  Micro-scale flow in cylindrical geometries can harness chaotic advection to
perform complex thermally activated biochemical reactions such as the
polymerase chain reaction (PCR). We have applied a 3D computational fluid
dynamics model to resolve the complex flow patterns in such geometries. The
resulting 3D flow trajectories are then used as input to a kinetic model to
resolve the time evolution of DNA replication process. A simple mass action
kinetic model was developed to couple these biochemical reactions with the
intricate flow. Residence time analysis of virtual particles in the flow
revealed that the flow has a strong chaotic component in wider geometries in
comparison with taller geometries (quasi periodic motion). This work shows, for
the first time that the chaotic aspect of the flow field plays a key role in
determining the strength of the coupling between the reactions and the flow.
Our model can quantify the doubling times of these reactions capturing the lag,
exponential and plateau phases of PCR. It predicts that doubling times are
lower in wider geometries, in agreement with experimental results.
