By Henrik Bruus

Книга Theoretical Microfluidics Theoretical MicrofluidicsКниги Физика Автор: Henrik Bruus Год издания: 2008 Формат: pdf Издат.:Oxford collage Press Страниц: 288 Размер: 2,9 Мб ISBN: 0199235090 Язык: Английский0 (голосов: zero) Оценка:Microfluidics is a tender and speedily increasing clinical self-discipline, which offers with fluids and suggestions in miniaturized structures, the so-called lab-on-a-chip platforms. It has functions in chemical engineering, pharmaceutics, biotechnology and medication. because the lab-on-a-chip structures develop in complexity, a formal theoretical realizing turns into more and more vital. the elemental suggestion of the e-book is to supply a self-contained formula of the theoretical framework of microfluidics, and even as provide actual motivation and examples from lab-on-a-chip know-how. After 3 chapters introducing microfluidics, the governing equations for mass, momentum and effort, and a few uncomplicated move options, the next 14 chapters deal with hydraulic resistance/compliance, diffusion/dispersion, time-dependent circulation, capillarity, electro- and magneto-hydrodynamics, thermal delivery, two-phase move, advanced stream styles and acousto-fluidics, in addition to the recent fields of opto- and nano-fluidics. in the course of the booklet basic versions with analytical strategies are awarded to supply the coed with an intensive actual realizing of order of magnitudes and diverse chosen microfluidic phenomena and units. The ebook grew out of a collection of well-tested lecture notes. it really is with its many pedagogical routines designed as a textbook for a complicated undergraduate or first-year graduate path. it's also like minded for self-study.

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002 mPa s. 21) The viscosity of water has a strong dependence on temperature as seen in Fig. 2. A table of viscosity values for other ﬂuids is given in Appendix A. 22) is a good approximation. 4 Rate of change in momentum due to body forces The body forces are external forces that act throughout the entire body of the ﬂuid. We shall, in particular, work with the gravitational force (in terms of the density ρ and the acceleration of gravity g ) and the electrical force (in terms of the charge density ρel of the ﬂuid and the external electric ﬁeld E).

By insertion of Eq. 36) into the Navier–Stokes equation for incompressible ﬂuids, Eq. 37) which after reduction becomes ˜ v ˜ p˜ + ∇ ˜ 2v ˜+ v ˜. 38) Here, we have introduced the dimensionless number Re, the so-called the Reynolds number, Re ≡ ρV0 L0 . 39) ˜ 2v ˜ dominates, whereas We clearly see from Eq. 38) that for Re 1 the viscous term ∇ ˜ v ˜ ·∇ ˜ is the most important term. in steady state for Re 1 the inertia term v The corresponding dimensionless form of the incompressibility condition ∂i vi = 0 is quite simple since ∂i = (1/L0 )∂˜i and vi = V0 v˜ i , ∂˜i v˜ i = 0.

48) This ﬁve-parameter model describes well the experimentally observed transition from the zero-shear-stress viscosity η0 to the inﬁnite-shear-stress viscosity η∞ , which happens around the time scale λ. The curvature at the transition-point in a log(η)−log(|γ|) ˙ plot is controlled by a, while the slope of the curve in the transition region of the plot is determined by n. 49) η |γ| ˙ = m |γ| ˙ n−1 , n > 1, non-Newtonian shear thickening. We note that the power-law model is identical to the Carreau–Yasuda model in the largea 1 when taking η∞ = 0 and η0 λn−1 = m.