shell thickness $\alpha$ pushes the bifurcation to larger $R$, and also increase $h_e$ by making the sphere more buoyant. This modification allows us to consider $R\approx10\,\mu$m in the next section, where PFA should be accurate. For only $3\,\mu$m spheres and $500$ nm separations in fluids, we previously found that the correction to PFA (which scales as $d/R$ to lowest order [@gies06:PFA; @Maia-Neto; @Mazzitelli]) was only about 15%. For the three times larger radii and somewhat smaller separations in the next section the corrections to PFA are typically $< 5$%, sufficient for our current purposes.

Nonzero Temperature and Experiments {#sec:temp}
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In this section, we address a number of questions of consequence to an experimental realization of the teflon/silicon two-sphere dicluster of [Fig. \[fig:fig1\]]{}. In particular, we consider several ways in which a nonzero temperature can disrupt the observation of stable equilibria. A nonzero temperature will manifest itself in at least two important ways. First, there will be a change in the Casimir force between the objects due to the presence of real (non-virtual) photons in the system. Second, the inclusion of nonzero temperature will cause the spheres to experience Brownian motion arising from the thermal agitations in the fluid [@Risken]. 