Mixing is crucial in the dispersion of two immiscible fluids. The rational design of an impeller is necessary to form suitable flow conditions and improve fluid mixing efficiency. A double rigid-flexible combination impeller was designed by connecting the upper and lower rigid impeller blades with flexible pieces. Experimental measurements were performed in a laboratory-scale mixer-settler under different impeller types. The largest Lyapunov exponent (LLE) and multi-scale entropy (MSE) were investigated using Matlab. Results showed that the double rigid-flexible combination impeller enhanced liquid-liquid mixing in the mixer-settler through the multiple-body motion behavior triggered by the swings of flexible pieces. At the optimum mixing point of each impeller, the LLEs of the double impeller, double rigid combination impeller, and double rigid-flexible combination impeller were 0.018, 0.055, and 0.057, respectively. At 75 rpm, the MSE of the combination impellers was obviously greater than that of the double impeller, and the rigid-flexible combination impeller had larger MSE than the double rigid combination impeller. The mixing efficiency of the rigid-flexible combination impeller increased with increasing width and quantity of the flexible piece. The quantity of rigid blade slice also influenced the enhancement of mixing ability. The double rigid-flexible combination impeller intensified the chaotic mixing of the two-phase fluid by changing the flow field structure and energy dissipation mode, ultimately achieving an efficient-mixing operation. (C) 2014 Elsevier B.V. All rights reserved.