Solutocapillary bubble centering in a confined ethanol plume in water

Abstract

This study investigates the radial centering of gas bubbles within a buoyant plume of ethanol injected into a co-flowing water sheath flow in a vertical capillary. Bubbles nucleate in the ethanol stream due to CO$_2$ supersaturation and rapidly migrate toward the plume axis via solutocapillary (Marangoni) forces driven by interfacial tension gradients in the ethanol-water mixture. Experiments reveal that bubbles of varying sizes reliably align along the plume centerline, facilitated by steep radial concentration gradients near the plume boundary. A reduced-order model supports robust centering across a wide range of bubble radii. For larger bubbles, axial Marangoni effects modulate ascent velocities and can even induce upstream migration under transient conditions, highlighting the complex feedback between bubble dynamics and plume distortion. The results demonstrate that solutocapillary migration provides a reliable mechanism for contact-free bubble focusing, with implications for bubble manipulation in microfluidics, reactors, and phase-separation processes.

Figures (7)

• Figure 1: Sketch of the experimental setup. The outer square capillary has inner dimensions of 2 by 2. The inner tip diameter of the inner capillary is 30. Ethanol is indicated in lilac and water in blue. The length of the outer capillary is approximately 6.
• Figure 2: Radial centering of bubbles. (a) pure and (b) carbonated ethanol injected into a sheath flow of water. In (b), a chain of CO$_2$ bubbles rises in the plume of carbonated ethanol. (c) shows a detailed view of the nozzle region indicated by the dashed region in panel (b). Panels (d-e) show simulation results of an ethanol plume injected into a sheath flow of water. The left split in panel (d) shows the ethanol mass fraction, the right split displays the velocity field on a logarithmic scale together with streamlines. In (e), the axial velocity (top) and ethanol mass fraction (bottom) are shown as a function of the radial coordinate, at several positions $z$ downstream of the nozzle. In all cases shown the sheath flow rate was set to $Q_\text{H$_2$O}$ = 200 µl/min, while the ethanol flow rate was $Q_\text{EtOH}$ = 45 µl/min in (a), 42 µl/min in (b), and 23 µl/min in (c-e).
• Figure 3: Computed radial centering of bubbles in a diffusively broadening jet of initial radius $r_\text{jet}=100$ µm. (a) Trajectories $r(t)$ of bubbles with diameter $R=1$ µm initially located a different radial positions $r_0$ (black lines). (b) Trajectories of bubbles with radii in the range $R=(10^{-9}, 10^{-8},$…$, 10^{-5})$ m, initially positioned at $r_0 = r_\text{jet}$. The same trajectories are shown in (c) using rescaled nondimensional coordinates. The dashed lines correspond to the short-time limit (\ref{['eq:shortTimeSolRadial']}--\ref{['eq:shortTimeSolRadial_parameters']}). In (a) and (b) the ethanol mass fraction $\omega_\text{EtOH}$ is shown in the background with gray isolines at contour levels $10^{-9}, 10^{-8}, \ldots, 10^{-1}$ and $1- 10^{-1},\ldots, 1-10^{-9}$. The contours 0.1 and 0.9 are visible in the colorbar.
• Figure 4: (a, c--e) CO$_2$ bubbles of various diameters rising inside the ethanol jet. Magenta circles with corresponding label indicate the respective diameters. In (b) a space-time slice of the video corresponding to the frame in (a) is shown. The vertical axis corresponds to the center pixel column in the frame in (a) while the horizontal axis shows time. Parallel straight dashed lines indicate evenly spaced trajectories of a chain of bubbles separated at distance $l$ rising at velocity $U_0$, specified above the figure. For all experiments shown, carbonated ethanol at a flow rate of $Q_\text{EtOH} = 23$ µl/min is injected into a $Q_\text{H2O} = 200$ µl/min sheath flow of water.
• Figure 5: Time-series showing bubble centering and axisymmetric plume modulation under transient conditions. For large enough bubbles, Marangoni flow in axial direction can significantly influence the velocity of ascend, even leading to upstream migration. $Q_\text{EtOH}$ = 23 µl/min, $Q_\text{H$_2$O}$ = 200 µl/min.