Derive the van der Waal interaction between 2 spheres.

[Red]

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!

 

[maajdl]

Read this:

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

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.

 

[Red]

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

And yes the gecko is a master of VDW forces!

 

[maajdl]

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

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.

 

[Red]

Thank you for your help. Mathematica does help.