Viscous fluid mixing in a tilted tank by periodic shear

A tilted-partially filled rotating tank is studied, both experimentally and theoretically at small Reynolds and capillary numbers, to study mixing viscous fluid by periodic shear. The maximum mixed cross-sectional area, Amax(α)=A(Δtmax(α))Amax(α)=A(Δtmax(α)), and mixing rate, 1/Δtmax(α)1/Δtmax(α), are estimated as a function of the flow parameters, which are the tilt angle, αα, and free surface height, H0H0. A nonlinear flow model is found by expanding linear solid body rotation about a curved rotation axis that is needed to satisfy the zero shear stress and no normal velocity component for the flow in the vicinity of the free surface. A linear analysis of the nonlinear solution reveals an underlying periodic shear that is responsible for fluid mixing. The analysis suggests that the rate of mixing per unit area is a maximum near α=52π/180α=52π/180. Laser fluorescence experiments are performed to examine the mixing patterns via experimental Poincaré mapping [Fountain, G.O., Khakhar, D.V., Ottino, J.M., 1998. Visualization of three-dimensional chaos. Science 281, 683–686.]. Steady-state images of the mixed cross-sectional area are compared with the theory as a function of the flow parameters.