>From: "David Nemeth" 
>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.

For two dissimilar dielectrics distributed arbitrarily between horizontal
capacitor plates, their net polarization under a given electric field is
bounded below by that of a horizontally stratified distribution, and above
by that of a vertically stratified distribution (cf. Feynman LOP II-11-4,
or derive it by comparing respectively series and parallel capacitors
as extreme configurations).

Horizontal stratification gives your 1/(1-x) figure for K, or more precisely
1/(1-x(1-1/r)) where r>1 is the ratio of the polarizabilities, since the less
polarizable dielectric's thickness is reduced by 1-x thus increasing the
capacitance by that much, while the other, which is effectively connected
in series, combines thickness x with the factor r to make it almost a
short circuit.  In the case at hand r is between 100 and 2500.

For vertical stratification however the polarization can be much larger.
In the case at hand, the volume ratio (.025% or 4000) is close to the
polarizability ratio (10000 to 4 in the extreme case, or 2500).  Had these
ratios been equal, the dielectric constant would double, since in effect
we would be connecting two equal capacitors in parallel.

>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

Right, this is the vertically stratified case.  Dielectrics prefer
configurations that increase capacitance, in order to decrease the potential
energy stored in the electric field.  A filamentary structure will achieve
this, but then K can get far higher than the 1/(1-x) increase for the
horizontally stratified case, approaching the above doubling possibility.
I have no idea whether vertical stratification would actually happen here
however, it might take too long, and/or be shaken up too much by the ambient
temperature.  One plausible outcome is that at high temperatures and/or high
frequencies the dielectric constant increase might be as low as 1/(1-x),
increasing to nearly double at sufficiently low temperatures and frequencies.

But this is all just theoretical musings, I'd love to know how this actually
turns out in practice!

Vaughan Pratt