A new strategy for mixing inside drops is introduced utilizing the action of surface shear viscosity. A drop is constrained by two sharp-edged contact rings that are differentially rotating. Differential rotation of the rings is conveyed by surface shear viscosity into the bulk fluid, thus enhancing the mixing when compared to the quiescent case. Primarily, mixing was considered in a configuration where one hemisphere is initially at a different concentration than the other. When inertia becomes important, the mixing time is reduced by an order of magnitude compared to the case where the two rings are stationary. Various driving speeds of one ring or counter rotation of two rings are considered for the hemispherical initial concentration. Mixing of a core-shell initial concentration was also considered. This approach to mixing in a drop is found to be an effective containerless mixer and may be utilized in chemical and biological applications where solid-wall interactions are deleterious. (C) 2018 Elsevier Ltd. All rights reserved.