.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/analytical/chromatography/plot_04_golay_open_tubular_column.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_analytical_chromatography_plot_04_golay_open_tubular_column.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_analytical_chromatography_plot_04_golay_open_tubular_column.py:


Golay's open-tubular column: the van Deemter equation with A = 0
===================================================================

An open capillary has no packing, so Golay's equation for it is the van
Deemter equation with no eddy-diffusion term: :math:`H=B/u+Cu`. Using
:func:`~chemistrykit.analytical.van_deemter_H` with :math:`A=0` for a
capillary and :math:`A>0` for a packed column shows the lower plate
height, and hence the many more plates a long capillary delivers.

.. GENERATED FROM PYTHON SOURCE LINES 13-33

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.analytical import minimum_plate_height, optimum_flow_velocity, van_deemter_H

    u = np.linspace(1.0, 100.0, 3000)  # cm/s
    # Illustrative GC coefficients (H in cm): packed column vs. open-tubular capillary.
    packed = {"A": 0.05, "B": 0.4, "C": 0.002, "length_cm": 200.0}
    capillary = {"A": 0.0, "B": 0.4, "C": 0.0005, "length_cm": 3000.0}

    fig, ax = plt.subplots(figsize=(7, 4.5))
    for name, p in (("packed column (A > 0)", packed), ("open tubular, Golay (A = 0)", capillary)):
        H = van_deemter_H(u, p["A"], p["B"], p["C"])
        H_min = minimum_plate_height(p["A"], p["B"], p["C"])
        u_opt = optimum_flow_velocity(p["B"], p["C"])
        N = p["length_cm"] / H_min  # N = L / H
        print(f"{name:30s}: H_min = {H_min * 10:.3f} mm at u = {u_opt:.1f} cm/s; {p['length_cm'] / 100:.0f} m column -> N = {N:,.0f} plates")
        ax.plot(u, H * 10, label=name)
        ax.plot([u_opt], [H_min * 10], "o", color=ax.lines[-1].get_color())




.. image-sg:: /api/gallery/analytical/chromatography/images/sphx_glr_plot_04_golay_open_tubular_column_001.png
   :alt: plot 04 golay open tubular column
   :srcset: /api/gallery/analytical/chromatography/images/sphx_glr_plot_04_golay_open_tubular_column_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    packed column (A > 0)         : H_min = 1.066 mm at u = 14.1 cm/s; 2 m column -> N = 1,877 plates
    open tubular, Golay (A = 0)   : H_min = 0.283 mm at u = 28.3 cm/s; 30 m column -> N = 106,066 plates




.. GENERATED FROM PYTHON SOURCE LINES 34-41

.. code-block:: Python

    ax.set_ylim(0, 2.0)
    ax.set_xlabel("linear velocity u (cm/s)")
    ax.set_ylabel("plate height H (mm)")
    ax.set_title("Removing the eddy-diffusion term lowers H")
    ax.legend()
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/analytical/chromatography/images/sphx_glr_plot_04_golay_open_tubular_column_002.png
   :alt: plot 04 golay open tubular column
   :srcset: /api/gallery/analytical/chromatography/images/sphx_glr_plot_04_golay_open_tubular_column_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.017 seconds)


.. _sphx_glr_download_api_gallery_analytical_chromatography_plot_04_golay_open_tubular_column.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_04_golay_open_tubular_column.ipynb <plot_04_golay_open_tubular_column.ipynb>`

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

      :download:`Download Python source code: plot_04_golay_open_tubular_column.py <plot_04_golay_open_tubular_column.py>`

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

      :download:`Download zipped: plot_04_golay_open_tubular_column.zip <plot_04_golay_open_tubular_column.zip>`


.. only:: html

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

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