BiconeDrag is a software package that allows one to perform a flow field based data processing of dynamic interfacial rheology data pertaining to surfactant laden air-fluid interfaces obtained by means of a rotational bicone shear rheometer. MATLAB and Python versions of the program are provided. The bicone fixture is widely used to transform a conventional bulk rotational rheometer into an interfacial shear rheometer. Typically, such systems are made of a bicone bob, which is mounted on the rheometer rotor, and a cylindrical cup. Usually, the experiment consists of measuring the response of the interface under an oscillatory stress. The program takes the values of the torque/angular displacement amplitude ratio and phase difference to compute the interfacial dynamic moduli (or complex viscosity) by consistently taking into account the hydrodynamic flow both at the interface and the subphase. This is done by numerically solving the Navier-Stokes equations for the subphase velocity field together with the Boussinesq-Scriven boundary condition at the interface, and no slip boundary conditions elsewhere. Furthermore, the program implements a new iterative scheme devised by solving for the complex Boussinesq number in the rotor's torque balance equation. PROGRAM SUMMARYProgram Title: "BiconeDrag" Program Files doi: http://dx.doi.org/10.17632/4tmy9k4ys3.1 Licensing provisions(please choose one): GPLv3 Programming language: MATLAB (compatible with GNU Octave) and Python Operating System: Windows, Linux and Mac OS X Nature of problem(approx. 50-250 words): Obtaining the interfacial dynamic moduli, or the complex viscosity, of a surfactant laden air-liquid interface from the experimental data obtained by means of a bicone fixture mounted on the rotor of a conventional bulk rotational rheometer. The experimental data consist on the amplitude ratio and phase difference between the torque and the angular displacement of the rotor. The coupling between the surface and subphase fluid flows require a proper representation of the hydrodynamic velocity field both at the surface and at the liquid subphase. Solution method(approx. 50-250 words): We use a proper hydrodynamic model of the problem through the Navier-Stokes equations for the velocity field at the subphase, supplemented with the Boussinesq-Scriven boundary condition at the interface and no slip conditions elsewhere. The hydrodynamic equations are solved by means of a centered second order finite difference method and the flow field is used to compute the hydrodynamic drags exerted by the subphase and the interface on the bicone probe. Both calculated drags are later used in the rotor torque balance equation together with the rotor inertia term. Solving for the Boussinesq number in the torque balance equation then allows one to devise an iterative scheme that yields improved values of the complex Boussinesq number: starting from a convenient seed one obtains a converged value of the complex Boussinesq number such that the experimental and calculated values of the torque...

Flow field-based methods are becoming increasingly popular for the analysis of interfacial shear rheology data. Such methods take properly into account the subphase drag by solving the Navier–Stokes equations for the bulk phase flows, together with the Boussinesq–Scriven boundary condition at the fluid–fluid interface and the probe equation of motion. Such methods have been successfully implemented on the double wall-ring (DWR), the magnetic rod (MR), and the bicone interfacial shear rheometers. However, a study of the errors introduced directly by the numerical processing is still lacking. Here, we report on a study of the errors introduced exclusively by the numerical procedure corresponding to the bicone geometry at an air–water interface. In our study, we set an input value of the complex interfacial viscosity, and we numerically obtained the corresponding flow field and the complex amplitude ratio for the probe motion. Then, we used the standard iterative procedure to obtain the calculated complex viscosity value. A detailed comparison of the set and calculated complex viscosity values was made in wide ranges of the three parameters herein used, namely the real and imaginary parts of the complex interfacial viscosity and the frequency. The observed discrepancies yield a detailed landscape of the numerically-introduced errors.

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Flow field based methods are becoming increasingly popular for the analysis of interfacial shear rheology data. Such methods take properly into account the subphase drag by solving the Navier-Stokes equations for the bulk phases flows, together with the Boussinesq-Scriven boundary condition at the fluid-fluid interface, and the probe equation of motion. Such methods have been successfully implemented at the double wall-ring (DWR), the magnetic rod (MR), and the bicone interfacial shear rheometers. However, a study of the errors introduced directly by the numerical processing is still lacking. Here we report on a study of the errors introduced exclusively by the numerical procedure corresponding to the bicone geometry at an air-water interface. In our study we directly input a preset the value of the complex interfacial viscosity and we numerically obtain the corresponding flow field and the complex amplitude ratio for the probe motion. Then we use the standard iterative procedure to obtain the calculated complex viscosity value. A detailed comparison of the set and calculated complex viscosity values is made upon changing different parameters such as real and imaginary parts of the complex interfacial viscosity and frequency. The observed discrepancies yield a detailed landscape of the numerically introduced errors.