Interdisciplinary Applied Mathematics

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The National Nano Initiative, established first in the USA (

and subsequently in many other countries, has pushed the length scale range of interest from microns down to nanometers. Flows in these regimes start to challenge the fundamental assumptions of continuum mechanics (Chapter 1). The effects of the molecules in the bulk of the fluid versus those molecules in proximity to a solid boundary become differentiated (Chapter 10). These are extremely intriguing aspects to be investigated for flows in small configurations. The demarcation between the continuum and the noncontinuum boundary has yet to be determined and inevitably will have a tremendous influence on the understanding of small-scale fluid behavior as well as system design.

The ratio between the size of the channel and that of the molecule is not the only parameter that validates the continuum assumption. In biological applications, for example, molecules with large conformation changes, electrical charges, and polar structures are frequently encountered. These variables make it impossible to determine whether a flow can be considered a continuum based only on a ratio of sizes (Chapter 11). When a continuum flow of a Newtonian fluid is assumed, molecular effects are defined by the governing equations of traditional fluid mechanics. Interactions among fluid molecules are expressed by a physical constant, which is viscosity. The no-slip condition represents the interactions between the fluid and the solid surface molecules. Both viscosity and the no-slip condition are concepts developed under the framework of continuum. Deviations from the bulk viscosity and the no-slip condition can lead to other results due to the breakdown of the continuum assumption (Chapters 2 and 10).

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