System-Level Modeling and Design of Microfluidic Concentration Gradient Generators

This paper presents a systematic modeling and design methodology for microfluidic concentration gradient generators. The generator is decomposed into a system of microfluidic elements with relatively simple geometries. Parameterized models for such elements are analytically developed and hold for general sample concentration profiles and arbitrary flow ratios at the element inlet, hence they are valid for concentration gradient generators that rely on both complete and partial mixing. The element models are then linked through an appropriate set of parameters embedded at the element interfaces to construct a lumped-parameter and systematic representation of the entire generator network. The system model is verified by numerical analysis and experimental data and accurately captures the overall effects of network topologies, element sizes, flow rates and reservoir sample concentrations on the generation of sample concentration gradient. Finally, this modeling methodology is applied to propose a novel and compact microfluidic device that is able to create concentration gradients of complex shapes by juxtaposing simple constituent profiles along the channel width