Abstract
Abstract
We present an analytical formalism, supported by numerical simulations, for studying forces that act on curved walls following temperature quenches of the surrounding ideal Brownian fluid. We show that, for curved surfaces, the post-quench forces initially evolve rapidly to an extremal value, whereafter they approach their steady state value algebraically in time. In contrast to the previously-studied case of flat boundaries (lines or planes), the algebraic decay for curved geometries depends on the dimension of the system. Specifically, steady-state values of the force are approached in time as t
−d/2 in d-dimensional spherical (curved) geometries. For systems consisting of concentric circles or spheres, the exponent does not change for the force on the outer circle or sphere. However, the force exerted on the inner circles or sphere experiences an overshoot and, as a result, does not evolve to the steady state in a simple algebraic manner. The extremal value of the force also depends on the dimension of the system, and originates from curved boundaries and the fact that particles inside a sphere or circle are locally more confined, and diffuse less freely than particles outside the circle or sphere.
Funder
Clarendon Fund Scholarship
University of Cape Town
MPI
Leibniz Institute
Subject
Condensed Matter Physics,General Materials Science
Reference37 articles.
1. On the attraction between two perfectly conducting plates;Casimir;Proc. Kon. Ned. Akad. Wet.,1948
2. Wall phenomena in a critical binary mixture;Fisher;Comptes Rendus Hebd. Seances Acad. Sci. Ser. B,1978
3. The ‘friction’ of vacuum, and other fluctuation-induced forces;Kardar;Rev. Mod. Phys.,1999
4. Direct measurement of critical casimir forces;Hertlein;Nature,2008