Microfabricated integrated circuits revolutionized computation by vastly reducing the space, labor, and time required for calculations. Microfluidic systems hold similar promise for the large-scale automation of chemistry and biology, suggesting the possibility of numerous experiments performed rapidly and in parallel, while consuming little reagent. While it is too early to tell whether such a vision will be realized, significant progress has been achieved, and various applications of significant scientific and practical interest have been developed. Here a review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena. Specifically, this review explores the Reynolds number Re, addressing inertial effects; the Peclet number Pe, which concerns convective and diffusive transport; the capillary number Ca expressing the importance of interfacial tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, describing elastic effects due to deformable microstructural elements like polymers; the Grashof and Rayleigh numbers Gr and Ra, describing density-driven flows; and the Knudsen number, describing the importance of noncontinuum molecular effects. Furthermore, the long-range nature of viscous flows and the small device dimensions inherent in microfluidics mean that the influence of boundaries is typically significant. A variety of strategies have been developed to manipulate fluids by exploiting boundary effects; among these are electrokinetic effects, acoustic streaming, and fluid-structure interactions. The goal is to describe the physics behind the rich variety of fluid phenomena occurring on the nanoliter scale using simple scaling arguments, with the hopes of developing an intuitive sense for this occasionally counterintuitive world.

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Microfluidics: Fluid physics at the nanoliter scale

Microfluidic devices for manipulating fluids are widespread and finding uses in many scientific and industrial contexts. Their design often requires unusual geometries and the interplay of multiple physical effects such as pressure gradients, electrokinetics, and capillarity. These circumstances lead to interesting variants of well-studied fluid dynamical problems and some new fluid responses. We provide an overview of flows in microdevices with focus on electrokinetics, mixing and dispersion, and multiphase flows. We highlight topics important for the description of the fluid dynamics: driving forces, geometry, and the chemical characteristics of surfaces.

Engineering flows in small devices

This book is written as a reference on organic substances in natural waters and as a supplementary text for graduate students in water chemistry. The chapters address five topics: amount, origin, nature, geochemistry, and characterization of organic carbon. Of these topics, the main themes are the amount and nature of dissolved organic carbon in natural waters (mainly fresh water, although seawater is briefly discussed). It is hoped that the reader is familiar with organic chemistry, but it is not necessary. The first part of the book is a general overview of the amount and general nature of dissolved organic carbon. Over the past 10 years there has been an exponential increase in knowledge on organic substances in water, which is the result of money directed toward the research of organic compounds, of new methods of analysis (such as gas chromatography and mass spectrometry), and most importantly, the result of more people working in this field. Because of this exponential increase in knowledge, there is a need to pull together and summarize the data that has accumulated from many disciplines over the last decade.

Organic geochemistry of natural waters

/pdf/micro-total-analysis-systems-1-introduction-theory-and-27f7corp18.pdf

Micro Total Analysis Systems. 1. Introduction, Theory, and Technology

 Many atmospheric chemicals occur in the gas phase as well as in liquid cloud droplets and aerosol particles Therefore, it is necessary to understand the distribution between the phases According to Henry's law, the equilibrium ratio between the abundances in the gas phase and in the aqueous phase is constant for a dilute solution Henry's law constants of trace gases of potential importance in environmental chemistry have been collected and converted into a uniform format The compilation contains 17 350 values of Henry's law constants for 4632 species, collected from 689 references It is also available at http://wwwhenrys-laworg 

/pdf/compilation-of-henry-s-law-constants-version-4-0-for-water-58il9q0ogv.pdf

Compilation of Henry's law constants (version 4.0) for water as solvent

In the course of viscometric measurements of concentrated suspensions of spheres in Newtonian fluids using a Couette device, Gadala-Maria & Acrivos (1980) observed a decrease in the suspension viscosity after long periods of shearing even though the viscosity of the pure suspending fluid remained constant under identical conditions. In the present work we demonstrate that this phenomenon is due to the shear-induced migration of particles out of the sheared Couette gap and into the fluid reservoir, which reduces the particle concentration in the gap and thereby the observed viscosity. We show further that this rate of viscosity decrease is consistent with a gap-limited shear-induced diffusion process normal to the plane of shear, with the relevant diffusion coefficient being proportional to is the applied shear rate.Additional experiments also uncovered a new phenomenon - a short-term increase in the viscosity upon initial shearing of a suspension in a Couette device - which was attributed to the diffusive migration of particles across the width of the Couette gap and thus was used to infer values of the corresponding diffusion coefficient within the plane of shear parallel to gradients in fluid velocity.In the theoretical part we demonstrate that the particle migrations that led to these observed phenomena may be explained in terms of the irreversible interparticle interactions that occur in these suspensions. From simple arguments, these interactions are shown to lead to effective diffusivities both normal to the plane of shear and normal to the direction of fluid motion within the plane of shear whose estimated magnitudes are comparable with those that were inferred from the experimental measurements. Furthermore, these interactions should induce, within a shear flow, particle drifts from regions of high to low shear stress, which are estimated to be of sufficient intensity to account for the observed initial viscosity increase mentioned above.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112087002155

The shear-induced migration of particles in concentrated suspensions

A novel technique is presented for determining the coefficient of shear-induced particle self-diffusion in concentrated suspensions of solid spheres, which relies on the fact that this coefficient can be computed from the measured variations in the time taken by a single marked particle in the suspension to complete successive circuits in a Couette device. Since this method does not involve the direct measurement of the lateral position of the marked particle, it requires a much simpler experiment than that used by Eckstein, Bailey & Shapiro (1977) which is shown to be constrained by wall effects at high particle concentration. The diffusion coefficient thus determined was found to be proportional to the product γa2, where γ is the shear rate and a the particle radius, and to have the asymptotic form 0.5γa2ϕ2 in the dilute limit when the particle concentration ϕ → 0.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112087000880

Measurement of shear-induced self-diffusion in concentrated suspensions of spheres

The total stress of a concentrated suspension of noncolloidal spheres in a Newtonian fluid was characterized by independent measurements in viscometric flows. Using a suspension balance formulation, the normal stress in the vorticity direction (Σ33) for a suspension undergoing simple shear was extracted from Acrivos et al.’s [Int. J. Multiphase Flow 19, 797 (1993)] resuspension data in a Couette device. Employing a new correlation for the relative viscosity μr which obeys the Einstein relation in the dilute limit while diverging at random close packing, it was found that Σ33/τ (where τ is the magnitude of the shear stress) was a strong function of the solid volume fraction φ, scaling as φ3e2.34φ. The relative viscosity, measured in a parallel plate viscometer, was in good agreement with the proposed correlation, while the normal stress differences N1 and N2 for concentrated suspensions (φ=0.30–0.55) were characterized using parallel plate and cone-and-plate geometries, as well as laser profilometry measur...

The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids

The contribution from purely viscous forces to the liftL on a sphere of radiusa touching a plane in the presence of a shear flow field of strength
 
$$\dot \gamma $$

 is zero. An exact integral expression for the lift to leading order in the Reynolds number
 
$$R \equiv \dot \gamma a^2 /v$$

 is derived using known creeping flow solutions to related problems. The integral is evaluated numerically to obtain the value of the lift
 
$${L \mathord{\left/ {\vphantom {L {\dot \gamma \mu a^2 }}} \right. \kern-\nulldelimiterspace} {\dot \gamma \mu a^2 }}\dot = 9.22R$$

 orL/F

 x
 ≐0.287R whereF
x is the lateral viscous force on the sphere.

David T. Leighton

Papers

The shear-induced migration of particles in concentrated suspensions

Measurement of shear-induced self-diffusion in concentrated suspensions of spheres

The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids

The lift on a small sphere touching a plane in the presence of a simple shear flow

Shear-induced transport of a particle layer along a porous wall