The recent research and development of microfluidic systems for biological and chemical analysis has enabled interfacing and analyzing single or small population of biological cells. In this thesis, we describe a passive microfluidic device with dual spiral geometry for the separation and single cell trapping from a heterogeneous mixture. The device makes use of two spirals to sort and trap cells. Cells flowing in the primary channel experience centrifugal acceleration as they travel along the spiral. A combination of Dean drag force and inertial lift force acting on the cells in the primary channel, cause them to migrate towards the outer wall. The outer wall is lined with traps to capture single cells that have laterally migrated due to centrifugal force. A local suction force is created at each trap by the use of the secondary spiral channel to provide an additional lateral force to assist in cell trapping. The microfabricated devices were tested with polystyrene microbeads, glass microbeads and adult rat hippocampal stem cells at various microfluidic conditions. Using the proposed technology, an average trapping efficiency of >50% was achieved. Besides providing a high trapping efficiency, this unique dual-spiral configuration has the potential to facilitate single-cell studies by providing a convenient way to load /unload agent and regent solutions through the secondary channel and to create a concentration gradient of factors in both the primary and secondary channels.