Interdisciplinary Applied Mathematics

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Foreword by Chih-Ming Ho


Fluid flow through small channels has become a popular research topic due to the emergence of biochemical lab-on-the-chip systems and micro electromechanical system fabrication technologies, which began in the late 1980s. This book provides a comprehensive summary of using computational tools (Chapters 14-18) to describe fluid flow in micro and nano configurations. Although many fundamental issues that are not observed in macro flows are prominent in microscale fluid dynamics, the flow length scale is still much larger than the molecular length scale, allowing for the continuum hypothesis to still hold in most cases (Chapter 1). However, the typical Reynolds number is much less than unity, due to the small transverse length scale, which results in a high-velocity gradient. For example, a 105 sec-1 shear rate is not an uncommon operating condition, and thus high viscous forces are prevalent, resulting in hundreds or thousands of ф hydrodynamic pressure drops across a single fluidic network. Consequently, it is not a trivial task to design micropumps that are able to deliver the required pressure head without suffering debilitating leakage. Electrokinetic and surface tension forces (Chapters 7 and 8) are used as alternatives to move the embedded particles and/or bulk fluid. The high viscous damping also removes any chance for hydrodynamic instabilities, which are essential for effective mixing. Mixing in micro devices is often critical to the overall system’s viability (Chapter 9). Using electrokinetic force to reach chaotic mixing is an interesting research topic. In these cases, the electrical properties, e.g., dielectric constants, rather than the viscosity determine the efficiency of transport.

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