Dispersion in microchannels with temporal temperature variations

Abstract

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.

Taylor dispersion in polymerase chain reaction in a microchannel

“…Since the total amount of enzyme does not change on the long time scale, their average equations can be determined by substituting appropriate diffusivities into the average equations for the DNA in the absence of reaction. 32 Including various DNA states into the model is complex and it requires detailed reaction kinetics of the PCR process which is not currently available.…”

“…We use the method of multiple time scales to average the convectiondiffusion equations over the short time scale of reaction and lateral diffusion. [32][33][34][35] The averaged equations are solved and the results are compared with full numerical solutions to the convection-diffusion-reaction equations for both the DNA and the NTPs for a variety of situations. Finally, the averaged equations are solved to simulate PCR to illustrate some interesting aspects of this operation in a microfluidic device.…”

“…[20][21][22][23][24][25][26][27][28][29][30][31] Recently, we computed the dispersion coefficients for time periodic flows driven by temporal temperature changes that correspond to the PCR operation. 32 While the temporal temperature changes were included in our model, the amplification was ignored. In this paper we explore the effect of the chemical reaction on the dispersion of a plug that undergoes temporal temperature changes inside a microchannel.…”

Theory of band broadening during cycling temperature capillary electrophoresis

“…(2.9) and (2.10) permits a multiple-time scales analysis of the averaged transport over the entire length of the capillary. This standard asymptotic technique [18] has recently been used to study other time-oscillating DNA analysis techniques [19,20]. In this method, the probability densities are assumed to possess the asymptotic expansions, …”

Capabilities and limitations of 2-dimensional and 3-dimensional numerical methods in modeling the fluid flow in sudden expansion microchannels

“…For example, 2-D simulations assume that the depth (i.e., the z-direction) of the microchannel geometry is infinite or that the flow takes place at a low Reynolds number. However, in many cases, the commonly used 2-D (Jen and Lin 2002;Tonomura et al 2004;Sundaram and Tafti 2004;Pan et al 2004;D'Agro 2004, 2005;Townsend et al 2005) or 3-D (Koo and Kleinstreuer 2003;Tripathi et al 2005; numerical methods successfully provide accurate predictions of the flow behavior inside microchannels. In general, the success of using 2-D numerical methods depends upon the characteristics of the flow, e.g., the Reynolds number, Strouhal number, etc.…”