BiconeDrag—A data processing application for the oscillating conical bob interfacial shear rheometer

Abstract

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: BiconeDragProgram Files doi:http://dx.doi.org/10.17632/c245bmgf5n.1Licensing provisions: GPLv3Programming language: MATLAB (compatible with GNU Octave) and PythonNature of problem: 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 in 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 requires a proper representation of the hydrodynamic velocity field both at the surface and at the liquid subphase.Solution method:: 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/angle amplitude ratio coincide within a user selected tolerance. The values of the rheological variables are obtained directly from the value of the complex Boussinesq number.Additional comments including restrictions and unusual features: The program is valid only for air/fluid interfaces. The interface may have or not a thin film either newtonian or viscoelastic. The subphase fluid may be newtonian or viscoelastic (having non negligible storage and loss moduli) though the user must take care of the possible frequency dependence of the dynamic moduli.