.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/volcanology/plot_14_shaw_magma_viscosity.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_volcanology_plot_14_shaw_magma_viscosity.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_volcanology_plot_14_shaw_magma_viscosity.py:


Shaw's magma viscosity (1972)
=============================

Herbert Shaw found that the logarithm of the viscosity of silicate melts is a
straight line in ``1/T`` whose slope depends only on composition, and that the
lines for basalt to rhyolite all pass near one point. That makes Shaw's law an
Arrhenius law with activation energy ``s * 1e4 * R``. Rhyolite at eruption
temperature is about a hundred million times stiffer than basalt.

.. GENERATED FROM PYTHON SOURCE LINES 11-31



.. image-sg:: /api/gallery/volcanology/images/sphx_glr_plot_14_shaw_magma_viscosity_001.png
   :alt: Shaw's lines pivot near 10^4/T = 1.5
   :srcset: /api/gallery/volcanology/images/sphx_glr_plot_14_shaw_magma_viscosity_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.constants import R_GAS
    from earthsciencekit.volcanology import arrhenius_viscosity, shaw_viscosity

    temperature = 1e4 / np.linspace(1.4, 10.5, 200)  # out to the pivot, far above any magma temperature
    fig, ax = plt.subplots()
    for slope, name in [(2.5, "basalt"), (3.2, "andesite"), (4.0, "rhyolite")]:
        viscosity = shaw_viscosity(temperature, slope)
        assert np.allclose(arrhenius_viscosity(temperature, shaw_viscosity(1300, slope), slope * 1e4 * R_GAS, 1300), viscosity)
        ax.semilogy(1e4 / temperature, viscosity, label=f"{name}, s = {slope}")
    assert shaw_viscosity(1073, 4.0) / shaw_viscosity(1473, 2.5) > 1e7
    ax.axvline(1.5, color="0.5", ls=":", lw=1)
    ax.axvspan(1e4 / 1500, 1e4 / 950, color="0.9", label="magmatic temperatures")
    ax.set(xlabel="10^4 / T [1/K]", ylabel="viscosity [Pa s]", title="Shaw's lines pivot near 10^4/T = 1.5")
    ax.legend()

    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.139 seconds)


.. _sphx_glr_download_api_gallery_volcanology_plot_14_shaw_magma_viscosity.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../lite/lab/index.html?path=api/gallery/volcanology/plot_14_shaw_magma_viscosity.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_14_shaw_magma_viscosity.ipynb <plot_14_shaw_magma_viscosity.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_14_shaw_magma_viscosity.py <plot_14_shaw_magma_viscosity.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_14_shaw_magma_viscosity.zip <plot_14_shaw_magma_viscosity.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_