DWR-drag: A new generation software for the double wall-ring interfacial shear rheometer's data analysis

The double wall-ring (DWR) rotational configuration is nowadays the instrument of choice regarding interfacial shear rheometers (ISR) in rotational configurations. Complex numerical schemes must be used in the analysis of the output data in order to appropriately deal with the coupling between interfacial and bulk fluid flows, and to separate viscous and elastic contribution or the interfacial response. We present a second generation code for analyzing the interfacial shear rheology experimental results of small amplitude oscillatory measurements made with a DWR rotational rheometer. The package presented here improves significantly the accuracy and applicability range of the previous available software packages by implementing: i) a physically motivated iterative scheme based on the probe's equation of motion, ii) an increased user selectable spatial resolution, and iii) a second order approximation for the velocity gradients at the ring surfaces. Moreover, the optimization of the computational effort allows, in many cases, for on-the-fly execution during data acquisition in real experiments.

Program summary

Program Title: DWR-Drag

CPC Library link to program files: https://doi.org/10.17632/vw8k79tmr6.1

Licensing provisions: GPLv3

Programming language: MATLAB and Python

Supplementary material: An additional document illustrating further software tests regarding flow structure and details about the numerical method used is provided as a Supplementary Material.

Nature of problem: How to determine the interfacial dynamic moduli of fluid–fluid interfaces from experimental data has been a challenge in the rheologists community because it requires i) to accurately separate the contributions of the drags exerted by the interface and the adjacent bulk phases, and ii) to accurately separate the viscous and elastic contributions to the interface response. Moreover, in most cases, the velocity profiles at the interface and the bulk phases are not linear and, consequently, simplifying hypothesis about the interfacial and bulk phases velocity fields are useless.

Solution method: The physical model includes the upper and lower bulk fluid phases, represented as Newtonian fluids (Navier-Stokes equations), the equilibrium of stresses at a viscoelastic interface under shear (Boussinesq-Scriven equation), and the probe's equation of motion. The hydrodynamic problem is solved using a second order centered finite differences scheme. The representation of the drag on the probe is much improved by implementing a selectable spatial resolution based on the ring's cross-section dimension and by a second order representation of the velocity gradient close to the ring's walls. An iterative scheme allows for obtaining the flow configuration that best matches the experimental data (the complex amplitude ratio) and, consequently, the optimal value of the interfacial dynamic moduli or, equivalently, the interfacial complex viscosity.