2007
DOI: 10.1017/cbo9780511800245
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Advanced Transport Phenomena

Abstract: Advanced Transport Phenomena is ideal as a graduate textbook. It contains a detailed discussion of modern analytic methods for the solution of fluid mechanics and heat and mass transfer problems, focusing on approximations based on scaling and asymptotic methods, beginning with the derivation of basic equations and boundary conditions and concluding with linear stability theory. Also covered are unidirectional flows, lubrication and thin-film theory, creeping flows, boundary layer theory, and convective heat a… Show more

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Cited by 932 publications
(482 citation statements)
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“…The relative importance of inertia can be quantified by Reynolds number (Re ¼ qUD h =l) which describes the ratio of inertial to viscous forces, with q; l, and U being 1=2 /viscous force the density, viscosity, and mean velocity of the fluid, respectively, while D h is the hydraulic diameter of the channel implying the actual diameter in case of a circular tube and equal to 2WH=ðW þ HÞ for a rectangular channel with width W and height H. It can be shown 41 that in the limit of zero Reynolds number, i.e., Stokes flow, lateral migration of a neutrally buoyant particle suspended in a confined flow of a Newtonian fluid is nonexistent due to linearity and thus reciprocality of the system. But in the flow regime where Re տ Oð1Þ, in addition to the drag force in the axial direction, transverse forces are exerted on the suspended particles compelling them to migrate laterally towards final stable locations, also known as equilibrium positions.…”
Section: A Inertial Effectsmentioning
confidence: 99%
“…The relative importance of inertia can be quantified by Reynolds number (Re ¼ qUD h =l) which describes the ratio of inertial to viscous forces, with q; l, and U being 1=2 /viscous force the density, viscosity, and mean velocity of the fluid, respectively, while D h is the hydraulic diameter of the channel implying the actual diameter in case of a circular tube and equal to 2WH=ðW þ HÞ for a rectangular channel with width W and height H. It can be shown 41 that in the limit of zero Reynolds number, i.e., Stokes flow, lateral migration of a neutrally buoyant particle suspended in a confined flow of a Newtonian fluid is nonexistent due to linearity and thus reciprocality of the system. But in the flow regime where Re տ Oð1Þ, in addition to the drag force in the axial direction, transverse forces are exerted on the suspended particles compelling them to migrate laterally towards final stable locations, also known as equilibrium positions.…”
Section: A Inertial Effectsmentioning
confidence: 99%
“…at the creeping-flow limit, which is known as Stoke's law [41], where a is the particle radius,ũ is the fluid velocity,ũ p is the particle velocity andm is the viscosity of the liquid. The DEP force for a spherical particle is given in Eq.…”
Section: Optimization Of the Separation Channelmentioning
confidence: 99%
“…When the particle moves close to the channel wall, there exists a strong dielectric [42] and hydrodyanmic [41] interaction between the particle and the channel wall, resulting in a repulsive force. Therefore, at some critical spacing between particle and the channel wall, repulsion force on the particle balances the DEP force, which would prevent the sticking of the particle on the channel wall.…”
Section: Simulation Of the Particle Trajectorymentioning
confidence: 99%
“…w(0) = w (0) = w(L) = w (L) = 0 (with primes denoting differentiation with respect to x). To determine the pressure within the liquid, p(x), we use lubrication theory [25], consistent with our assumption of small slopes, |dw/dx| 1. Using standard methods, the pressure may be expressed [30] as…”
mentioning
confidence: 99%