Viscous flows in curved spaces

From geophysical flows, to bursting soap bubbles, to the application of moisturiser on our skin, flows in curved geometries are not exceptional in nature, they are the norm. In stark contrast, our understanding of viscous flows in curved spaces remains mostly limited to simple spherical and cylindrical geometries.

Using model microfluidic experiments, we explain how long range flow perturbations naturally arise when viscous fluids are driven past curvature heterogeneities. We then quantitatively explain and generalize our experimental findings by combining analytic theory and numerical simulations.