User instructions for dataset associated with "An analytical velocity profile of a Bingham fluid through a curved channel"

The files within the dataset are compiled for plotting using Python. The files are labelled as the following:
    "cross_sec_1.dat"   (cross-section position 1)
    "cross_sec_2.dat"   (cross-section position 2)
    "cross_sec_3.dat"   (cross-section position 3)
    "cross_sec_4.dat"   (cross-section position 4)
    "cross_sec_5.dat"   (cross-section position 5)
    "cross_sec_6.dat"   (cross-section position 6)
    "cross_sec_7.dat"   (cross-section position 7)
    "plug_area_transition.dat" (plug area values - numerical and analytical)

# Python
All the figures are produced by compiling files on Python, which can be downloaded from https://www.python.org/downloads/.

For linux users, one could compile the files with extension .py in Python using command line:

python fig_2_critical.py

Each file generates one or more png file containing the figures shown in the published article.

# Datafile "cross_sec_*.dat"
The data for each cross-sections (labelled by cross_sec_*.dat) consist of two columns, the first column contains the radial values and second contains the values of speed.

The data is plotted by compiling the files "fig_10a_velocity_transition.py" and "fig_10a_velocity_transition.py" on Python, with further details on plotting in the form of comments within the files.

The data files "cross_sec_*.dat" are produced by compiling the file "fig_10_velocity_transition.edp" on FreeFem++ (https://freefem.org/), which is done using the command line:

FreeFem++ fig_10_velocity_transition.edp

For Fig. 10, we only consider one value of B and kappa, but these are easily varied by changing parameters Bn (Bingham number), Ri and h (with kappa = h/ Ri).

# Datafile "plug_area_transition.dat"
The data for the plug regions (labelled by "plug_area_transition.dat") contains the plug areas for each Bingham number B = 0.2, 0.4, 0.6. The values of the area computed numerically where calculated using data collected by running simulations on FreeFem++ (https://freefem.org/) using "fig_11.edp" by using the command line:

FreeFem++ fig_11.edp

The first three columns denote the areas computed numerically and columns 4-6 denote the areas computed analytically using eq. (30).

The 7th column contains the respective value of curvature kappa, which ranges between 0 and 1.

The data is plotted by compiling the file "fig_12_plug_area.py" on Python, with further details on plotting in the form of comments within the file.