Effective slip length of confined fluid with wavy fluid-solid interfaces

We have studied the effective slip length of confined fluid with nano-structured fluid-solid interfaces. A formula bridging the effective slip length and nano structures of the interfaces has been obtained analytically. For the application of the formula, a confined fluid with wavy fluid-solid interfaces has been studied as an example. In the study, the criteria of the formula have been detailed, and verified by the finite element method.