Mixing liquids of different viscosity

We experimentally characterize the deformation of a blob of viscosity η' subjected to a simple shear in a fully miscible bath of viscosity η. We show that increasing the viscosity ratio η'/η results in a sharp stretching-to-rolling transition, with dramatic consequences on the blob mixing timescale. For low viscosity ratios (0 < η'/ η ≤ 2), the blob elongates continuously and linearly into a thin lamella. In contrast, for large viscosity ratios (η'/η > 4), the blob essentially rotates, following periodic orbits with a small elongation. For intermediate ratios, η'/η ∼ 4, the blob follows a continuous sub-stretching regime and, eventually, destabilizes by folding. From these qualitatively different kinematic regimes — in good agreement with analytical predictions based on Eshelby's theory of elastic deformation — we will discuss how, and to which extent, the viscosity ratio affects the mixing of the blob.