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

http://experimentationlab.berkeley.edu/sites/default/files/AFMImages/butt_AFM.pdf

Force measurements with the atomic force microscope: Technique, interpretation and applications

This review discusses the use of the combination of surface roughness and hydrophobicity for engineering large slip at the fluid-solid interface. These superhydrophobic surfaces were initially inspired by the unique water-repellent properties of the lotus leaf and can be employed to produce drag reduction in both laminar and turbulent flows, enhance mixing in laminar flows, and amplify diffusion-osmotic flows. We review the current state of experiments, simulations, and theory of flow past superhydrophobic surfaces. In addition, the designs and limitations of these surfaces are discussed, with an eye toward implementing these surfaces in a wide range of applications.

Slip on Superhydrophobic Surfaces

For several centuries fluid dynamics studies have relied upon the assumption that when a liquid flows over a solid surface, the liquid molecules adjacent to the solid are stationary relative to the solid. This no-slip boundary condition (BC) has been applied successfully to model many macroscopic experiments, but has no microscopic justification. In recent years there has been an increased interest in determining the appropriate BCs for the flow of Newtonian liquids in confined geometries, partly due to exciting developments in the fields of microfluidic and microelectromechanical devices and partly because new and more sophisticated measurement techniques are now available. An increasing number of research groups now dedicate great attention to the study of the flow of liquids at solid interfaces, and as a result a large number of experimental, computational and theoretical studies have appeared in the literature. We provide here a review of experimental studies regarding the phenomenon of slip of Newtonian liquids at solid interfaces. We dedicate particular attention to the effects that factors such as surface roughness, wettability and the presence of gaseous layers might have on the measured interfacial slip. We also discuss how future studies might improve our understanding of hydrodynamic BCs and enable us to actively control liquid slip.

https://iopscience.iop.org/article/10.1088/0034-4885/68/12/R05/pdf

Boundary slip in Newtonian liquids: a review of experimental studies

The slip effects of water flow in hydrophilic and hydrophobic microchannels of 1 and 2 μm depth are examined experimentally. High-precision microchannels were treated chemically to enhance their hydrophilic and hydrophobic properties. The flow rates of pure water at various applied pressure differences for each surface condition were measured using a high-precision flow metering system and compared to a theoretical model that allows for a slip velocity at the solid surface. The slip length was found to vary approximately linearly with the shear rate with values of approximately 30 nm for the flow of water over hydrophobic surfaces at a shear rate of 105 s−1. The existence of slip over the hydrophilic surface remains uncertain, due to the sensitivity of the current analysis to nanometer uncertainties in the channel height.

Apparent slip flows in hydrophilic and hydrophobic microchannels

The slip effects of water flow in hydrophilic and hydrophobic microchannels of 1 and 2 μm depth are examined experimentally. Fabrication processes for silicon/Pyrex microchannels were chosen to ensure good control of the channel height and to obtain atomically smooth surfaces. Hydrophilic surfaces were prepared with an RCA-1 cleaning, while hydrophobic surfaces were created by coating the channel surface with the self-assembled monolayer of octadecyltrichorosilane (OTS). The flow rates of pure DI water at various applied pressure differences for each surface condition were measured using a high precision flow metering system and it was observed that the flow rates in hydrophobic channels is larger than in the same hydrophilic channel. The increase of the flow rate can be explained by assuming a slip velocity at the wall. The slip effects become more pronounced as the channel height decreases and the wall shear rate increases. The slip length was found to vary as approximately the square root of the shear rate and had values of approximately 40 nm in the hydrophobic channels and 15 nm in the hydrophilic channels at a shear rate of 105 s−1 .Copyright © 2002 by ASME

To Slip or Not to Slip: Water Flows in Hydrophilic and Hydrophobic Microchannels

Infrared Diagnostics for the Measurement of Fluid and Solid Motion in Micromachined Devices

Liquid Transport Properties in Sub-Micron Channel Flows

An experimental procedure designed for rheological testing of shear-dependent viscosities using small sample volumes is described. Excellent results are obtained with simple (Newtonian) fluids at flow rates smaller than 1 nl/s using a channel with 0.9 µm gap height. However, anomalous behavior is observed with aqueous (ionic) solutions, stressing the importance of chemical and/or electrokinetical surface effects.

K. Johan A. Westin

Papers

Apparent slip flows in hydrophilic and hydrophobic microchannels

To Slip or Not to Slip: Water Flows in Hydrophilic and Hydrophobic Microchannels

Infrared Diagnostics for the Measurement of Fluid and Solid Motion in Micromachined Devices

Liquid Transport Properties in Sub-Micron Channel Flows

Rheological Shear Experiments in Micron Scale Geometries