In the absence of gravity, spontaneous capillary flow along an interior corner is a significant portion of liquid behavior in spacecraft. To effectively control the space liquid, the design of fluids management processes in the low-gravity environment of space requires a rapid and accurate prediction of capillary flow in interior corners. So far, the previous studies have been focused on the capillary flow along the straight interior corner. However, the curved interior corner is far more common. A comprehensive theoretical model is established to study the curved corner effects based on previous studies. By analysis, the centrifugal force caused by the curve motion is the decisive factor which makes the capillary flow in curved interior corners different from that in straight interior corners. The influences of centrifugal force on the free surface and friction factor are discussed, and high-precision approximation modeling method is used in free surface modeling to speed up the solving process. To validate the theoretical model, a series of microgravity drop tower experiments are conducted. By comparison, the theoretical results agree well with the experimental results. The results show that the liquid rises faster as the channel curvature increases. This feature can be used to transport and manage liquid better in spacecraft. A modified Suratman number Su is introduced to judge the curved corner effects. When Su = 3, the relative error e caused by neglecting the curved corner effects is up to 36% which means the curved corner effects have a great influence on the capillary flow. When Su << 1, the relative error e is close to 0 which means the curved corner effects can be neglected. (C) 2018 Elsevier Ltd. All rights reserved.