The Casimir Interaction between Spheres Immersed in Electrolytes

Renan O Nunes,Benjamin Spreng,Felipe S S Rosa,Gert-Ludwig Ingold,Reinaldo De Melo E Souza,Paulo A Maia Neto

doi:10.3390/universe7050156

Abstract

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

Highlights

IntroductionAccepted: 14 May 2021Since the seminal results of H
Accepted: 14 May 2021Since the seminal results of H
We have considered the Casimir interaction between two dielectric spherical particles immersed in aqueous solution

Summary

Introduction

Accepted: 14 May 2021Since the seminal results of H. Great advances in computational power, numerical methods [7,8,9,10], and analytical techniques [11,12,13,14,15,16] led to the exploration of many different geometries, such as spheres [17,18,19,20], cylinders [21,22], gratings [23,24,25,26,27], etc, and of a vast landscape of materials, from “simple” dielectrics and conductors [2] to magneto-optical materials [28,29,30], spatially dispersive media [31,32,33,34,35], anisotropic media [36,37,38], superconductors [39,40], phase-changing materials [41,42], and many more. A second wave almost thirty years later [45,46,47,48,49,50] was able to probe larger distances and non-trivial geometries, establishing important results for conductors

Objectives

Results

Conclusion