Systematic linearisation of a microfluidic gradient network with unequal solution inlet viscosities demonstrated using glycerol

Abstract

This paper presents a mathematical and experimental study of the effect of inlet concentration (and therefore viscosity) of glycerol solutions on the perfor- mance of a microfluidic network. This was achieved with analytical modelling, implemented in MATLAB, and optical measurement of the entire concentration distribu- tion of the network. A mathematical proposal to improve the linearity of the outlet profile is also implemented and successfully verified experimentally. The concentration gradients of a two inlet-six outlet (2-6) microfluidic net- work device were obtained with inlet solutions of 10- 40 wt% glycerol and flow rates of up to 5 ll/s per inlet. The mathematical model developed gave a good agreement with the experimental results obtained. 'S' shaped outlet profiles were obtained for the four glycerol cases studied and the closest results to the model were achieved at an optimised flow rate of 1ll/s for 10 wt% glycerol, 5 ll/s for both 20 and 30 wt% glycerol and 1.5 ll/s for 40 wt% glycerol. The linearity of the outlet profiles for the 20, 30 and 40 wt% inlet glycerol experiments were improved from R 2 of 0.977, 0.946 and 0.966, respectively (before linearisation) to their new values of 0.997, 0.995 and 0.974, respectively (after the linearisation). This was performed by application of the mathematical model, at controlled inlet flow rate ratios of 0.77, 0.63 and 0.52 with respect to the viscous inlet, for 20, 30 and 40 wt% glycerol experi- ments, again with very good agreement of the outlet performance between the experimental and the mathe- matical results.