Impact of magnetic nanoparticles on the Casimir pressure in three-layer systems

The Casimir pressure is investigated in three-layer systems where the intervening stratum possesses magnetic properties. This subject is gaining in importance in connection with ferrofluids and their use in various microelectromechanical devices. We present general formalism of the Lifshitz theory adapted to the case of ferrofluid sandwiched between two dielectric plates (walls). The Casimir pressure is computed for the cases of kerosene- and water-based ferrofluids containing a $5\%$ fraction of magnetite nanoparticles with different diameters between silica glass walls. For this purpose, we have found the dielectric permittivities of magnetite and kerosene along the imaginary frequency axis employing the available optical data and used the familiar dielectric properties of silica glass and water, as well as the magnetic properties of magnetite. We have also computed the relative difference in the magnitudes of the Casimir pressure which arises on addition of magnetite nanoparticles to pure carrier liquids. It is shown that for nanoparticles of 20 nm diameter at 2 $\mu \mathrm{m}$ separation between the walls this relative difference exceeds $140\%$ and $25\%$ for kerosene- and water-based ferrofluids, respectively. An interesting effect is found that at a fixed separation between the walls an addition of magnetite nanoparticles with some definite diameter makes no impact on the Casimir pressure. The physical explanation for this effect is provided. Possible applications of the obtained results are discussed.

Figure 1

The dielectric permittivities of magnetite nanoparticles and silica glass are shown as functions of imaginary frequency by the top and bottom lines, respectively. The vertical line indicates the position of the first Matsubara frequency.

Figure 2

The dielectric permittivities of kerosene- and water-based ferrofluids with $5\%$ concentration of magnetite nanoparticles (lines 1 and 2, respectively) and of silica glass are shown as functions of imaginary frequency normalized to the first Matsubara frequency.

Figure 3

The magnitudes of the Casimir pressure between ${\mathrm{SiO}}_2$ walls through a ferrofluid with $5\%$ fraction of magnetite nanoparticles are shown as functions of separation between the walls by the pairs of solid and dashed lines labeled 1 and 2 for the kerosene and water carrier liquids, respectively. Solid and dashed lines are computed with disregarded and included conductivity of magnetite at low frequencies, respectively. In each pair the lower line is for nanoparticles with $d=10$ nm diameter and the upper line is for nanoparticles with $d=20$ nm.

Figure 4

The relative change in the magnitude of the Casimir pressure on addition of a $5\%$ fraction of magnetite nanoparticles to kerosene is shown as a function of separation by the pairs of solid and dashed lines labeled 1 and 2 for nanoparticles with $d=10$ nm and 20 nm diameter, respectively. In each pair, the solid and dashed lines are computed with disregarded and included conductivity of magnetite at low frequencies, respectively.

Figure 5

The relative change in the magnitude of the Casimir pressure on addition of a $5\%$ fraction of magnetite nanoparticles to kerosene is shown as a function of nanoparticle diameter by the pairs of solid and dashed lines computed with disregarded and included conductivity of magnetite at low frequencies, respectively, for separation between ${\mathrm{SiO}}_2$ walls (a) 200 nm and (b) $2\mu \mathrm{m}$.

Figure 6

The relative change in the magnitude of the Casimir pressure on addition of a $5\%$ fraction of magnetite nanoparticles to water is shown as a function of separation by the pairs of solid and dashed lines labeled 1 and 2 for nanoparticles with $d=10$ and 20 nm diameter, respectively. In each pair, the solid and dashed lines are computed with disregarded and included conductivity of magnetite at low frequencies, respectively.

Figure 7

The relative change in the magnitude of the Casimir pressure on addition of a $5\%$ fraction of magnetite nanoparticles to water is shown as a function of nanoparticle diameter by the solid and dashed lines computed with disregarded and included conductivity of magnetite at low frequencies, respectively, for separation between ${\mathrm{SiO}}_2$ walls (a) 200 nm and (b) $2\mu \mathrm{m}$.