At a water/oil interface, C10 E8 could be described with an adsorption-sensitive model, while SDS was better described when the model included short-lived transport beneath the interface. The finding comes from a laboratory study of interfacial tension, the tension at the boundary between two liquids, using a microfluidic instrument designed to separate surfactant adsorption from transport through the liquid.
The manuscript is an arXiv preprint dated 31 Aug 2026. It combines equilibrium measurements, diffusion measurements and dynamic interfacial-tension curves, then determines equilibrium, transport and kinetic parameters sequentially before combining them in a nonequilibrium model.
The setup, called EDGE, uses an oil meniscus in a shallow pore while the aqueous solution is continuously renewed. Releasing a droplet and varying the waiting time provide a controlled interface age and a corresponding tension measurement.
A faster view at short times
The contrast appeared most clearly at short interface ages. EDGE measured much faster short-time tension relaxation than classical rising-drop tensiometry, while the long-time limiting tensions were comparable. The comparison reflects different transport regimes, an important qualification when the curves are read as evidence about adsorption rates.
For C10 E8, the dilute rising-drop analysis gave a diffusion coefficient of 1.0 × 10−9 square metres per second. The equilibrium fit gave a maximum surface excess, the fitted amount per unit area at the interface, of 2.20 × 10−6 moles per square metre, and an equilibrium adsorption constant of 2,074 cubic metres per mole. Its root-mean-square deviation, a measure of the gap between the measurements and model, was 0.45 millinewtons per metre.
With those constraints in place, one adsorption-limited kinetic pair described the fitted C10 E8 range, from 0.01 to 1 times the critical micelle concentration, or CMC. The adsorption rate constant was 17.2 cubic metres per mole per second, and the desorption rate constant was 8.3 × 10−3 per second. The overall root-mean-square error across the dynamic fit was 1.75 millinewtons per metre.
A calculated regime parameter stayed below one throughout the analyzed relaxation. Under the study’s criterion, that supports an adsorption-sensitive interpretation of the fitted constants. The conclusion depends on the model-based regime criterion and fixed transport parameters.
SDS reveals the transport problem
SDS was less fully described by adsorption alone. Its equilibrium fit yielded a maximum surface excess of 6.0 × 10−6 moles per square metre, an equilibrium adsorption constant of 5.18 cubic metres per mole and an electrostatic tension factor of 0.15. Some electrostatic and lateral-interaction parameters were fixed rather than fitted simultaneously.
An adsorption-only fit across four SDS concentrations produced an adsorption rate constant of 9.63 cubic metres per mole per second, a desorption rate constant of 1.86 per second and an overall root-mean-square error of 1.32 millinewtons per metre. It captured the overall timescale and concentration dependence, but systematic deviations remained in the complete relaxation shape.
The regime analysis, which compares adsorption demand with mass transport, put the maximum effective parameter at about 0.50, below one. This indicated that adsorption kinetics remained identifiable under the study’s criterion, but transport effects were not negligible. The simplifying assumption that subsurface concentration equals bulk concentration was not guaranteed throughout the relaxation.
The mixed model allowed the bulk and subsurface concentrations to differ. It represented initial depletion near the interface followed by diffusive replenishment over about 70 milliseconds. The fit gave an adsorption rate constant of 10.62 cubic metres per mole per second, a desorption rate constant of 2.05 per second and an effective subsurface storage length of 6.95 micrometres. Its reported root-mean-square error was 0.936 millinewtons per metre, compared with 1.32 for the adsorption-only fit.
The two SDS fits placed the adsorption rate constants at 9.63 and 10.62 cubic metres per mole per second. The authors interpret this modest shift as indicating that transient subsurface transport matters to the relaxation shape, while the inferred adsorption rate changes only moderately when that memory is included.
A method with boundaries
The result is a measurement framework, not evidence that the fitted rates are universal. The C10 E8 interpretation rests on a model-based regime criterion and fixed transport parameters. In the SDS analysis, some electrostatic and lateral-interaction terms were fixed, and the storage length is an effective model parameter rather than a directly measured molecular-layer thickness. The reported fits do not include confidence intervals.
The tested evidence covers C10 E8 and SDS in one water/oil setup. It leaves open whether the fitted rates transfer across other surfactants, geometries, renewal velocities or ionic strengths.
The acknowledgements report doctoral funding from IFP Energies nouvelles and laboratory and equipment access from Wageningen University and Research.
Paper data and sources
Original title: Geometry-Controlled Dynamic Tensiometry Resolves Intrinsic Surfactant Adsorption Kinetics
Authors: Camille Brigodiot, Boxin Deng, Christine Dalmazzone et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
Original paper · Full text