A different ending for the liquid thread
At 0.1 g/L of BSA, the liquid thread in the experiment stayed centered as it thinned and produced no satellite drops, the secondary droplets that can appear during pinch-off. The study combined these breakup observations with interfacial-rheology measurements, a theoretical model, and a proposed scaling law.
The reported boundary between satellite-drop and no-satellite-drop behavior varied with both concentration and aging time. It moved from 0.1 g/L at 100 seconds of aging to 0.02 g/L at 600 seconds. Satellite-drop radius also fell as concentration and aging time increased, with the authors reporting effective elimination at an amount on the order of 10 to 100 parts per million of BSA.
The thinning pattern itself changed between the concentration ranges. At or below 0.01 g/L, the minimum neck radius followed a two-thirds-power relation with time to pinch-off. At or above 0.1 g/L, the late-stage exponent was approximately one, meaning the radius followed an approximately linear scaling with that time variable.
The signal appeared at the surface
The team worked with BSA dissolved in sodium chloride buffer across concentrations from 0.001 to 5 g/L and aging times from 100 to 600 seconds. The cylindrical thread had an initial radius of 0.32 mm and a length of about four times that radius, then was thinned quasi-statically between identical blunt needles.
To examine the interface, the researchers measured its response to oscillatory shear with a double-wall ring module on a rotational shear rheometer. They measured its dilatational response, or response to changes in surface area, with an oscillating pendant-drop method.
Both the surface dilatational elastic modulus and surface shear viscosity increased with BSA concentration and aging time. For concentrations at or above 0.05 g/L, the dilatational elastic modulus was between 50 and 70 mN per meter.
The bulk liquid, however, was reported to retain unchanged properties after trace BSA addition, with the Ohnesorge number staying between 0.006 and 0.008 across cases. A separate SDBS control, tested over a wide concentration range that included its critical micelle concentration, showed breakup behavior and satellite-drop sizes similar to the neat solution.
A model points to surface shear viscosity
The study then used a numerical model to compare the observed breakup patterns with calculated thread evolution. The model equations were solved with a finite-difference method using a fifth-order WENO scheme.
Numerical solutions for clean and BSA-coated threads reproduced the reported evolution of the thread profile and whether satellite drops appeared. The authors said this supported the model's description of the pinch-off dynamics.
In the model's late-stage force analysis, surface shear viscous force was identified as balancing capillary force and exceeding the other listed forces. The fastest-thinning position remained at the center, and the modeled thread had no satellite drop. That gives the report's proposed explanation for the centered neck and absent satellite drops under the tested model condition.
The authors also propose a near-pinch-off scaling law for the surface-viscosity-modulated regime: . In that expression, rmin is the minimum neck radius after scaling, Ohs-mu is the surface Ohnesorge number, and tau is the scaled time to pinch-off; the relation says the radius scales with tau multiplied by one divided by Ohs-mu.
A finding tied to its test setup
A separate model comparison highlighted surface dilatational elasticity. When the model set the surface elastocapillary number Ecd to zero, it produced a long, thin thread late in breakup; the authors interpret surface dilatational elasticity as associated with a shorter thread and fewer new necks beyond the center.
The report's evidence stays close to the systems it tested: clean aqueous threads, BSA in sodium chloride buffer, an SDBS control, and the corresponding model cases. The physical experiment used a quasi-static cylindrical thread between identical blunt needles, so the reported regime is tied to that geometry and thinning procedure. The document is an arXiv version 1 preprint dated 28 Aug 2026.
Paper data and sources
Original title: How Surface Viscoelasticity Eliminates Satellite Drops
Authors: Xiaocong Yang, Qingfei Fu, Lijun Yang, Bingqiang Ji
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
Original paper · Full text