The Casimir Interaction between Spheres Immersed in Electrolytes

We investigate the Casimir interaction between two dielectric spheres immersed in an electrolyte solution. Since ionized solutions typically correspond to a plasma frequency much smaller than kBT/? at room temperature, only contribution of zeroth Matsubara is affected by ionic screening. follow electrostatic fluctuational approach and derive zero-frequency from linear Poisson-Boltzmann (Debye-Hückel) equation for geometry spherical surfaces arbitrary radii. show that monopole fluctuations, which reminiscent Kirkwood-Shumaker interaction, arises exclusion charge volume occupied spheres. Alongside dipole such monopolar term provides leading-order energy very small Finally, we also large sphere limit conditions validity proximity force (Derjaguin) approximation. Altogether, our results represent first step towards full scattering screening takes into account nonlocal response