Resolving Singular Forces in Cavity Flow: Multiscale Modeling from Atomic to Millimeter Scales

Flow driven by moving a wall that bounds a fluid-filled cavity is a classic example of a multiscale problem. Continuum equations predict that every scale contributes roughly equally to the total force on the moving wall, leading to a logarithmic divergence, and that there is an infinite hierarchy of vortices at the stationary corners. A multiscale approach is developed that retains an atomistic description in key regions. Following the stress over more than six decades in length in systems with characteristic scales of up to millimeters and milliseconds allows us to resolve the singularities and determine the force for the first time. We find a universal dependence on the macroscopic Reynolds number, and large atomistic effects that depend on wall velocity and interactions.