Micro-reactors based on slug flow are among the most promising developments for improving the efficiencies of chemical reactions and unit operations in chemical engineering. Quantitative understanding of the local and global fluid dynamics and their effects on fluid mixing is required for designing effective slug flow micro-reactors. This paper proposes a new method for quantitative two-dimensional assessment of fluid mixing in slug flow. Pixel-wise calculation of local entropy inside a slug is discussed. The proposed method is based on two-phase simulation using the volume of fraction (VOF) algorithm and is thus applicable to the flow pattern in arbitrary wall-shaped micro-reactors. The method consists of three steps. (1) Flow analysis using two-phase VOF algorithm: A series of two-dimensional velocity fields inside the slug along time is obtained for a certain duration. (2) Backward particle tracking from the target image to the initial image: The slug in the initial image is divided into small regions, and each region is assigned a different label. Accumulation of backward particle tracking results reveals a two-dimensional distribution of labels in the target image. (3) Pixel-wise calculation of entropy on the obtained distribution of labels: The resulting image is a quantitative two-dimensional mixing pattern inside the slug. The proposed method was applied to three types of microchannels with different bumps on the walls. The results could quantitatively distinguish the differences in fluid mixing capability among the systems. (C) 2019 Published by Elsevier Ltd.