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Derive the van der Waal interaction between 2 spheres.

  1. Apr 25, 2014 #1

    Red

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    Hi guys, I need some help on this question:

    Derive the van der Waal interaction potential between 2 spheres of radius R_1 and R_2 using the Hamaker approach. Take the distance between the center of each sphere to be D.

    Thank you very much for your help!
     
  2. jcsd
  3. Apr 25, 2014 #2

    maajdl

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    Gold Member

    Read this:

    http://dept.lamar.edu/chemicalengineering/www/tadmor/papers/vanderwaalsforces/vdw1.pdf [Broken]

    Could you explain me a little bit more about that?
    Or some reference?
    I know nothing about it.

    Is the van der Waal interaction a starting point, or is it a consequence?
    Is there a short (fast) derivation for formula (1) somewhere available?

    Interresting because of the geeko.
     
    Last edited by a moderator: May 6, 2017
  4. Apr 25, 2014 #3

    Red

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    The Hamaker approach assume a pairwise addition, so the derivation start with a double volume integration of density_1 and density_2 and c over r^6, where r is the separation between the small volume in the integration, and c is a constant. Not sure if I make myself clear here.

    Maybe this pdf will help, please refer to page 2, equation (1) for the mathematical description of what I had describe above. Thanks! Here is the link: http://chemeng.queensu.ca/courses/CHEE460/lectures/documents/CHEE4602010Lecture4.pdf [Broken]

    And yes the gecko is a master of VDW forces!
     
    Last edited by a moderator: May 6, 2017
  5. Apr 25, 2014 #4

    maajdl

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    I don't know if it is helpfull, but here is a link to the original paper by Hamaker:

    http://www.utwente.nl/tnw/pcf/education/jmbc_course_on_capillarity_driv/Articles/anton_darhuber/surface_tension_etc/Hamaker_Physica1937_vdW_attract_spherical_particles.pdf [Broken]

    It is a little bit lengthy and even boring.
    It looks like it is only about calculating the integral of formula (1) in the paper.
    Probably a piece of cake if you have 1 hour free and Mathematica.

    Thanks for the reference: it is very clear and readable.
     
    Last edited by a moderator: May 6, 2017
  6. May 1, 2014 #5

    Red

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    Thank you for your help. Mathematica does help.
     
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