Interdisciplinary Applied Mathematics

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In the nanoflow regime, not many molecules are situated far away from the channel wall. Therefore, the motion of the bulk fluid is significantly affected by the potential fields generated by the molecules near the solid wall. Near the surface, the fluid molecules do not flow freely. At a distance of a few fluid molecule layers above the surface, the flow has very different physical constants from the bulk flow. The surface effects are strong not only in nano configurations (Chapter 10); even in microfluidic devices, the performance, e.g., surface fouling, is dependent on the surface property. We frequently spend more time on modifying the surface properties than on designing and fabricating devices. As a result of our limited understanding of fluidic behavior within nanoscale channels (Chapters 10 through 13), many vital systematic processes of today’s technology are arduously, yet imperfectly, designed. Delivering and stopping a picoliter volume of fluid to a precise location with high accuracy as well as the separation and mixing of nano/micro particles in a fluid medium of high ionic concentration remains a challenging task. By furthering the understanding of fluid interactions in the nano world, many of the interesting mysteries and challenges that have puzzled scientists will be revealed.

Chih-Ming Ho

June 2004, Los Angeles, California, USA


In the early 1990s, microchannel flow experiments at the University of Pennsylvania by the groups of H. Bau and J. Zemel revealed intriguing results for both liquids and gases that sparked excitement and new interest in the study of low Reynolds number flows in microscales. Another influential development at about the same time was the fabrication of the first microchannel with integrated pressure sensors by the groups of C.M. Ho (UCLA) and Y.C. Tai (Caltech). While the experimental results obtained at the University of Pennsylvania indicated global deviations of microflows from canonical flows, pointwise measurements for gas flows with pressure sensors, and later with temperature sensors, revealed a new flow behavior at microscales not captured by the familiar continuum theory. In microgeometries the flow is granular for liquids and rarefied for gases, and the walls “move.” In addition, other phenomena such as thermal creep, electrokinetics, viscous heating, anomalous diffusion, and even quantum and chemical effects may become important. Most important, the material of the wall and the quality of its surface play a very important role in the momentum and energy exchange. One could argue that at least for gases the situation is similar to low-pressure high-altitude aeronautical flows, which were studied extensively more than 40 years ago. Indeed, there is a similarity in a certain regime of the Knudsen number. However, most gas microflows correspond to a low Reynolds number and low Mach number, in contrast to their aeronautical counterparts. Moreover, the typical microgeometries are of very large aspect ratio, and this poses more challenges for numerical modeling, but also creates opportunities for obtaining semianalytical results. For liquids no such analogy exists and their dynamics in confined microgeometries, especially at the submicron range, is much more complex.

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