Electrokinetic generation of micro-flow patterns has advanced in recent years and received significant attention due to promising applications in biotechnology. Basic flow fields like bi-directional shear flow and out-of-plane vortices have been generated electrokinetically in microchannel liquid flow using various surface-charge patterns. In this paper, in-plane vortex flows, which presented a higher challenge since positive and negative charge regions on the same surface are required, are firstly demonstrated. Focusing on one vortex cell, the fluid motion, using micro-particle technique, is intensively studied and compared with the numerical result of a commercial CFD code. In the same charge pattern arrangement, another interesting flow, serpentine-like vortical motion, has been observed in the presence of mean flow. Since a high consistence has been found between the experimental and CFD results, the detailed electrokinetically-driven in-plane vortical flow field is explored using the same code. Different flow patterns in surface charge pattern arrangement for generating a single in-plane vortex have been characterized by the dominant control geometric parameters. An interesting phenomenon, vortex splitting, has been observed in single in-plane vortex dynamics, due to the weaken interaction between top and bottom driving charged patterns. The criterion for the onset of this phenomenon is discussed.