Casimir microsphere diclusters and three-body effects in fluids

Abstract

Our previous article [Phys. Rev. Lett. 104, 060401 (2010)] predicted that Casimir forces induced by the material-dispersion properties of certain dielectrics can give rise to stable configurations of objects. This phenomenon was illustrated via a dicluster configuration of non-touching objects consisting of two spheres immersed in a fluid and suspended against gravity above a plate. Here, we examine these predictions from the perspective of a practical experiment and consider the influence of non-additive, three-body, and nonzero-temperature effects on the stability of the two spheres. We conclude that the presence of Brownian motion reduces the set of experimentally realizable silicon/teflon spherical diclusters to those consisting of layered micro-spheres, such as the hollowcore (spherical shells) considered here.

Many-body effects for critical Casimir forces

“…7 we show schematically the system considered in Ref. [10] [(a) and (b)] and the system considered here [(c), (d), and (e)]. For the quantum-electrodynamic Casimir effect, the dielectric spheres are represented by circles of equal radii, with the green one corresponding to a polystyrene sphere and the red one to a silicon sphere.…”

“…7 (a) and (b) are chosen as to illustrate the findings in Ref. [10], according to which the sign of the lateral many-body force is the same as the one of the strongest normal pairwise sphere-plate force: attractive in (a) and repulsive in (b).…”

“…In the case of the quantumelectrodynamic interaction [(a) and (b)] and alluding to the system studied in Ref. [10], the circles represent the projections of dielectric spheres with equal radii, the green one corresponding to polystyrene and the red one to silicon; the rectangles represent semi-infinite plates with their surfaces perpendicular to the x − z plane, the gray and the yellow one being Teflon and gold, respectively. The system is immersed in ethanol, which is not indicated in the figure.…”

“…The authors of Ref. [10] analyze the effect of nonadditivity for the above system by studying the influence of an additional, adjacent substrate on the equilibrium separation d between two nanometer size dielectric spheres. To They also find that "the sphere-plate interaction changes the sphere-sphere interaction with the same sign as D becomes smaller", which means that if the sphere-plate force is repulsive (attractive), the sphere-sphere one will become more repulsive (attractive) upon decreasing the distance from the plate D. By construction these changes are genuine many-body contributions.…”

“…These latter effects can lead, e.g., to a strengthening or weakening of the total force acting on a particle surrounded by more than a single other one, a change of sign of that force, or the appearance of stable or unstable configurations. Many-body effects appear in rather diverse systems such as nuclear matter [1], superconductivity [2], colloidal suspensions [3,4], quantumelectrodynamic Casimir forces [5][6][7][8][9][10], polymers [11,12], nematic colloids [13], and noble gases with van der Waals forces acting among them [14][15][16][17]. Each of these systems is characterized by a wide range of time and length scales.…”