Dispersion in microchannels with temporal temperature variations

While amplifying DNA strands in a microfluidic device, the sample is subjected to cyclic changes in temperature. We investigate the dispersion of molecules in a microchannel, as these undergo a contraction-expansion flow that is driven by temporally changing temperatures. In this paper, the method of multiple time scales with regular expansions is used to obtain the effective dispersivity and the analytical results are compared with computational fluid dynamics simulations. Due to the thermal expansion of the carrier fluid, the cyclic temperature variations lead to both axial and lateral velocities. These periodic velocity profiles lead to an increase in axial dispersion. The dispersion coefficient increases as the square of the channel position from the center of the microchannel. Due to the quadratic variation of the dispersion coefficient in the axial direction, the concentration profile is non-Gaussian and a complex function of frequency and magnitude of the temporal oscillations and the dimensions of the microchannel. Analytical expressions for dispersion coefficient are derived for cyclic profiles of any shape; and results are computed and discussed for particular cases of cosine and step-function temperature cycles. The value for effective dispersion is also evaluated for a sample temperature profile that occurs in the microfluidic DNA amplification processes. The dispersion coefficient for step changes in temperature is found to be substantially larger than that for the case of sinusoidal temperature changes at low frequencies. We believe that the results of this study will enhance our understanding of transport in microscale systems that are subjected to temporally changing temperatures, and likely lead to technological advances in diverse areas relevant to microreactor design and DNA amplification. (c) 2005 American Institute of Physics.