

Conclusions and implications
The study provides the first comprehensive experimental, numerical, and theoretical demonstration that Marangoni stresses can reverse the direction of droplet motion in a confined co‑flow of a multicomponent liquid. This insight is relevant for microfluidic applications such as dispersive liquid–liquid micro‑extraction, controlled emulsification, and the design of multiphase reactors where concentration gradients are intrinsic. More broadly, it highlights that in any channel flow involving multicomponent mixtures, surface‑tension gradients can dominate over conventional forces, leading to unexpected transport phenomena that must be accounted for in device design and process optimization.