# The effect of agglomeration of magnetic nanoparticles on the Casimir pressure through a ferrofluid

## TL;DR

This study examines how nanoparticle agglomeration in ferrofluids influences Casimir pressure between plates, revealing conditions under which the force's sign can change, with implications for microdevice design and Casimir force theory.

## Contribution

It demonstrates that nanoparticle clustering can alter the Casimir force's magnitude and sign, depending on the optical model used and nanoparticle clustering parameters.

## Key findings

- Agglomeration causes quantitative changes in Casimir pressure for dielectric plates.
- Using the plasma model, nanoparticle clustering can reverse the force's sign.
- The effect varies with nanoparticle size, clustering degree, and plate separation.

## Abstract

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 (SiO_2) plates, as well as for one dielectric (SiO_2) and another one metallic (Au) plates, 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 by 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.