in a shaken drop

We performed visualization and quantification of mixing process during orbital shaking with theoretical analysis. Visualization of mixing reveals that a circulation flow occurs due to fluid rotation inside a drop or a fluid container during orbital shaking. The intensity of the circulation flow increases as the shaking speed and radius of shaking trajectory increase. In order to quantify the degree of mixing, we define a mixing index based on the acquired images and plot its change over time. We theoretically study internal flow patterns and surface deformation. Mathematical expressions for flow field and surface deformation are obtained as a linear superposition of basis functions which satisfy the governing equations and boundary conditions. The theoretical model predicts a rotating motion of the fluid and a secondary flow circulating inside a drop.