2017/04/30 by Daniel Dantchev, Vassil Vassilev, Vassil M. Vassilev +2 · 1 citation
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Boundary value problem #Casimir effect #Classical mechanics #Condensed matter physics #Field (mathematics) #Force field (fiction) #Function (biology) #Geometry #Material Dynamics and Properties #Mathematics #Mechanics #Phase Equilibria and Thermodynamics #Physics #Position (finance) #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Scaling #Simple (philosophy) #Statistical physics #Type (biology) #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.physa.2018.07.001
published as Physica A 510, 2018, pp. 302-315 · 19 pages, 5 figures; two references and the text needed to incorporate them added, one reference updated
openalex created_date 2017/05/12 · arxiv created 2017/12/15 · openalex publication_date 2018/07/02 · arxiv updated 2018/11/06 · openalex updated_date 2026/08/05
We present both analytical and numerical results for the behaviour of the Casimir force in a Ginzburg-Landau type model of a film of a simple fluid or binary liquid mixture in which the confining surfaces are strongly adsorbing but preferring different phases of the simple fluid, or different components of the mixture. Under such boundary conditions an interface is formed between the competing phases inside the system which are forced to coexist. We investigate the force as a function of the temperature and in the presence of an external ordering field and determine the (temperature-field) relief map of the force. We prove the existence of a single global maximum of the force and find its position and value. We find the asymptotic behavior of the force when any of the scaling fields becomes large while the other one is negligible. Contrary to the case of symmetric boundary conditions we find, as expected, that the finite system does not possess a phase transition of its own for any finite values of the scaling variables corresponding to the temperature and the ordering field. We perform the study near the bulk critical temperature of the corresponding bulk system and find a perfect agreement with the finite-size scaling theory.