Effect of agglomeration of magnetic nanoparticles on the Casimir pressure through a ferrofluid

The impact of agglomeration of magnetic nanoparticles on the Casimir pressure is investigated in the configuration of two material plates and a layer of ferrofluid confined between them. Both cases of similar and dissimilar plates are considered in the framework of the Lifshitz theory of dispersion forces. It is shown that for two dielectric (${\mathrm{SiO}}_2$) plates, as well as for one dielectric (${\mathrm{SiO}}_2$) and one metallic (Au) plate, an agglomeration of magnetite nanoparticles results in only quantitative differences in the values of the Casimir pressure if the optical data for Au are extrapolated to low frequencies by means of the Drude model. If, however, an extrapolation by means of the plasma model is used in computations, which is confirmed in experiments on measuring the Casimir force, one finds that the pressure changes its sign when some share of magnetic nanoparticles of sufficiently large diameter is merged into clusters of two or three items. The revealed effect of sign change is investigated in detail at different separations between the plates, diameters of magnetic nanoparticles, and shares of particles merged into clusters of different sizes. The obtained results may be useful when developing ferrofluid-based microdevices and for resolution of outstanding problems in the theory of Casimir forces.

Figure 1

(a) Casimir pressure between Au and ${\mathrm{SiO}}_2$ plates through a water-based ferrofluid with 5% volume fraction of magnetite nanoparticles and (b) its magnitude are shown as functions of separation between the plates for nanoparticle diameters (a) $d=10$ nm and (b) $d=20$ nm. The solid, short-dashed, and long-dashed lines are plotted for single nanoparticles of each type and for the cases when half of them are merged into clusters of two and three, respectively. Au is described using an extrapolation of the optical data by means of the plasma model.

Figure 2

Casimir pressure between Au and ${\mathrm{SiO}}_2$ plates through a water-based ferrofluid with 5% volume fraction of magnetite nanoparticles is shown as a function of separation between the plates by the top and bottom pairs of lines for nanoparticle diameters $d=10$ and 20 nm, respectively. In each pair, the solid and dashed lines are plotted for single nanoparticles of each type and for the case when half of them are merged into clusters of three, respectively. Au is described using an extrapolation of the optical data by means of the Drude model.

Figure 3

Magnitude of the Casimir pressure between two ${\mathrm{SiO}}_2$ plates through a water-based ferrofluid with 5% volume fraction of magnetite nanoparticles is shown as a function of separation between the plates by the top and bottom pairs of lines for nanoparticle diameters $d=20$ and 10 nm, respectively. In each pair, the solid and dashed lines are plotted for single nanoparticles of each type and for the case when half of them are merged into clusters of three, respectively.

Figure 4

Ratio of the Casimir pressure between Au and ${\mathrm{SiO}}_2$ plates through a water-based ferrofluid with 5% volume fraction of magnetite nanoparticles, of which the share ${\kappa }_k$ is merged into clusters of $k$ particles, to the same pressure computed for single nanoparticles is shown as a function of $\kappa$ at separation between the plates (a) $a=200$ nm and (b) $a=500$ nm, respectively. In each pair, the short-dashed and long-dashed lines are plotted for the clusters consisting of $k=2$ and 3 nanoparticles, respectively. Au is described using an extrapolation of the optical data by means of the plasma model.

Figure 5

Ratio of the Casimir pressure between Au and ${\mathrm{SiO}}_2$ plates through a water-based ferrofluid with 5% volume fraction of magnetite nanoparticles, of which the share ${\kappa }_k$ is merged into clusters by (a) $k=2$ particles and (b) $k=3$ particles, to the same pressure computed for single nanoparticles is shown as a function of nanoparticle diameter at separation between the plates $a=200$ nm. The lines counted from top to bottom are plotted for the share of merged particles equal to ${\kappa }_2$ and ${\kappa }_3=0.1$, 0.3, 0.5, 0.7, and 0.9, respectively. Au is described using an extrapolation of the optical data by means of the plasma model.