Howard A. Stone

Formation of dispersions using ‘‘flow focusing’’ in microchannels

A flow-focusing geometry is integrated into a microfluidic device and used to study drop formation in liquid–liquid systems. A phase diagram illustrating the drop size as a function of flow rates and flow rate ratios of the two liquids includes one regime where drop size is comparable to orifice width and a second regime where drop size is dictated by the diameter of a thin “focused” thread, so drops much smaller than the orifice are formed. Both monodisperse and polydisperse emulsions can be produced.

Microscopic artificial swimmers

Microorganisms such as bacteria and many eukaryotic cells propel themselves with hair-like structures known as flagella, which can exhibit a variety of structures and movement patterns. For example, bacterial flagella are helically shaped and driven at their bases by a reversible rotary engine, which rotates the attached flagellum to give a motion similar to that of a corkscrew. In contrast, eukaryotic cells use flagella that resemble elastic rods and exhibit a beating motion: internally generated stresses give rise to a series of bends that propagate towards the tip. In contrast to this variety of swimming strategies encountered in nature, a controlled swimming motion of artificial micrometre-sized structures has not yet been realized. Here we show that a linear chain of colloidal magnetic particles linked by DNA and attached to a red blood cell can act as a flexible artificial flagellum. The filament aligns with an external uniform magnetic field and is readily actuated by oscillating a transverse field. We find that the actuation induces a beating pattern that propels the structure, and that the external fields can be adjusted to control the velocity and the direction of motion.

Formation of monodisperse bubbles in a microfluidic flow-focusing device

This letter describes a method for generating monodisperse gaseous bubbles in a microfluidic flow-focusing device. The bubbles can be obtained in a range of diameters from 10 to 1000μm. The volume Vb of the bubbles scales with the flow rate q and the viscosity μ of the liquid, and the pressure p of the gas stream as Vb∝p∕qμ. This method allows simultaneous, independent control of the size of the individual bubbles and volume fraction of the dispersed phase. Under appropriate conditions, bubbles self-assemble into highly ordered, flowing lattices. Structures of these lattices can be adjusted dynamically by changing the flow parameters.

Experimental and theoretical scaling laws for transverse diffusive broadening in two-phase laminar flows in microchannels

This letter quantifies both experimentally and theoretically the diffusion of low-molecular-weight species across the interface between two aqueous solutions in pressure-driven laminar flow in microchannels at high Peclet numbers. Confocal fluorescent microscopy was used to visualize a fluorescent product formed by reaction between chemical species carried separately by the two solutions. At steady state, the width of the reaction–diffusion zone at the interface adjacent to the wall of the channel and transverse to the direction of flow scales as the one-third power of both the axial distance down the channel (from the point where the two streams join) and the average velocity of the flow, instead of the more familiar one-half power scaling which was measured in the middle of the channel. A quantitative description of reaction–diffusion processes near the walls of the channel, such as described in this letter, is required for the rational use of laminar flows for performing spatially resolved surface chemistry and biology inside microchannels and for understanding three-dimensional features of mass transport in shearing flows near surfaces.

Effective slip in pressure-driven Stokes flow

Nano-bubbles have recently been observed experimentally on smooth hydrophobic surfaces; cracks on a surface can likewise be the site of bubbles when partially wetting fluids are used. Because these bubbles may provide a zero shear stress boundary condition and modify considerably the friction generated by the solid boundary, it is of interest to quantify their influence on pressure-driven flow, with particular attention given to small geometries. We investigate two simple configurations of steady pressure-driven Stokes flow in a circular pipe whose surface contains periodically distributed regions of zero surface shear stress. In the spirit of experimental studies probing slip at solid surfaces, the effective slip length of the resulting flow is evaluated as a function of the degrees of freedom describing the surface heterogeneities, namely the relative width of the no-slip and no-shear stress regions and their distribution along the pipe. Comparison of the model with experimental studies of pressure-driven flow in capillaries and microchannels reporting slip is made and a possible interpretation of the experimental results is offered which is consistent with a large number of distributed slip domains such as nano-size and micron-size nearly flat bubbles coating the solid surface. Further, the possibility is suggested of a shear-dependent effective slip length, and an explanation is proposed for the seemingly paradoxical behaviour of the measured slip length increasing with system size, which is consistent with experimental results to date.

Heat transfer in open-cell metal foams

The paper explores the use of open-celled metal foams as compact heat exchangers, exploiting convective cooling. An analytical model is developed for model foams with simple cubic unit cells consisting of heated slender cylinders, based on existing heat transfer data on convective crossflow through cylinder banks. A foam-filled channel having constant wall temperatures is analyzed to obtain the temperature distribution inside the channel as a function of foam density, cell size and other pertinent heat transfer parameters. Two characteristic length scales of importance to the problem are discussed: the minimum channel length required for heating the fluid to its goal temperature and the thermal entry length beyond which the transfer of heat between fluid and channel wall assumes a constant coefficient. The overall heat transfer coefficient of the heat exchanging system is calculated, and the pressure drop experienced by the fluid flow obtained. These results are used to analyze and guide the design of optimum foam structures that would maximize heat transfer per unit pumping power. Two examples are given to demonstrate the applicability of the analytical model: heat sinks for high power electronic devices and multi-layered heat exchangers for aeronautical applications. The present model perhaps oversimplifies the calculation of transport in a metal foam consisting of non-circular, possibly sharp-edged ligaments, and so likely leads to overestimates. Nevertheless the trends of heat transfer predicted by the model (for dependence on foam relative density, duct geometries, fluid velocity, etc.) are expected to be valid for a wide range of open-cell foams and are in reasonable agreement with available experimental data on aluminum foams (Bastawros and Evans, Proc. Symp. Application of Heat Transfer in Microelectronics Packaging. IMECE, Dallas, TX, 1997).

Transition from squeezing to dripping in a microfluidic T-shaped junction

We describe the results of a numerical investigation of the dynamics of breakup of streams of immiscible fluids in the confined geometry of a microfluidic T-junction. We identify three distinct regimes of formation of droplets: squeezing, dripping and jetting, providing a unifying picture of emulsification processes typical for microfluidic systems. The squeezing mechanism of breakup is particular to microfluidic systems, since the physical confinement of the fluids has pronounced effects on the interfacial dynamics. In this regime, the breakup process is driven chiefly by the buildup of pressure upstream of an emerging droplet and both the dynamics of breakup and the scaling of the sizes of droplets are influenced only very weakly by the value of the capillary number. The dripping regime, while apparently homologous to the unbounded case, is also significantly influenced by the constrained geometry; these effects modify the scaling law for the size of the droplets derived from the balance of interfacial and viscous stresses. Finally, the jetting regime sets in only at very high flow rates, or with low interfacial tension, i.e. higher values of the capillary number, similar to the unbounded case.

Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid

In this paper we examine some general features of the time-dependent dynamics of drop deformation and breakup at low Reynolds numbers. The first aspect of our study is a detailed numerical investigation of the ‘end-pinching’ behaviour reported in a previous experimental study. The numerics illustrate the effects of viscosity ratio and initial drop shape on the relaxation and/or breakup of highly elongated droplets in an otherwise quiescent fluid. In addition, the numerical procedure is used to study the simultaneous development of capillary-wave instabilities at the fluid-fluid interface of a very long, cylindrically shaped droplet with bulbous ends. Initially small disturbances evolve to finite amplitude and produce very regular drop breakup. The formation of satellite droplets, a nonlinear phenomenon, is also observed.

Coalescence of liquid drops

When two drops of radius R touch, surface tension drives an initially singular motion which joins them into a bigger drop with smaller surface area. This motion is always viscously dominated at early times. We focus on the early-time behaviour of the radius rm of the small bridge between the two drops. The flow is driven by a highly curved meniscus of length 2rm and width rm around the bridge, from which we conclude that the leading-order problem is asymptotically equivalent to its two-dimensional counterpart. For the case of inviscid surroundings, an exact two-dimensional solution (Hopper 1990) shows that / r 3 m and rm (t= )l n [t=(R)]; and thus the same is true in three dimensions. We also study the case of coalescence with an external viscous fluid analytically and, for the case of equal viscosities, in detail numerically. A signicantly dierent structure is found in which the outer-fluid forms a toroidal bubble of radius / r 3=2 m at the meniscus and rm (t=4 )l n [t=(R)]. This basic dierence is due to the presence of the outer-fluid viscosity, however small. With lengths scaled by R a full description of the asymptotic flow for rm(t) 1 involves matching of lengthscales of order r 2 m , r 3=2 m , rm, 1 and probably r 7=4 m .

An experimental study of transient effects in the breakup of viscous drops

A computer-controlled four-roll mill is used to examine two transient modes of deformation of a liquid drop: elongation in a steady flow and interfacial-tension-driven motion which occurs after the flow is stopped abruptly. For modest extensions, drop breakup does not occur with the flow on, but may occur following cessation of the flow as a result of deterministic motions associated with internal pressure gradients established by capillary forces. These relaxation and breakup phenomena depend on the initial drop shape and the relative viscosities of the two fluids. Capillary-wave instabilities at the fluid-fluid interface are observed only for highly elongated drops. This study is a natural extension of G. I. Taylors original studies of the deformation and burst of droplets in well-defined flow fields.