Measuring microfluidic flow rates: Monotonicity, convexity, and uncertainty

Abstract We consider a class of non-linear integro-differential equations describing microfluidic measurements. We prove that under reasonable conditions, solutions to these equations are convex functions of a flow-rate parameter ξ used in metrology. The key elements of our analysis are: (i) elevation of ξ to an independent variable through reformulation of the problem as a partial-differential equation (PDE); and (ii) extension of techniques from the theory of ordinary differential equations to the PDE setting.