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

Abstract

We present a new improved version of BiconeDrag, a code that allows one to obtain the values of interfacial dynamic moduli from dynamic experiments performed in rotational interfacial shear rheometers with bicone probes. The general structure of the program remains the same: starting from the values of the torque/angular displacement amplitude ratio, and by using the equations of the hydrodynamic field, it is possible to decouple the contribution of the subphase (bulk) drag from the true interfacial drag. In this new version we have improved the implementation of the boundary condition at the interface so that now it is built as second order centered finite differences (SOCFD hereafter) with the help of a line of phantom nodes. The new numerical implementation of the interfacial boundary condition yields smoother velocity profiles at the bicone rim, which result in a more accurate separation of interfacial and subphase drags and, consequently, in a more precise calculation of the interfacial dynamic moduli. New version program summaryProgram Title: BiconeDragCPC Library link to program files:https://doi.org/10.17632/c245bmgf5n.2Code Ocean capsule:https://doi.org/10.24433/CO.5536863.v1Licensing provisions: GPLv3Programming language: MATLAB (compatible with GNU Octave)Journal reference of previous version: Comput. Phys. Commun. 239 (2019) 184–196Does the new version supersede the previous version?: YesReasons for the new version: Remodeling the implementation of the interfacial boundary condition.Nature of problem: The different horizontal (second order centered finite differences) and vertical (first order finite differences) discretization schemes at the interface rendered radial and vertical velocity profiles that showed a mild non-smooth behavior at the bicone rim, that resulted in errors in the interfacial torque. Though small, such errors affected the values obtained for the dynamic moduli from the iterative process.Solution method: We have fully reworked the vertical discretization scheme at the interface, by using a line of fictitious nodes. Now the scheme is SOCFD in both the radial and the vertical coordinates everywhere.Summary of revisions: BiconeDrag [1] is a computer program for Flow field-based data analysis of the experimental data obtained with interfacial shear rheometers with bicone probes [2–4]. In the new version, we have reformulated the combination of the discretized Boussinesq-Scriven boundary condition and the Navier-Stokes equations for nodes at the interface. The original program was developed by adapting to the bicone geometry the ideas already used in references [5–8] for the magnetic needle ISR, [9] for the double wall-ring interfacial rheometer, and [2] for the oscillating rotational bicone rheometer. A complete account of the so-called Flow field-based data analysis techniques has been given elsewhere [4].The new discretization is now SOCFD in both spatial directions at the subphase and, more importantly, at the interface. In order to achieve the formulation of the SOCFD at the interface, a line of phantom nodes has been defined above the interface. However, an adequate combination of the discretized Boussinesq-Scriven boundary condition and the Navier-Stokes equations yields expressions for the matrix elements corresponding to the interface nodes in which the values of the velocity field at the phantom nodes are not present and, consequently, the values of the velocity field at the phantom nodes do not appear explicitly in the numerical formulation of the problem. Using the notation in Ref. [3] the new expression reads:(1)iRegj,1⁎=N2(1+2Mh¯Bo⁎)(gj+1,1⁎+gj−1,1⁎−2gj,1⁎+gj+1,1⁎−gj−1,1⁎2(j−1)−gj,1⁎(j−1)2)+2(Mh¯)2(gj,2⁎−gj,1⁎),∀j∈Z/⌊NRb¯⌋+2≤j≤N. Moreover, the limit of negligible interfacial viscoelasticity, i.e., null complex Boussinesq number (Bo⁎=0), is well behaved because in such a case the above expression reduces to the one corresponding to a free interface condition (∂g⁎∂z¯=0, at the interface).The differences in the velocity field with respect to the previous version are located at the interface and nearby. The radial velocity gradient for non-linear interfacial flow-fields is better defined. The new implementation of the vertical discretization and interfacial boundary condition yields more regular velocity fields that allow for a reduction of the computational errors. Such an error reduction may be relevant for interfacial viscosities ηs≤10−3 Ns/m, where the errors show a strong increase upon decreasing ηs. The new version also shows a remarkably increased consistency when calculating the complex interfacial torque, Tsurf⁎, where for ηs>10−4Ns/m, even low resolution meshes (200×100 nodes) yield errors below 5%.