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This paper presents a systematic modeling 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 either complete or partial mixing. The element models are then linked through an appropriate set of parameters embedded at the element interfaces. This yields a systematic, lumped-parameter representation of the entire generator in terms of a network of gradient-generation elements. 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.

Since its discovery more than 60 years ago, the drag reduction phenomenon has achieved many notable energy saving effects. These achievements have encouraged researchers to study drag reduction further and further so that it can be utilized better. But due to the complex characteristics of turbulent flow, recent theories cannot explain all the phenomena of drag reduction. To give an overview of drag reduction and corresponding heat transfer for further understanding, this paper summarizes the main advancements of drag reduction during these 60 years, including background, application, development, theory, and research methods of different drag reducers. Future directions of development are also discussed.

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