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

A front-tracking method for viscous, incompressible, multi-fluid flows

Surface-tension-driven flows and, in particular, their tendency to decay spontaneously into drops have long fascinated naturalists, the earliest systematic experiments dating back to the beginning of the 19th century. Linear stability theory governs the onset of breakup and was developed by Rayleigh, Plateau, and Maxwell. However, only recently has attention turned to the nonlinear behavior in the vicinity of the singular point where a drop separates. The increased attention is due to a number of recent and increasingly refined experiments, as well as to a host of technological applications, ranging from printing to mixing and fiber spinning. The description of drop separation becomes possible because jet motion turns out to be effectively governed by one-dimensional equations, which still contain most of the richness of the original dynamics. In addition, an attraction for physicists lies in the fact that the separation singularity is governed by universal scaling laws, which constitute an asymptotic solution of the Navier-Stokes equation before and after breakup. The Navier-Stokes equation is thus continued uniquely through the singularity. At high viscosities, a series of noise-driven instabilities has been observed, which are a nested superposition of singularities of the same universal form. At low viscosities, there is rich scaling behavior in addition to aesthetically pleasing breakup patterns driven by capillary waves. The author reviews the theoretical development of this field alongside recent experimental work, and outlines unsolved problems.

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Nonlinear dynamics and breakup of free-surface flows

We review transport characteristics of pressure-driven, multiphase flows through microchannel networks tens of nanometres to several hundred of micrometres wide with emphasis on conditions resulting in enhanced mixing and reduced axial dispersion. Dimensionless scaling parameters useful in characterizing multiphase flows are summarized along with experimental flow visualization techniques. Static and dynamic stability considerations are also included along with methods for stabilizing multiphase flows through surface modifications. Observed gas–liquid and immiscible liquid–liquid flows are summarized in terms of flow regime diagrams and the different flows are related to applications in chemistry and materials synthesis. Means to completely separate multiphase flows on the microscale and guidelines for design of scalable multiphase systems are also discussed.

Multiphase microfluidics: from flow characteristics to chemical and materials synthesis

We summarize procedures for producing 'nanoemulsions' comprised of nanoscale droplets, methods for controlling the droplet size distribution and composition, and interesting physical properties of nanoemulsions. In contrast to more common microscale emulsions, nanoemulsions exhibit optical transparency at high droplet volume fractions, , surprisingly strong elasticity at low , and enhanced diffusive transport and shelf stability. For these reasons, nanoemulsions have great potential in a wide range of industries including pharmaceuticals, foods, and personal care products.

https://iopscience.iop.org/article/10.1088/0953-8984/18/41/R01/pdf

J M Rallison

Papers

The Deformation of Small Viscous Drops and Bubbles in Shear Flows