In Classical Electrodynamics, section 4.4, Jackson shows that a dielectric
sphere with radius a and dielectric constant ep in constant field E will
have an induced dipole moment

p = E*a^3*(ep-1)/(ep+2)

For large epsilon (as you have with barium titanate), (ep-1)/(ep+2) ~= 1
(That is, they act nearly like conducting spheres) so the variation in
epsilon shouldn't matter that much.

Also, because the induced dipole moment is proportional to the volume of the
sphere, the total polarization (which is the total induced dipole moment
divided by the volume) is independent of the sizes of the spheres.  The only
assumption is that they are more or less uniformly distributed.

So, I would proceed by first grabbing a Junior level physics text on E+M,
working out the total induced dipole moment of all the spheres, and divide
by the total volume of the suspension to get the polarization.  Once you
have the polarization in terms of the applied electric field, you will have
the dielectric constant.

Honestly, I would grab a first year grad student or senior undergrad in
physics, who's just gone over this stuff.  I've forgotten enough of the
details at this point, that's become my basic approach to these sorts of
problems.

Now, one interesting possible effect is that the spheres will be attracted
to each other under an applied field, so the end distribution might not be
uniform.  You might even end up with some sort of filamentary structure

My intuition tells me that you'll find the dielectric constant is increasedd
by 1/(1-x), where x is the volume fraction occupied by the barium titanate
spheres, so that you'd see a constant of about 4.1 for .025 volume fraction.
In other words, not much change for small concentrations.

David Nemeth
Senior Engineer
Sophia Wireless, Inc.
14225-C Sullyfield Circle
Chantilly, VA

-----Original Message-----
From: [email protected]
[mailto:[email protected]]On
Behalf Of paul safier
Sent: Friday, January 16, 2004 4:37 PM
To: [email protected]
Subject: [mems-talk] Effective Dielectric Constant of a Suspension of
Spheres


Hello,

I need to estimate the effective dielectric constant for a dilute suspension
of spheres of barium titanate (0.025 Vol %, epsilon=300-10,000) in castor
oil (epsilon=4). Can anyone offer a suggestion?

Thank you.
Paul Safier



**********************************************************************
Paul Safier
Department of Chemical Engineering
University of Arizona
(520) 275-0824
**********************************************************************

_________________________________________________________________
Get a FREE online virus check for your PC here, from McAfee.
http://clinic.mcafee.com/clinic/ibuy/campaign.asp?cid=3963


_______________________________________________
[email protected] mailing list: to unsubscribe or change your list
options, visit http://mail.mems-exchange.org/mailman/listinfo/mems-talk
Hosted by the MEMS Exchange, providers of MEMS processing services.
Visit us at http://www.memsnet.org/