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Capillary breakup of free and wetting liquid bridges of aqueous xanthan gum solutions

This study experimentally investigates the capillary breakup of aqueous xanthan gum liquid bridges, revealing that while free bridges exhibit distinct inertia-capillary, elasto-capillary, and viscous-capillary regimes, wetting bridges display a unified viscous-capillary response that collapses onto a master curve due to flow history effects and shows reduced sensitivity to substrate wettability.

Original authors: Salar Farrokhi, Peyman Rostami, Günter K. Auernhammer, Steffen Hardt

Published 2026-07-29

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Salar Farrokhi, Peyman Rostami, Günter K. Auernhammer, Steffen Hardt

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world where liquids don't just flow; they dance, stretch, and sometimes snap like rubber bands. This is the playground of interfacial fluid mechanics, a branch of physics that studies how liquids behave when they meet air or solid surfaces. At the heart of this story is the liquid bridge: a tiny column of liquid suspended between two points, like a drop of water hanging from a faucet or a puddle stretching between your fingers. When these bridges get too thin, they break, or "pinch off." For simple liquids like water, this happens in a predictable, conical snap. But when you add long, stringy molecules called polymers (think of them as microscopic spaghetti), the liquid gets stretchy and behaves very differently. Scientists care about this because these "snapping" moments happen everywhere in real life, from how inkjet printers spray tiny dots of ink to how we spray paint or even how our bodies process fluids. Understanding exactly how and why these bridges break helps engineers design better products and scientists understand the hidden rules of fluid motion.

Now, let's dive into the specific story of xanthan gum, a common ingredient in food (like salad dressing) that makes things thick and gooey. Researchers at Technische Universität Darmstadt and the Leibniz Institute of Polymer Research wanted to see how this specific "spaghetti" liquid behaves when its bridges break. They set up a fascinating experiment comparing two scenarios: free bridges (liquid floating in mid-air, like a drop falling from a needle) and wetting bridges (liquid stuck to a solid surface, like a puddle being pulled apart on a table).

The Mid-Air Snap: A Three-Act Play

When the team watched the free bridges (the ones floating in air), they saw a dramatic, three-part performance.

The Inertia-Capillary Act: At first, the bridge thins quickly, driven by surface tension, much like a water drop falling.
The Elasto-Capillary Act: Suddenly, the xanthan gum molecules get stretched out. They act like a tiny, invisible rubber band, fighting back against the thinning. This creates a short-lived "kink" where the bridge slows down its thinning speed. The researchers found this elastic phase is very brief for xanthan gum, unlike some other polymers that hold the stretch longer.
The Terminal Viscous-Capillary Act: Finally, the molecules are fully stretched and aligned. The bridge enters a steady state where it thins at a constant speed.

Here is the magic trick the researchers discovered: Even though the xanthan gum solutions were thick and crowded with molecules (what scientists call "semi-dilute"), their stretching behavior acted as if they were thin and sparse ("dilute"). When they adjusted their math to account for the amount of gum and the thickness of the water, all the different liquids collapsed onto a single, perfect curve. It's as if every drop, regardless of how much gum was in it, was following the exact same secret recipe for breaking apart.

The Sticky Floor: A Different Story

The plot thickens when the liquid touches a solid surface. The team created wetting bridges on silicon wafers coated with different chemicals to make them either "hydrophilic" (water-loving) or "hydrophobic" (water-fearing).

In this scenario, the drama changed completely. The neat three-act play vanished. There was no distinct elastic "rubber band" phase. Instead, the wetting bridges seemed to skip straight to the final, steady thinning phase from the very beginning. The researchers suggest this is because the liquid has a "bad memory" of its past. As the bridge formed and was pulled across the surface, the friction against the floor and the flow of the liquid itself likely scrambled the polymer molecules before the breakup even started. This "flow history" smoothed out the distinct stages, making the whole process look like one long, steady stretch.

Another surprising finding was how little the surface type mattered. For normal liquids, changing the surface from water-loving to water-fearing changes how fast the bridge breaks by a huge amount (about three times faster or slower). But for the xanthan gum solutions, the surface type barely mattered at all. The thick, stretchy gum seemed to overpower the friction of the surface, making the breakup speed almost the same whether the floor was sticky or slippery.

The Universal Shape

Finally, the team looked at the shape of the bridges as they broke. By resizing the images to a standard scale, they found something beautiful: whether the bridge was free-floating or stuck to a surface, and whether it was made of a little gum or a lot, the shape of the breaking bridge followed a nearly universal pattern. It's like finding out that no matter the size of the dancer or the music playing, the final pose before the curtain falls is always the same.

In short, this paper suggests that while floating and stuck liquid bridges follow different rules, they can both be understood through a unified mathematical lens. The presence of a solid surface seems to erase the complex "elastic" stages seen in free-floating drops, replacing them with a simpler, steady thinning process driven by the unique way xanthan gum molecules stretch and align. This helps us understand that we can't just assume what happens in a floating drop will happen on a surface; the floor changes the dance.

Technical Summary: Capillary Breakup of Free and Wetting Liquid Bridges of Aqueous Xanthan Gum Solutions

Problem Statement
The capillary-driven breakup of liquid bridges is a fundamental phenomenon in interfacial fluid mechanics with applications ranging from inkjet printing to microfluidics. While the dynamics of Newtonian liquids and flexible polymer solutions are relatively well-understood, the behavior of semi-flexible polymers, such as xanthan gum (XG), presents distinct challenges. Previous studies have highlighted that XG solutions exhibit different extensional rheology compared to flexible polymers, often showing a short-lived elasto-capillary response. However, a significant gap exists in understanding how these semi-flexible polymers behave in wetting liquid bridges (where the liquid remains attached to solid substrates). Unlike free bridges, wetting bridges involve coupled extensional-shear deformations, non-axisymmetric geometries, and contact line friction (CLF). It remains unclear whether the breakup dynamics of wetting XG bridges are governed primarily by shear-thinning behavior or if extensional dynamics and molecular architecture play a dominant role, and how substrate wettability influences these processes.

Methodology
The authors conducted high-speed imaging experiments to investigate the breakup dynamics of aqueous XG solutions in two configurations:

Free Liquid Bridges: Formed between two parallel plates (dripping setup) in air.
Wetting Liquid Bridges: Formed on solid substrates (microfluidic chip setup) where the liquid bridges connect two channel outlets on a surface.

The study utilized XG solutions with varying concentrations (up to 400 ppm) and solvent viscosities (water/glycerol mixtures). Substrates were coated with silanes to create hydrophilic (TFPTS) and hydrophobic (PFDTS) surfaces. To minimize electrostatic effects, all setups were grounded.

The primary analytical tool was a phase-space representation, plotting breakup velocity ( $U$ ) against the minimum bridge diameter/width ( $d$ ). This approach was chosen over simple time-evolution plots ( $d$ vs. $t$ ) to better reveal instantaneous thinning dynamics, identify regime transitions, and provide an objective framework for comparing different liquids without relying on the precise determination of instability onset or breakup time.

Key Results

Free Liquid Bridges:
- Three distinct dynamic regimes were identified: an initial inertia-capillary (IC) regime, a short-lived elasto-capillary (EC) regime, and a terminal viscous-capillary (TVC) regime.
- The onset of the EC regime was marked by a "kink" or local maximum in the $U-d$ curve. The study found that the critical velocity at this onset scales with solvent viscosity ( $U_c \sim \eta_s^{-0.54}$ ) but is nearly independent of polymer concentration, suggesting the transition is driven by a critical strain rate related to molecular orientation.
- In the TVC regime, the effective extensional viscosity scaled linearly with both polymer concentration and solvent viscosity ( $\eta_{eff} \propto c \eta_s$ ). This indicates an effectively dilute-like extensional response despite the solutions being semi-dilute under equilibrium conditions. The authors attribute this to the semi-flexible nature of XG, which aligns with flow rather than undergoing a dramatic coil-stretch transition, thereby limiting intermolecular interactions even at higher concentrations.
- Rescaling the bridge profiles by the critical diameter ( $d_c$ ) revealed a nearly universal evolution of the free bridge shape.
Wetting Liquid Bridges:
- Unlike free bridges, wetting bridges exhibited no distinct regime transitions. The dynamics remained consistent with a single, terminal viscous-capillary-like response throughout the entire breakup process.
- The same scaling law that collapsed the TVC regime of free bridges ( $U \propto \gamma / (c \eta_s)$ ) successfully collapsed the breakup dynamics of wetting bridges for various concentrations and solvent viscosities onto a master curve.
- The authors hypothesize that the combined flow history (bridge formation, substrate-induced shear, and capillary thinning) modifies polymer conformations early in the process, obscuring the EC regime transitions observed in free bridges.
- Substrate Wettability: XG wetting bridges showed a markedly weaker dependence on substrate wettability (hydrophilic vs. hydrophobic) compared to Newtonian liquids. While Newtonian bridges showed significant changes in breakup velocity with wettability, XG solutions were largely insensitive, except at very low concentrations. This is attributed to the dominance of bulk viscous stresses over contact line friction (CLF) in XG solutions.
- Wetting XG bridges exhibited greater axial elongation and suppressed the formation of secondary necks compared to Newtonian liquids, further supporting the reduced influence of CLF.
- Rescaling the contact line profiles by the characteristic length $d_1$ (associated with the first velocity maximum) revealed a universal evolution of the wetting contact line profile.

Significance and Claims
The paper claims to provide new insights into the capillary breakup of semi-flexible polymer solutions by demonstrating that:

Unified Scaling: Despite the fundamental differences in flow geometry (free vs. wetting), both systems can be described within a unified scaling framework based on effective extensional viscosity.
Suppression of EC Regime: The presence of a solid substrate fundamentally alters the evolution of polymer conformations, suppressing the distinct elasto-capillary response typically seen in free bridges of semi-flexible polymers.
Extensional vs. Shear Dominance: The results suggest that for wetting bridges of semi-flexible polymers, the breakup dynamics are dominated by extensional-like viscous stresses rather than shear-thinning effects or contact line friction, even though the flow field is coupled.
Limitations of Extrapolation: The study emphasizes that conclusions drawn from free liquid bridge experiments cannot be directly extended to substrate-supported geometries, as the substrate significantly modifies the dynamic regimes and the role of molecular architecture.

The authors remain modest regarding the precise mechanisms behind the suppression of the EC regime in wetting bridges, noting that the exact interplay of flow history and polymer conformation warrants further investigation. They also acknowledge that the overlap concentration ( $c^*$ ) for XG is subject to uncertainty due to ionic strength variations, though they argue the observed scaling is robust across the tested range.

The Mid-Air Snap: A Three-Act Play

The Sticky Floor: A Different Story

The Universal Shape

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