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...
This work considers the timescales associated with the global order parameter and the interlayer synchronization of coupled Kuramoto oscillators on multiplexes. For the two-layer multiplexes with initially high degree of synchronization in each layer, the difference between the average phases in each layer is analyzed from two different perspectives: the spectral analysis and the non-linear Kuramoto model. Both viewpoints confirm that the prior timescales are inversely proportional to the interlayer coupling strength. Thus, increasing the interlayer coupling always shortens the transient regimes of both the global order parameter and the interlayer synchronization. Surprisingly, the analytical results show that the convergence of the global order parameter is faster than the interlayer synchronization, and the latter is generally faster than the global synchronization of the multiplex. The formalism also outlines the effects of frequencies on the difference between the average phases of each layer, and identifies the conditions for an oscillatory behavior. Computer simulations are in fairly good agreement with the analytical findings and reveal that the timescale of the global order parameter is at least half times smaller than timescale of the multiplex.
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