How elasticity affects bubble pinch-off

TL;DR

This study shows that viscoelasticity fundamentally alters bubble pinch-off differently from drop pinch-off: in the dilute regime, elasticity does not produce a persistent air-thread and pinch-off is largely inertia-driven with $h o 0$ following an $h o (Bt)^{1/2}$ scaling. Through experiments on PEO solutions, Basilisk-based Oldroyd-B simulations, and a 2D slender-jet theory, the authors demonstrate that elastic stresses diverge radially as $rac{\sigma_{rr}}{G} o ig(rac{h_0}{h}ig)^2$, but this divergence is too weak to arrest pinch-off unless polymer concentration exceeds the overlap threshold. Only at higher concentrations is a thread observed, often accompanied by altered breakup modes and satellite bubbles dependent on needle size. The findings clarify why bubble pinch-off lacks a universal viscoelastic thinning law in the dilute limit and suggest that viscoelastic bubble dynamics could serve as a rheological probe at higher concentrations, motivating further modeling with advanced polymer constitutive equations. Overall, the work highlights a clear distinction between viscoelastic drop and bubble pinch-off and provides a framework for interpreting elasticity-driven effects in bubbly systems.

Abstract

The pinch-off of bubbles in viscoelastic liquids is a fundamental process that has received little attention compared to viscoelastic drop pinch-off. While these processes exhibit qualitative similarities, the dynamics of the pinch-off process are fundamentally different. When a drop of a dilute polymer solution pinches off, a thread is known to develop that prevents breakup due the diverging polymer stresses. Conversely, our experiments reveal that this thread is absent for bubble pinch-off in dilute polymer solutions. We show that a thread becomes apparent only for high polymer concentrations, where the pinch-off dynamics become very sensitive to the size of the needle from which the bubble detaches. The experiments are complemented by numerical simulations and analytical modeling using the Oldroyd-B model, which capture the dilute regime. The model shows that polymer stresses are still singular during bubble pinch-off, but the divergence is much weaker as compared to drop pinch-off. This explains why, in contrast to droplets, viscoelastic bubble-threads do not appear for dilute suspensions but require large polymer concentrations

Figures (12)

• Figure 1: Cartoon of viscoelastic drop and bubble pinch-off. (a) When a drop pinches off, the polymers become stretched longitudinal direction $z$, following the stretching of the neck. (b) When a bubble pinches off, the neck is still stretched in the longitudinal direction, but the polymers are stretched in the radial direction $r$. Note that the polymers are not drawn to scale.
• Figure 2: Snapshots of the bubble pinch-off process for different PEO concentrations ($M_W = 4.0 \times 10^6 \, \textrm{g/mol}$). (a) Overview image of the bubble pinch-off process, where the red square roughly indicates the region in which pinch-off occurs. (b), (c) and (d) show the bubble pinch-off process for a polymer concentration of $0$wt. %, $1/32\, \textrm{wt.}\, \%$ and $1\, \textrm{wt.}\, \%$, respectively. The scale bar in (b), (c) and (d) is $20$ µ m.
• Figure 3: Snapshots of the drop pinch-off process for different PEO concentrations ($M_W = 4.0 \times 10^6 \, \textrm{g/mol}$). (a) Overview image of the drop pinch-off process, where the red square indicates roughly the region where the images in (b), (c) and (d) are taken. (b), (c) and (d) show the drop pinch-off process for a polymer concentration of $0\, \textrm{wt.}\%$, $1/32\, \textrm{wt.}\%$ and $1\, \textrm{wt.}\%$, respectively. The scale bar in (b), (c) and (d) is $250$ µ m.
• Figure 4: The width of the neck at the center is normalized by the diameter of the needle ($d_{needle} = 1.54$ mm) over time ($t-t_0$) for different concentrations of PEO ($M_W = 4.0 \times 10^6 \, \textrm{g/mol}$).
• Figure 5: The effect of needle diameter $d_{needle}$. (a) The normalized width of the neck $h/d_{needle}$ plotted against time ($t-t_0$) at a concentration of $1\, \textrm{wt.} \, \%$ PEO ($M_W = 4.0 \times 10^6 \, \textrm{g/mol}$). (b) For the largest needle size used $d_{needle} = 1.54$ mm, the thread disintegrates into smaller bubbles over a period of approximately 400 µ s. (c) For the smallest needle size used $d_{needle} = 0.41$ mm, the thread ruptures after milliseconds and retracts towards the bubble. The scale bar in (b) and (c) is $20$ µ m.