Micro- and Nanoscale Fluid Mechanics: Transport in by Brian J. Kirby

By Brian J. Kirby

This article specializes in the physics of fluid shipping in micro- and nanofabricated liquid-phase structures, with attention of gasoline bubbles, stable debris, and macromolecules. this article was once designed with the aim of bringing jointly a number of components which are usually taught individually - particularly, fluid mechanics, electrodynamics, and interfacial chemistry and electrochemistry - with a targeted target of getting ready the trendy microfluidics researcher to investigate and version continuum fluid mechanical structures encountered whilst operating with micro- and nanofabricated units. this article isn't really a precis of present examine within the box, and it omits any dialogue of microfabrication ideas or any try to summarize the technological state-of-the-art. this article serves as an invaluable reference for working towards researchers yet is designed essentially for lecture room guide. labored pattern difficulties are inserted all through to help the scholar, and routines are integrated on the finish of every bankruptcy to facilitate use in sessions.

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Streamlines are the most common tool used analytically to understand flows, because streamlines are analytically simple to generate and provide a clear image of the instantaneous velocity in a system. Pathlines and streaklines, in contrast, are straightforward to reproduce in the laboratory and are thus the most common experimental tools used for visualization. In particular, compelling simplifications for two-dimensional (2D) flows are achieved with the stream function, which is related to the streamlines in the system.

7 The viscosity is thus the fundamental link between velocity gradients and the surface stresses that result from that velocity gradient. The Newtonian model postulates that ␩ is a property of the fluid, but not a property of the local strain rate. GENERAL NEWTONIAN RELATION FOR SHEAR STRESS IN A 3D FLOW For Newtonian fluids, the shear stress tensor and the viscous component of the strain rate tensor are linearly related: Newtonian postulate for viscous stress tensor in terms of strain rate tensor ␶ visc = 2␩␧ .

6 in Appendix C. 3 Governing Equations for Incompressible Flow Convective momentum fluxes for a differential Cartesian control volume. Fig. 4 For an incompressible fluid, we assume that the density ␳ is uniform. Applying the divergence theorem and using the conservation of mass relation, we can write the conservation of momentum equation in differential form as Cauchy momentum equation ␳ ∂u + ␳ u · ∇u = ∇ · ␶ + ∂t fi . 27) i In this general form, the conservation of momentum equation is referred to as the Cauchy momentum equation.

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