The displacement of one fluid by another is one of the most common processes involving interfacial instabilities. It is universally accepted that, in a uniform medium, flow displacement is unstable when a low-viscosity fluid invades a fluid of higher viscosity: the classical viscous fingering instability 1-4 . Consequently, once fluid properties are specified, opportunities for control become very limited. However, real systems where displacement instabilities occur, such as porous structures 5,6 , lung airways 7,8 and printing devices 9-11 , are rarely uniform. We find that the simplest heterogeneity-a gradient in the flow passage 12-15 -can lead to fundamentally different displacement behaviours. We use this finding to either inhibit or trigger an instability and, hence, to devise a strategy to manipulate instabilities in fluid-fluid systems. The control setting we identify has a wide spectrum of applications ranging from small-scale technologies such as microfluidics to largescale operations such as enhanced oil recovery.Interfacial instabilities impact, to give a few examples, the dendritic shape of snow flakes 16 , early failure in zinc alkaline batteries 17 , breath sounds caused by surfactant deficiency in lungs 7 and the protection of the stomach from its own gastric acids 18 . Morphological patterns and periodic structures are often the form in which interfacial instabilities are manifested. For instance, patterns are detected on the surface of metal casts due to shrinkage on solidification of the metal 19,20 , and the wavy interface of lubrication oil confined in journal bearings and between printing rollers is a signature of the so-called printer's instability 9-11 . In most cases, interfacial instabilities hinder the operation of processes and limit their efficiency. Moreover, instabilities at the interface of two distinct fluids remain a major challenge for enhanced oil recovery processes such as water flooding 21 . On the other hand, these instabilities can be beneficial to chromatographic separation and can improve mixing in non-turbulent systems and small-scale devices 22 . The fact that depending on the application either a stable or an unstable interface is desirable makes the ability to control interfacial instabilities 23,24 essential in design and technology.In the early twentieth century, petroleum and mining engineers noticed that water does not displace oil uniformly 25 . Rather, water penetrates through oil, a phenomenon now known as fingering owing to the finger-like interfacial patterns. The stability of the interface between the invading and the displaced fluids was first analysed in the 1950s (refs 1,5,26). Most notably, Saffman and Taylor found 1 that when a fluid of low viscosity invades a fluid of higher viscosity in the narrow space confined between two parallel plates (a Hele-Shaw cell), the interface is always unstable. The instability, which occurs at any flow speed, takes the form of propagating narrow fingers of the low-viscosity fluid, leaving behind the more viscous fluid. ...

We present a theoretical study of a variant of the classical viscous fingering instability, which occurs when a high viscosity fluid is displaced by a low viscosity fluid in a Hele-Shaw cell. In our system, the Hele-Shaw cell is tapered in the direction of fluid displacement. We consider two tapered Hele-Shaw geometries (rectilinear and radial), which have a constant depth gradient in the flow direction. We find that the presence of a depth gradient can alter the stability of the interface offering opportunities to control and tune fingering instabilities. In particular, the stability of the interface is now determined by both the viscosity contrast of the fluids and the ratio of the depth gradient to the capillary number of the system. We also demonstrate several applications of our analysis, including the inhibition of viscous fingering by controlling the injection flow rate in a radially tapered Hele-Shaw cell.

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The incomplete growth of nanowires that are synthesized by template-assisted electrodeposition presents a major challenge for nanowire-based devices targeting energy and electronic applications. In template-assisted electrodeposition, the growth of nanowires in the pores of the template is complex and unstable. Here we show theoretically and experimentally that the dynamics of this process is diffusion-limited, which results in a morphological instability driven by a race among nanowires. Moreover, we use our findings to devise a method to control the growth instability. By introducing a temperature gradient across the porous template, we manipulate ion diffusion in the pores, so that we can reduce the growth instability. This strategy significantly increases the length of nanowires. In addition to shedding light on a key nanotechnology, our results may provide fundamental insights into a variety of interfacial growth processes in materials science such as crystal growth and tissue growth in scaffolds.

The integration of Microbial Fuel Cells (MFCs) in a microfluidic geometry can significantly enhance the power density of these cells, which would have more active bacteria per unit volume. Moreover, microfluidic MFCs can be operated in a continuous mode as opposed to the traditional batch-fed mode. Here we investigate the effect of fluid flow on the performance of microfluidic MFCs. The growth and the structure of the bacterial biofilm depend to a large extent on the shear stress of the flow. We report the existence of a range of flow rates for which MFCs can achieve maximum voltage output. When operated under these optimal conditions, the power density of our microfluidic MFC is about 15 times that of a similar-size batch MFC. Furthermore, this optimum suggests a correlation between the behaviour of bacteria and fluid flow.