Dripping-onto-droplet rheometry of sodium alginate solutions

In this experimental and theoretical study, we assess the extensional relaxation time of sodium alginate solutions by using dripping-onto-droplet capillary breakup rheometry (DoD), e.g., the capillary thinning and breakup of viscoelastic filaments formed following the coalescence of a millimetric-nozzle-generated pendant drop with a lower droplet cap of the same fluid contained in a millimetric pool in ambient air.

Hence, we extend the analyses conducted by El Khoury et al.

(2026) from Newtonian to viscoelastic fluids.

Our approach relies on experiments recorded with a high-speed camera using sodium alginate in deionised water, with alginate concentrations ranging from 0.1% to 8% by weight.

The results are depicted by considering the dynamics of fluid filament thinning, stress balances, and scaling laws.

Extensional relaxation times are resolved from the filament diameter evolution.

Three flow regimes are highlighted: capillary-inertial, capillary-elastic, and mixed capillary-inertio-elastic.

The findings are summarised in a two-dimensional diagram that correlates the filament breakup time with different flow regimes using the important dimensionless parameter of the problem, e.g., the intrinsic Deborah number (which relates the extensional relaxation time to the characteristic capillary-inertial time).

This diagram can be used to quantify both the solution's extensional relaxation time and the liquid/air surface tension solely from filament breakup times.