Exact results for the behavior of the thermodynamic Casimir force in a model with a strong adsorption

Abstract

When massless excitations are limited or modified by the presence of material bodies one observes a force acting between them generally called Casimir force. Such excitations are present in any fluid system close to its true bulk critical point. We derive exact analytical results for both the temperature and external ordering field behavior of the thermodynamic Casimir force within the mean-field Ginzburg-Landau Ising type model of a simple fluid or binary liquid mixture. We investigate the case when under a film geometry the boundaries of the system exhibit strong adsorption onto one of the phases (components) of the system. We present analytical and numerical results for the (temperature-field) relief map of the force in both the critical region of the film close to its finite-size or bulk critical points as well as in the capillary condensation regime below but close to the finite-size critical point.

17 pages, 4 figures. arXiv admin note: text overlap with arXiv:1603.08435

References in corpus (15)

• The Casimir effect: from quantum to critical fluctuations
• Critical Casimir force in ${}^4$He films: confirmation of finite-size scaling
• Experiment and theory in the Casimir effect
• Critical Casimir Effect in superfluid wetting films
• Thinning of superfluid films below the critical point
• Classical and fluctuation-induced electromagnetic interactions in micronscale systems: designer bonding, antibonding, and Casimir forces
• Control of the Casimir Force Using Semiconductor Test Bodies
• Interplay of critical Casimir and dispersion forces
• Critical Casimir forces steered by patterned substrates
• The Casimir effect in the nanoworld
• Critical adsorption and critical Casimir forces for geometrically structured confinements
• Critical Casimir Interactions Between Spherical Particles in the Presence of the Bulk Ordering Fields
• Casimir and van der Waals forces: Advances and problems
• Finite-size effects on the behavior of the susceptibility in van der Waals films under $+,+$ boundary conditions
• Finite-size effects in presence of gravity: The behavior of the susceptibility in ${}^{3}He$ and ${}^{4}He$ films near the liquid-vapor critical point

Cited by in corpus (2)

• Probing interface localization-delocalization transitions by colloids
• Exact solution for the order parameter profiles and the Casimir force in ${}^4$He superfluid films in an effective field theory