Trapping in a Casimir Force Set-Up Controlled by Solution Permeability

We have designed a system enabling tuning Casimir attraction/repulsion transitions between a polystyrene sphere attached to an atomic force microscope tip near a Teflon surface in a magnetic fluid mixture. Notably, the trapping distances can be changed by several orders of magnitude by changes in zero-frequency transverse electric contributions to the Casimir force. We demonstrate that this can be achieved via modifications in the average diameter for the magnetite particles while keeping the magnetite volume fractions fixed.