Droplet impact on surfactant-laden thin liquid films: Vortex ring dynamics

Abstract

Droplet impact on surfactant-laden thin liquid films is investigated experimentally with emphasis on vortex ring dynamics. Bottom- and side-view imaging reveal that increasing surfactant concentration progressively stabilize vortex rings, suppress azimuthal instabilities and promote concentric mixing patterns. A regime map is established in terms of film thickness, Reynolds number, and surface-tension ratio, yielding an empirical instability threshold. Shadowgraphy observations suggest that Marangoni stresses modify early capillary-wave dynamics, potentially altering vortex ring formation and delaying instability onset. These findings clarify the link between interfacial stresses, vortex ring dynamics, and mixing patterns in thin-film droplet impact.

Figures (7)

• Figure 1: Vortex ring dynamics and associated mixing patterns during droplet impact on liquid films in the absence of surfactants. (a) For thick films ($\delta=0.90$), impact generates a primary vortex ring (PVR) that expands radially after interaction with the wall. Scale bar is equivalent to 1 mm. (b) For thin films ($\delta=0.45$), stronger wall interaction promotes boundary layer lift-off (BLL) and the formation of secondary (SVR) and tertiary (TVR) vortex rings, eventually leading to vortex rings breakdown. Scale bar is equivalent to 1 mm. (c-f) Bottom-view fluorescence visualizations showing the evolution of mixing patterns. Scale bar is equivalent to 3 mm. (c) expansion of primary vortex ring. (d) concentric ring structures corresponding to multiple vortex rings regime. (e) Vortex ring instability leading to breakdown. (f) Onset of azimuthal perturbations for thinner films ($\delta=0.09$). The red boxes highlight the region where vortex rings entrain droplet and film liquid in different proportions, producing concentration variations that appear in the bottom view as successive concentric mixing rings
• Figure 2: (a) Schematic illustration of bottom-view experimental setup, together with a side-view shadowgraphy configuration for visualizing the interface evolution. (1) Syringe pump, (2) z-Traverse, (3) Cannula, (4) Liquid film on FTO glass substrate, (5) High power LED, (6) x,y,z-Traverse, (7) HS-Camera, (8) Dichroic mirror ($\lambda_L>550nm$) with bandpass filters (absorption $532nm$ and emission $575nm$), (9) Microscope Objective, 10) HS-Camera + lens, 11) LED. (b) Schematic representation of the side-view experimental configuration used for investigating vortex-ring dynamics illustrating the droplet generator, laser sheet illumination ($\lambda_L=532nm$) and high-speed camera with Lens and Longpass filter ($\lambda_L>560nm$).
• Figure 3: Influence of surfactant concentration on mixing patterns following droplet impact on thin liquid films. Bottom-view fluorescence visualizations are shown for water droplets impacting aqueous films of pure water $\sigma^*=1$ and sodium dodecyl sulfate (SDS) solutions at different concentrations corresponding to $\sigma^*=0.93$ (0.01 CMC), $\sigma^*=0.87$ (0.1 CMC) and $\sigma^*=0.5$ (1.3 CMC). Cases are presented for different film thicknesses and impact conditions. (a)$\delta=0.09$, $Re=3000$ and $We=54$. (b)$\delta=0.22$, $Re=3000$ and $We=54$. (c)$\delta=0.09$, $Re=3300$ and $We=64$. (d)$\delta=0.22$, $Re=3300$ and $We=64$. Scale bar is equivalent to 2 mm.
• Figure 4: Side-vie LIF visualizations at $t=60ms$ illustrating the influence of surfactant concentration on vortex ring dynamics following droplet impact on thin liquid films ($\delta=0.45$, $Re=3000$, $We=54$). A water droplet impacts aqueous films of pure water $\sigma^*=1$ and sodium dodecyl sulfate (SDS) solutions at increasing concentrations corresponding to $\sigma^*=0.93$ (0.01 CMC), $\sigma^*=0.87$ (0.1 CMC) and $\sigma^*=0.5$ (1.3 CMC). Scale bar is equivalent to 1 mm.
• Figure 5: Regime map for the onset of azimuthal vortex ring instability in terms of dimensionless film thickness, Reynolds number and surface tension ratio ($\delta,Re,\sigma^*$). Red markers denote cases exhibiting vortex ring instability, whereas green markers correspond to stable, axisymmetric vortex evolution. The shaded surface represents the instability boundary inferred from a non-linear support vector machine classifier, while the colored regions indicate stable (green) and unstable (red) regimes. The boundary shifts toward higher Reynolds numbers with decreasing $\sigma^*$, reflecting the progressive stabilization by surfactant-induced Marangoni stresses.