Using Analytical Solutions to Evaluate the Variability of the Distribution of Concentrations of the Components of Specific Reactions in Microfluidic Systems

Abstract

A number of methods for analyzing liquid media are based on carrying out specific reactions with the component to be determined. In microfluidic devices, due to the laminarity of the flow, it is difficult to organize uniform mixing of the reaction components, which deteriorates the reproducibility of the results of the reactions and the quality of the analysis. To improve the efficiency of passive mixing in microfluidic systems, you can use the input channel samples of variable geometry, in particular, with bends, or with a variable width. The mixing efficiency is directly related to the variability of reagent concentrations in the working area, and this characteristic is adequately evaluated through the dispersion of the concentration profile. To obtain an estimate of the dispersion of the concentration distribution, an analytical solution of the convective–diffusion equation using the method of moments is proposed. For this, the sample entry system—a straight section of constant width with an additional linearly expanding channel—is approximately replaced by an equivalent channel of constant width. Also, the values of convective velocity and diffusion coefficient are approximately replaced by averaged ones. The dispersion estimates obtained on the basis of an approximate analytical solution have an acceptable agreement with the results of numerical 2D modeling of convective mass transfer in COMSOL MULTYPHYSICS.