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Lim et al. (2003) fabricated a multi-width multidepth microchannel using a direct write laser technology to resemble physiological vascular systems according to Murray's law. Emerson et al. (2006) extended Murray's law to arbitrary cross-sections and provide a framework for constructing a simple but elegant biomimetic design rule for hierarchical microfluidic networks. McCulloh et al. (2003) have performed computer simulations of the hydraulic conductance of a branched transport system to prove water transport in plants obeys Murray's law. Based on the biomimetic principle, Barber and Emerson (2008) focused specifically on microfluidic manifolds composed of constant-depth rectangular-or trapezoidal-sectioned channels which can be created using standard micro-fabrication techniques. Cieslicki and Piechna (2009) carried out investigations of mixing process in microfluidic manifold designed according to biomimetic rule. They stated the superiority of the micromixers obeying the fractal theory which outperform the one which does not follow this rule. The main integral flow parameters, such as the Poiseuille number, the momentum flux correction factor, the kinetic energy correction factor, the asymptotic incremental pressure drop number and the approximate value of the hydrodynamic entrance length are numerically evaluated for trapezoidal and double-trapezoidal cross sections of the silicon microchannels (Morini 2004). A design rule based on the mean shear stress is used to predict and control the stress distribution within the hierarchical microfluidic network. A range of alternative biomimetic and hydrodynamic scaling principles are also discussed, including power and Reynolds number, which enable different parameters to be controlled in each successive generation (Emerson et al. 2006). A computational "toolbox" for a priori design of optimized microfluidic components is presented. The generation and use of advection maps is described, and Abstract Two-dimension Y-type micromixers and T-type micromixers have been systematically researched based on fractal theory and generalized Murray's law. Effect of geometry parameters on mixing efficiency and pressure drop was analyzed. For Y-type micromixers, bifurcation angle is a very important parameter that influences mixing performance. The bifurcation angles θ = 30°, θ = 45°, θ = 60°, θ = 75°, θ = 90°, θ = 105°, and θ = 120° were studied, and the best bifurcation angle was obtained. For T-type micromixers, T Symmetry, Semicircle-T Symmetry, T Asymmetry and Semicircle-T Asymmetry were compared. A comprehensive series of simulations were performed and the optimum structure was obtained.

Applications of membranes in microfluidics solved many thorny problems for analytical chemistry and bioscience, so that the use of membranes in microfluidics has been a topic of growing interest. Many different examples have been reported, demonstrating the versatile use of membranes. This work reviews a lot of applications of membranes in microfluidics. Membranes in microfluidics for applications including chemical reagents detection, gas detection, drug screening, cell, protein, microreactor, electrokinetical fluid, pump and valve and fluid transport control and so on, have been analyzed and discussed. In addition, the definition and basic concepts of membranes are summed up. And the methods of manufacturing membranes in microfluidics are discussed. This paper will provide a helpful reference to researchers who want to study applications of membranes in microfluidics.