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We present an analytical formalism, supported by numerical simulations, forstudying forces that act on curved walls following temperature quenches of thesurrounding ideal Brownian fluid. We show that, for curved surfaces, thepost-quench forces initially evolve rapidly to an extremal value, whereafterthey approach their steady state value algebraically in time. In contrast tothe previously-studied case of flat boundaries (lines or planes), the algebraicdecay for the curved geometries depends on the dimension of the system.Specifically, the steady-state values of the force are approached in time as$t^{-d/2}$ in d-dimensional spherical (curved) geometries. For systemsconsisting of concentric circles or spheres, the exponent does not change forthe force on the outer circle or sphere. However, the force exerted on theinner circle or sphere experiences an overshoot and, as a result, does notevolve towards the steady state in a simple algebraic manner. The extremalvalue of the force also depends on the dimension of the system, and originatesfrom the curved boundaries and the fact that particles inside a sphere orcircle are locally more confined, and diffuse less freely than particlesoutside the circle or sphere.

The role of dimensionality and geometry in quench-induced nonequilibrium forces