In this work, we numerically examine the two dimensional flow of a Newtonian fluid in the gap formed between two opposing cavities. The fluid is driven by the motion of the upper cavity and the case considered represents a simplified version of the geometry found in Low Consistency (LC) refiners. Numerical studies were conducted in which we characterized the effect of gap size on the flow field. Then, we examine material transport between the cavities by introducing a passive scalar to represent the motion of tracer particles. A large number of unsteady simulations were conducted over the range of velocities and gap sizes. Over the range of parameters studied, we identify two characteristic flow fields, defined as either steady or unsteady.