Polymerase chain reaction ͑PCR͒ is commonly used for a wide range of DNA applications such as disease detection, genetic fingerprinting, and paternity testing. The importance of PCR has led to an increased interest in performing PCR in a microfluidic platform with a high throughput while using very small DNA quantities. In this paper we solve convection-diffusion equations for the DNA and deoxynucleoside triphosphate ͑dNTP͒ under conditions suitable for PCR operation in a microchip. These include pressure driven flow accompanied by temporal temperature changes that lead to an amplification reaction, which is modeled as a first order reaction. The convection-diffusion-reaction equations are solved by using the method of multiple time scales to yield average equations that can be solved to obtain the long time evolution of the concentration profiles. The results obtained by solving the averaged equations agree well with full numerical solutions. The averaged equations are also solved to simulate the PCR to illustrate some interesting aspects of this operation in a microfluidic device. It is shown that insufficient nucleotide concentrations can lead to complete depletion of NTP at certain axial locations, which leads to termination of DNA amplification at these locations, resulting in formation of a plateau in DNA concentration.

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