Interdisciplinary Applied Mathematics

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mean concentration/fluorescence value of the mixture. This definition is analogous to the Euclidean error norm, and measures deviations from a perfect mix. Therefore, smaller M values show better mixing in the domain, with M ^ 0 for a perfect mix. It is often useful to plot the time variation of M (or M-1) in logarithmic scale, which enables accurate comparisons between various mixing states.


Simple Fluids in Nanochannels

With the growing interest in the development of faster, smaller, and more efficient biochemical analysis devices, nanofluidic systems and hybrid mi-cro/nano fluidic systems have attracted considerable attention in recent years. In nanoscale systems, the surface-to-volume ratio is very high, and the critical dimension can be comparable to the size of the fluid molecules. The influence of the surface and the finite-size effect of the various molecules on fluid transport needs to be understood in detail, while such effects may be largely neglected for liquid flows in macroscopic channels. In this chapter, we discuss the analysis of simple fluids such as Lennard-Jones liquids in confined nanochannels. A key difference between the simulation of the fluidic transport in confined nanochannels, where the critical channel dimension can be a few molecular diameters, and at macroscopic scales is that the well-established continuum theories based on Navier-Stokes equations may not be valid in confined nanochannels. Therefore, atomistic scale simulations, in which the fluid atoms are modeled explicitly or semiexplicitly and the motion of the fluid atoms is calculated directly, shed fundamental insights on fluid transport. The most popular technique for atomistic simulation of liquid transport is molecular dynamics (MD), which is discussed in detail in Chapter 16. After presenting some details on the atomistic simulation of simple fluids, we discuss density profiles, diffusion transport, and validity of the Navier-Stokes equations for simple fluids in confined nanochannels. In the last section we discuss in detail the slip condition at solid-liquid interfaces and present experimental and computational results as well as conceptual models of slip. We also revisit the lubrication problem, first discussed in Chapter 7, and we present the Reynolds-Vinogradova

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