Measuring Microfluidic Flow Rates: Monotonicity, Convexity and Uncertainty
Paul N. Patrone, Qing Hai Li, Gregory A. Cooksey, Anthony J. Kearsley
A class of non-linear integro-differential equations characterizing microfluidic measurements is considered. Under reasonable conditions, these non-linear integro-differential equations admit solutions that are convex functions of an interesting flow-rate model problem parameter. A novel element of the analysis is the elevation of this parameter to an independent variable through recasting of the problem as a partial-differential equation (PDE) by employing ordinary differential equations (ODE) theory.