Condensed Matter Theory

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.