A titled-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(alpha) = A(Delta t(max)(alpha)), and mixing rate, 1/Delta t(max)(alpha), are estimated as a function of the flow parameters, which are the tilt angle, alpha,., and free surface height, Ho. 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 alpha=52 pi/180. Laser fluorescence experiments are performed to examine the mixing patterns via experimental Poincare 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. (c) 2007 Elsevier Ltd. All rights reserved.