Swelling-induced patterning in soft microchannels.

We study the effect of inflation on the swelling-induced wrinkling of thin elastic membranes in a set-up that is commonly used to create microchannels in lab-on-chip applications. Using a combination of experiments and associated numerical simulations, we demonstrate that the out-of-plane deformation of the inflated membrane and the resulting anisotropic stress lead to two distinct instabilities as the swelling progresses. The membrane first develops small-amplitude wrinkles that retain the cross-channel symmetry. Their wavelength depends on the pressure and is set in a process similar to the axisymmetric buckling of pressurised, uni-axially compressed cylindrical shells. As swelling increases, the membrane undergoes a secondary instability during which the wrinkles coarsen into large-amplitude folds whose morphology can be controlled by the degree of pre-inflation. We elucidate the fundamental mechanisms responsible for this behaviour and explain how inflation can be used as a control mechanism in the manufacture of microchannels.

Dielectric-free electrowetting on graphene.

Electrowetting is a simple way to induce the spreading and retraction of electrolyte droplets. This method is widely used in "device" applications, where a dielectric layer is applied between the electrolyte and the conducting substrate. Recent work, including contributions from our own laboratory, have shown that reversible electrowetting can be achieved directly on conductors. We have shown that graphite surfaces, in particular when combined with highly concentrated electrolyte solutions, show a strong wetting effect. The process is driven by the interactions between the electrolyte ions and the surface, hence models of double-layer capacitance are able to explain changes in the equilibrium contact angles. Herein, we extend the approach to the investigation of electrowetting on graphene samples of varying thickness, prepared by chemical vapor deposition. We show that the use of highly concentrated aqueous electrolytes induces a clear yet subtle electrowetting response due to the adsorption of ions and the suppression of the negative effect introduced by the surface impurities accumulating during the transfer process. The latter have been previously reported to fully hinder electrowetting at lower electrolyte concentrations. An amplified wetting response is recorded in the presence of strongly adsorbed/intercalated anions in both aqueous and non-aqueous electrolytes. The phenomenon is interpreted based on the anion-graphene interactions and their influence on the energetics of the interface. By monitoring the dynamics of wetting, an irreversible behaviour is identified in all cases as a consequence of the irreversibility of anion adsorption and/or intercalation. Finally, the effect of the underlying reactions on the timescales of wetting is also examined.

Robust fabrication of ultra-soft tunable PDMS microcapsules as a biomimetic model for red blood cells.

Microcapsules with liquid cores encapsulated by thin membranes have many applications in science, medicine and industry. In this paper, we design a suspension of microcapsules which can flow and deform like red blood cells (RBCs), as a valuable tool to investigate microhaemodynamics. A reconfigurable and easy-to-assemble 3D nested glass capillary device is used to robustly fabricate water-oil-water double emulsions which are then converted into spherical microcapsules with hyperelastic membranes by cross-linking the polydimethylsiloxane (PDMS) layer coating the droplets. The resulting capsules are monodisperse to within 1% and can be made in a wide range of size and membrane thickness. We use osmosis to deflate by 36% initially spherical capsules of diameter 350 µm and a membrane thickness of 4% of their radius. Hence, we can match the reduced volume of RBCs but not their biconcave shape, since our capsules adopt a buckled shape. We compare the propagation of initially spherical and deflated capsules under constant volumetric flow in cylindrical capillaries of different confinements. We find that only deflated capsules deform broadly like RBCs over a similar range of capillary numbers Ca - the ratio of viscous to elastic forces. Similarly to the RBCs, the microcapsules transition from a symmetric 'parachute' to an asymmetric 'slipper'-like shape as Ca increases within the physiological range, demonstrating intriguing confinement-dependent dynamics. In addition to biomimetic RBC properties, high-throughput fabrication of tunable ultra-soft microcapsules could be further functionalized and find applications in other areas of science and engineering.

Anion Intercalation into Graphite Drives Surface Wetting.

The unique layered structure of graphite with its tunable interlayer distance establishes almost ideal conditions for the accommodation of ions into its structure. The smooth and chemically inert nature of the graphite surface also means that it is an ideal substrate for electrowetting. Here, we combine these two unique properties of this material by demonstrating the significant effect of anion intercalation on the electrowetting response of graphitic surfaces in contact with concentrated aqueous and organic electrolytes as well as ionic liquids. The structural changes during intercalation/deintercalation were probed using in situ Raman spectroscopy, and the results were used to provide insights into the influence of intercalation staging on the rate and reversibility of electrowetting. We show, by tuning the size of the intercalant and the stage of intercalation, that a fully reversible electrowetting response can be attained. The approach is extended to the development of biphasic (oil/water) systems that exhibit a fully reproducible electrowetting response with a near-zero voltage threshold and unprecedented contact angle variations of more than 120° within a potential window of less than 2 V.

The unpredictable nature of bubble evolution.

Unpredictable dynamics arising from a sensitivity to initial conditions is commonly associated with chaos. We demonstrate how similar unpredictability manifests in a nonlinear system that possesses a large number of long-term outcomes, namely the propagation of an air bubble within a viscous fluid-filled channel. The system under investigation supports various stable states of single-bubble propagation. In addition, bubbles can readily break up during their propagation. Upon subjecting steadily-propagating bubbles to finite-amplitude perturbations in the form of localised channel constrictions, we identify localised regions of the driving flow rate for which the resulting evolutions are unpredictable. Visibly-indistinguishable bubbles are observed to evolve towards a multitude of long-term outcomes, including each of the stable states available to the initial bubble and various states of permanently-changed bubble topology. By combining high-precision experimental results with simulations of a depth-averaged lubrication model of the system, we determine that this behaviour is driven by a sensitive dependence on initial conditions within the vicinity of an unstable periodic orbit.

Taming Electrowetting Using Highly Concentrated Aqueous Solutions.

Wetting of carbon surfaces is one of the most widespread, yet poorly understood, physical phenomena. Control over wetting properties underpins the operation of aqueous energy-storage devices and carbon-based filtration systems. Electrowetting, the variation in the contact angle with an applied potential, is the most straightforward way of introducing control over wetting. Here, we study electrowetting directly on graphitic surfaces with the use of aqueous electrolytes to show that reversible control of wetting can be achieved and quantitatively understood using models of the interfacial capacitance. We manifest that the use of highly concentrated aqueous electrolytes induces a fully symmetric and reversible wetting behavior without degradation of the substrate within the unprecedented potential window of 2.8 V. We demonstrate where the classical "Young-Lippmann" models apply, and break down, and discuss reasons for the latter, establishing relations among the applied bias, the electrolyte concentration, and the resultant contact angle. The approach is extended to electrowetting at the liquid|liquid interface, where a concentrated aqueous electrolyte drives reversibly the electrowetting response of an insulating organic phase with a significantly decreased potential threshold. In summary, this study highlights the beneficial effect of highly concentrated aqueous electrolytes on the electrowettability of carbon surfaces, being directly related to the performance of carbon-based aqueous energy-storage systems and electronic and microfluidic devices.

Red blood cell dynamics in extravascular biological tissues modelled as canonical disordered porous media.

The dynamics of blood flow in the smallest vessels and passages of the human body, where the cellular character of blood becomes prominent, plays a dominant role in the transport and exchange of solutes. Recent studies have revealed that the microhaemodynamics of a vascular network is underpinned by its interconnected structure, and certain structural alterations such as capillary dilation and blockage can substantially change blood flow patterns. However, for extravascular media with disordered microstructure (e.g. the porous intervillous space in the placenta), it remains unclear how the medium's structure affects the haemodynamics. Here, we simulate cellular blood flow in simple models of canonical porous media representative of extravascular biological tissue, with corroborative microfluidic experiments performed for validation purposes. For the media considered here, we observe three main effects: first, the relative apparent viscosity of blood increases with the structural disorder of the medium; second, the presence of red blood cells (RBCs) dynamically alters the flow distribution in the medium; third, symmetry breaking introduced by moderate structural disorder can promote more homogeneous distribution of RBCs. Our findings contribute to a better understanding of the cell-scale haemodynamics that mediates the relationship linking the function of certain biological tissues to their microstructure.

Sorting of capsules according to their stiffness: from principle to application.

We assess experimentally the ability of a simple flow-based sorting device, recently proposed numerically by [Zhu et al., Soft Matter, 2014, 10, 7705-7711], to separate capsules according to their stiffness. The device consists of a single pillar with a half-cylinder cross-section which partially obstructs a flow channel so that initially centred, propagating capsules deform and circumvent the obstacle into an expanding channel (or diffuser). We perform experiments with millimetric capsules of fixed size which indicate that the deviation of the capsule in the diffuser varies monotonically with a capillary number - the ratio of viscous to elastic stresses - where the elastic stresses are measured independently to include the effects of pre-inflation, membrane thickness and material properties. We find that soft capsules with resistance to deformation differing by a factor of 1.5 can be reliably separated in the diffuser but that experimental variability increases significantly with capsule stiffness. We extend the study to populations of microcapsules with size polydispersity. We find that the combined effects of increasing capsule deformability and relative constriction of the device with increasing capsule size enable the tuning of the imposed flow so that capsules can be separated based on their shear modulus but irrespectively of their size.

Flow-induced choking of a compliant Hele-Shaw cell.

After centuries of striving for structural rigidity, engineers and scientists alike are increasingly looking to harness the deformation, buckling, and failure of soft materials for functionality. In fluidic devices, soft deformable components that respond to the flow have the advantage of being passive; they do not require external actuation. Harnessing flow-induced deformation for passive functionality provides a means of developing flow analogs of electronic circuit components such as fluidic diodes and capacitors. The electronic component that has so far been overlooked in the microfluidics literature-the fuse-is a passive safety device that relies on a controlled failure mechanism (melting) to protect a circuit from overcurrent. Here, we describe how a compliant Hele-Shaw cell behaves in a manner analogous to the electrical fuse; above a critical flux, the flow-induced deformation of the cell blocks the outflow, interrupting (choking) the flow. In particular, the pressure distribution within the fluid applies a spatially variant normal force to the soft boundary, which causes nonuniform deformation. As a consequence of lateral confinement and incompressibility of the soft material, this flow-induced elastic deformation manifests as bulging near the cell outflow; bulges that come into contact with the rigid cell roof interrupt the flow. We identify two nondimensional parameters that govern the central deflection and the choking of the cell, respectively. This study therefore provides the mechanical foundations for engineering passive-flow limiters into fluidic devices.

The influence of invariant solutions on the transient behaviour of an air bubble in a Hele-Shaw channel.

We hypothesize that dynamical systems concepts used to study the transition to turbulence in shear flows are applicable to other transition phenomena in fluid mechanics. In this paper, we consider a finite air bubble that propagates within a Hele-Shaw channel containing a depth-perturbation. Recent experiments revealed that the bubble shape becomes more complex, quantified by an increasing number of transient bubble tips, with increasing flow rate. Eventually, the bubble changes topology, breaking into multiple distinct entities with non-trivial dynamics. We demonstrate that qualitatively similar behaviour to the experiments is exhibited by a previously established, depth-averaged mathematical model and arises from the model's intricate solution structure. For the bubble volumes studied, a stable asymmetric bubble exists for all flow rates of interest, while a second stable solution branch develops above a critical flow rate and transitions between symmetric and asymmetric shapes. The region of bistability is bounded by two Hopf bifurcations on the second branch. By developing a method for a numerical weakly nonlinear stability analysis we show that unstable periodic orbits (UPOs) emanate from the first Hopf bifurcation. Moreover, as has been found in shear flows, the UPOs are edge states that influence the transient behaviour of the system.

Sequential deposition of microdroplets on patterned surfaces.

We use a combination of experiments and numerical modelling to investigate the influence of physico-chemical-patterned substrates on the spreading of fluid deposited as a partially overlapping sequence of droplets via inkjet printing. Our investigation is motivated by the manufacture of polymeric organic light-emitting-diode displays, where the substrate is textured with a regular array of shallow recessed regions (pixels) that are highly wetting compared to the remainder of the substrate. We examine the roles of topography and wettability patterning separately and in combination. On a substrate with uniform wettability, we find that the presence of bounding side walls enhances the local spreading and facilitates fluid coverage of the entire recessed region, but containment within the pixel is not guaranteed. In contrast, wettability patterning alone leads to robust containment of the fluid within the wetting region, but fluid coverage is reduced in the absence of side walls. Our theoretical calculations use a simplified numerical model of fluid redistribution via purely capillary effects, augmented by a Cox-Voinov spreading law. The neglect of fluid viscosity in this model means that, after an initial period of agreement, the predicted evolution is faster than in the experiments. Nonetheless, the simplified model achieves excellent predictions both for the liquid morphologies and for the conditions required for successful pixel filling on substrates with topographical and wettability variations.

Bubble propagation on a rail: a concept for sorting bubbles by size.

We demonstrate experimentally that the introduction of a rail, a small height constriction, within the cross-section of a rectangular channel could be used as a robust passive sorting device in two-phase fluid flows. Single air bubbles carried within silicone oil are generally transported on one side of the rail. However, for flow rates marginally larger than a critical value, a narrow band of bubble sizes can propagate (stably) over the rail, while bubbles of other sizes segregate to the side of the rail. The width of this band of bubble sizes increases with flow rate and the size of the most stable bubble can be tuned by varying the rail width. We present a complementary theoretical analysis based on a depth-averaged theory, which is in qualitative agreement with the experiments. The theoretical study reveals that the mechanism relies on a non-trivial interaction between capillary and viscous forces that is fully dynamic, rather than being a simple modification of capillary static solutions.

Ultra-low voltage electrowetting using graphite surfaces.

The control of wetting behaviour underpins a variety of important applications from lubrication to microdroplet manipulation. Electrowetting is a powerful method to achieve external wetting control, by exploiting the potential-dependence of the liquid contact angle with respect to a solid substrate. Addition of a dielectric film to the surface of the substrate, which insulates the electrode from the liquid thereby suppressing electrolysis, has led to technological advances such as variable focal-length liquid lenses, electronic paper and the actuation of droplets in lab-on-a-chip devices. The presence of the dielectric, however, necessitates the use of large bias voltages (frequently in the 10-100 V range). Here we describe a simple, dielectric-free approach to electrowetting using the basal plane of graphite as the conducting substrate: unprecedented changes in contact angle for ultra-low voltages are seen below the electrolysis threshold (50° with 1 V for a droplet in air, and 100° with 1.5 V for a droplet immersed in hexadecane), which are shown to be reproducible, stable over 100 s of cycles and free of hysteresis. Our results dispel conventional wisdom that reversible, hysteresis-free electrowetting can only be achieved on solid substrates with the use of a dielectric. This work paves the way for the development of a new generation of efficient electrowetting devices using advanced materials such as graphene and monolayer MoS2.

Ribbon curling via stress relaxation in thin polymer films.

The procedure of curling a ribbon by running it over a sharp blade is commonly used when wrapping presents. Despite its ubiquity, a quantitative explanation of this everyday phenomenon is still lacking. We address this using experiment and theory, examining the dependence of ribbon curvature on blade curvature, the longitudinal load imposed on the ribbon, and the speed of pulling. Experiments in which a ribbon is drawn steadily over a blade under a fixed load show that the ribbon curvature is generated over a restricted range of loads, the curvature/load relationship can be nonmonotonic, and faster pulling (under a constant imposed load) results in less tightly curled ribbons. We develop a theoretical model that captures these features, building on the concept that the ribbon under the imposed deformation undergoes differential plastic stretching across its thickness, resulting in a permanently curved shape. The model identifies factors that optimize curling and clarifies the physical mechanisms underlying the ribbon's nonlinear response to an apparently simple deformation.

Fluctuations in viscous fingering.

Our experiments on viscous (Saffman-Taylor) fingering in Hele-Shaw channels reveal finger width fluctuations that were not observed in previous experiments, which had lower aspect ratios and higher capillary numbers Ca. These fluctuations intermittently narrow the finger from its expected width. The magnitude of these fluctuations is described by a power law, Ca(-0.64), which holds for all aspect ratios studied up to the onset of tip instabilities. Further, for large aspect ratios, the mean finger width exhibits a maximum as Ca is decreased instead of the predicted monotonic increase.