Fiber Buckling in Confined Viscous Flows: An Absolute Instability Described by the Linear Ginzburg-Landau Equation.

We explore the dynamics of a flexible fiber transported by a viscous flow in a Hele-Shaw cell of height comparable to the fiber height. We show that long fibers aligned with the flow experience a buckling instability. Competition between viscous and elastic forces leads to the deformation of the fiber into a wavy shape convolved by a Bell-shaped envelope. We characterize the wavelength and phase velocity of the deformation as well as the growth and spreading of the envelope. Our study of the spatiotemporal evolution of the deformation reveals a linear and absolute instability arising from a local mechanism well described by the Ginzburg-Landau equation.

Drops on the Underside of a Slightly Inclined Wet Substrate Move Too Fast to Grow.

Pendant drops suspended on the underside of a wet substrate are known to accumulate fluid from the surrounding thin liquid film, a process that often results in dripping. The growth of such drops is hastened by their ability to translate over an otherwise uniform horizontal film. Here we show that this scenario is surprisingly reversed when the substrate is slightly tilted (≈2°); drops become too fast to grow and shrink over the course of their motion. Combining experiments and numerical simulations, we rationalize the transition between the conventional growth regime and the previously unknown decay regime we report. Using an analytical treatment of the Landau-Levich meniscus that connects the drop to the film, we quantitatively predict the drop dynamics in the two flow regimes and the value of the critical inclination angle where the transition between them occurs.

Automated Analysis of Cerebrospinal Fluid Flow and Motile Cilia Properties in The Central Canal of Zebrafish Embryos.

Circulation of cerebrospinal fluid (CSF) plays an important role during development. In zebrafish embryo, the flow of CSF has been found to be bidirectional in the central canal of the spinal cord. In order to compare conditions and genetic mutants across each other, we recently automated the quantification of the velocity profile of exogenous fluorescent particles in the CSF. We demonstrated that the beating of motile and tilted cilia localized on the ventral side of the central canal was sufficient to generate locally such bidirectionality. Our approach can easily be extended to characterize CSF flow in various genetic mutants. We provide here a detailed protocol and a user interface program to quantify CSF dynamics. In order to interpret potential changes in CSF flow profiles, we provide additional tools to measure the central canal diameter, characterize cilia dynamics and compare experimental data with our theoretical model in order to estimate the impact of cilia in generating a volume force in the central canal. Our approach can also be of use for measuring particle velocity in vivo and modeling flow in diverse biological solutions.

Environmental Control of Amyloid Polymorphism by Modulation of Hydrodynamic Stress.

The phenomenon of amyloid polymorphism is a key feature of protein aggregation. Unravelling this phenomenon is of great significance for understanding the underlying molecular mechanisms associated with neurodegenerative diseases and for the development of amyloid-based functional biomaterials. However, the understanding of the molecular origins and the physicochemical factors modulating amyloid polymorphs remains challenging. Herein, we demonstrate an association between amyloid polymorphism and environmental stress in solution, induced by an air/water interface in motion. Our results reveal that low-stress environments produce heterogeneous amyloid polymorphs, including twisted, helical, and rod-like fibrils, whereas high-stress conditions generate only homogeneous rod-like fibrils. Moreover, high environmental stress converts twisted fibrils into rod-like fibrils both in-pathway and after the completion of mature amyloid formation. These results enrich our understanding of the environmental origin of polymorphism of pathological amyloids and shed light on the potential of environmentally controlled fabrication of homogeneous amyloid biomaterials for biotechnological applications.

Relaxation of capillary-gravity waves due to contact line nonlinearity: A projection method.

We present a physics-inspired mathematical model based on successive linear eigenmode projections to solve the relaxation of small-amplitude and two-dimensional viscous capillary-gravity waves with a phenomenological nonlinear contact line model. We show that each projection eventually induces a rapid loss of total energy in the liquid motion and contributes to its nonlinear damping.

Everything in its right place: controlling the local composition of hydrogels using microfluidic traps.

Many natural materials display locally varying compositions that impart unique mechanical properties to them which are still unmatched by manmade counterparts. Synthetic materials often possess structures that are well-defined on the molecular level, but poorly defined on the microscale. A fundamental difference that leads to this dissimilarity between natural and synthetic materials is their processing. Many natural materials are assembled from compartmentalized reagents that are released in well-defined and spatially confined regions, resulting in locally varying compositions. By contrast, synthetic materials are typically processed in bulk. Inspired by nature, we introduce a drop-based technique that enables the design of microstructured hydrogel sheets possessing tuneable locally varying compositions. This control in the spatial composition and microstructure is achieved with a microfluidic Hele-Shaw cell that possesses traps with varying trapping strengths to selectively immobilize different types of drops. This modular platform is not limited to the fabrication of hydrogels but can be employed for any material that can be processed into drops and solidified within them. It likely opens up new possibilities for the design of structured, load-bearing hydrogels, as well as for the next generation of soft actuators and sensors.

Transition from Exponentially Damped to Finite-Time Arrest Liquid Oscillations Induced by Contact Line Hysteresis.

To clarify the role of wetting properties on the damping of liquid oscillations, we studied the decay of oscillations of liquid columns in a U-shaped tube with controlled surface conditions. In the presence of sliding triple lines, oscillations are strongly and nonlinearly damped, with a finite-time arrest and a dependence on initial amplitude. We reveal that contact angle hysteresis explains and quantifies this solidlike friction.

Origin and role of the cerebrospinal fluid bidirectional flow in the central canal.

Circulation of the cerebrospinal fluid (CSF) contributes to body axis formation and brain development. Here, we investigated the unexplained origins of the CSF flow bidirectionality in the central canal of the spinal cord of 30 hpf zebrafish embryos and its impact on development. Experiments combined with modeling and simulations demonstrate that the CSF flow is generated locally by caudally-polarized motile cilia along the ventral wall of the central canal. The closed geometry of the canal imposes the average flow rate to be null, explaining the reported bidirectionality. We also demonstrate that at this early stage, motile cilia ensure the proper formation of the central canal. Furthermore, we demonstrate that the bidirectional flow accelerates the transport of particles in the CSF via a coupled convective-diffusive transport process. Our study demonstrates that cilia activity combined with muscle contractions sustain the long-range transport of extracellular lipidic particles, enabling embryonic growth.

Film thickness distribution in gravity-driven pancake-shaped droplets rising in a Hele-Shaw cell.

We study here experimentally, numerically and using a lubrication approach, the shape, velocity and lubrication film thickness distribution of a droplet rising in a vertical Hele-Shaw cell. The droplet is surrounded by a stationary immiscible fluid and moves purely due to buoyancy. A low density difference between the two media helps to operate in a regime with capillary number Ca lying between 0.03 and 0.35, where Ca =µo Ud /γ is built with the surrounding oil viscosity γ0 , the droplet velocity Ud and surface tension γ. The experimental data show that in this regime the droplet velocity is not influenced by the thickness of the thin lubricating film and the dynamic meniscus. For iso-viscous cases, experimental and three-dimensional numerical results of the film thickness distribution agree well with each other. The mean film thickness is well captured by the Aussillous & Quéré (Phys. Fluids, vol. 12 (10), 2000, pp. 2367-2371) model with fitting parameters. The droplet also exhibits the 'catamaran' shape that has been identified experimentally for a pressure-driven counterpart (Huerre et al., Phys. Rev. Lett., vol. 115 (6), 2015, 064501). This pattern has been rationalized using a two-dimensional lubrication equation. In particular, we show that this peculiar film thickness distribution is intrinsically related to the anisotropy of the fluxes induced by the droplet's motion.

Inertial manipulation of bubbles in rectangular microfluidic channels.

Inertial microfluidics is an active field of research that deals with crossflow positioning of the suspended entities in microflows. Until now, the majority of the studies have focused on the behavior of rigid particles in order to provide guidelines for microfluidic applications such as sorting and filtering. Deformable entities such as bubbles and droplets are considered in fewer studies despite their importance in multiphase microflows. In this paper, we show that the trajectory of bubbles flowing in rectangular and square microchannels can be controlled by tuning the balance of forces acting on them. A T-junction geometry is employed to introduce bubbles into a microchannel and analyze their lateral equilibrium position in a range of Reynolds (1 < Re < 40) and capillary numbers (0.1 < Ca < 1). We find that the Reynolds number (Re), the capillary number (Ca), the diameter of the bubble (D[combining macron]), and the aspect ratio of the channel are the influential parameters in this phenomenon. For instance, at high Re, the flow pushes the bubble towards the wall while large Ca or D[combining macron] moves the bubble towards the center. Moreover, in the shallow channels, having aspect ratios higher than one, the bubble moves towards the narrower sidewalls. One important outcome of this study is that the equilibrium position of bubbles in rectangular channels is different from that of solid particles. The experimental observations are in good agreement with the performed numerical simulations and provide insights into the dynamics of bubbles in laminar flows which can be utilized in the design of flow based multiphase flow reactors.

Bifurcation Dynamics of a Particle-Encapsulating Droplet in Shear Flow.

To understand the behavior of composite fluid particles such as nucleated cells and double emulsions in flow, we study a finite-size particle encapsulated in a deforming droplet under shear flow as a model system. In addition to its concentric particle-droplet configuration, we numerically explore other eccentric and time-periodic equilibrium solutions, which emerge spontaneously via supercritical pitchfork and Hopf bifurcations. We present the loci of these solutions around the codimension-two point. We adopt a dynamic system approach to model and characterize the coupled behavior of the two bifurcations. By exploring the flow fields and hydrodynamic forces in detail, we identify the role of hydrodynamic particle-droplet interaction which gives rise to these bifurcations.

Swimming with a cage: low-Reynolds-number locomotion inside a droplet.

Inspired by recent experiments using synthetic microswimmers to manipulate droplets, we investigate the low-Reynolds-number locomotion of a model swimmer (a spherical squirmer) encapsulated inside a droplet of a comparable size in another viscous fluid. Meditated solely by hydrodynamic interactions, the encaged swimmer is seen to be able to propel the droplet, and in some situations both remain in a stable co-swimming state. The problem is tackled using both an exact analytical theory and a numerical implementation based on a boundary element method, with a particular focus on the kinematics of the co-moving swimmer and the droplet in a concentric configuration, and we obtain excellent quantitative agreement between the two. The droplet always moves slower than a swimmer which uses purely tangential surface actuation but when it uses a particular combination of tangential and normal actuations, the squirmer and droplet are able to attain the same velocity and stay concentric for all times. We next employ numerical simulations to examine the stability of their concentric co-movement, and highlight several stability scenarios depending on the particular gait adopted by the swimmer. Furthermore, we show that the droplet reverses the nature of the far-field flow induced by the swimmer: a droplet cage turns a pusher swimmer into a puller, and vice versa. Our work sheds light on the potential development of droplets as self-contained carriers of both chemical content and self-propelled devices for controllable and precise drug deliveries.

Fluid dynamic instabilities: theory and application to pattern forming in complex media.

In this review article, we exemplify the use of stability analysis tools to rationalize pattern formation in complex media. Specifically, we focus on fluid flows, and show how the destabilization of their interface sets the blueprint of the patterns they eventually form. We review the potential use and limitations of the theoretical methods at the end, in terms of their applications to practical settings, e.g. as guidelines to design and fabricate structures while harnessing instabilities.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications'.

Ultralow Interfacial Tension Measurement through Jetting/Dripping Transition.

In this paper, we present a dynamic microfluidic tensiometer able to perform measurements over more than four decades and which is suitable for high throughput experimentations. This tensiometer is able to withstand hard conditions such as high pressure, high temperature, high salinity, and crude oil. It is made of two coaxial capillaries in which two immiscible fluids are injected. Depending on the flow rate of each phase, either droplets or jetting will be obtained. The transition between these two regimes relies on the Rayleigh-Plateau instability. This transition can be theoretically computed thanks to a linear analysis based on the convective and absolute instabilities theory. From this model, the interfacial tension between the two phases can be calculated.

Vortex-Breakdown-Induced Particle Capture in Branching Junctions.

We show experimentally that a flow-induced, Reynolds number-dependent particle-capture mechanism in branching junctions can be enhanced or eliminated by varying the junction angle. In addition, numerical simulations are used to show that the features responsible for this capture have the signatures of classical vortex breakdown, including an approach flow aligned with the vortex axis and a pocket of subcriticality. We show how these recirculation regions originate and evolve and suggest a physical mechanism for their formation. Furthermore, comparing experiments and numerical simulations, the presence of vortex breakdown is found to be an excellent predictor of particle capture. These results inform the design of systems in which suspended particle accumulation can be eliminated or maximized.

Self-consistent mean flow description of the nonlinear saturation of the vortex shedding in the cylinder wake.

The Bénard-von Kármán vortex shedding instability in the wake of a cylinder is perhaps the best known example of a supercritical Hopf bifurcation in fluid dynamics. However, a simplified physical description that accurately accounts for the saturation amplitude of the instability is still missing. Here, we present a simple self-consistent model that provides a clear description of the saturation mechanism and quantitatively predicts the saturated amplitude and flow fields. The model is formally constructed by a set of coupled equations governing the mean flow together with its most unstable eigenmode with finite size. The saturation amplitude is determined by requiring the mean flow to be neutrally stable. Without requiring any input from numerical or experimental data, the resolution of the model provides a good prediction of the amplitude and frequency of the vortex shedding as well as the spatial structure of the mean flow and the Reynolds stress.

Generic path for droplet relaxation in microfluidic channels.

In two-phase microfluidics, droplets often undergo deformations that drive them away from their circular equilibrium shape. Herein we concentrate on the relaxation of symmetrical deformations to a circle driven by surface tension effects, which are predominant at the micrometer scales. Working in a Hele-Shaw cell, we report a generic pathway for these types of relaxations. We simulate numerically the interface shape evolution and investigate it using linear stability analysis. Finally, we characterize this universal aspect of relaxation using a purely geometrical model that is tested in experiments.

Microchannel deformations due to solvent-induced PDMS swelling.

The compatibility of polydimethylsiloxane (PDMS) channels with certain solvents is a well known problem of soft lithography techniques, in particular when it leads to the swelling of the PDMS blocks. However, little is known about the modification of microchannel geometries when they are subjected to swelling solvents. Here, we experimentally measure the deformations of the roof of PDMS microchannels due to such solvents. The dynamics of impregnation of the solvents in PDMS and its relation to volume dilation are first addressed in a model experiment, allowing the precise measurement of the diffusion coefficients of oils in PDMS. When Hexadecane, a swelling solvent, fills a microchannel 1 mm in width and 50 µm in height, we measure that the channel roof bends inwards and takes a parabolic shape with a maximum deformation of 7 µm. The amplitude of the subsidence is found to increase with the channel width, reaching 28 µm for a 2 mm wide test section. On the other hand, perfluorinated oils do not swell the PDMS and the microchannel geometry is not affected by the presence of perfluorodecalin. Finally, we observe that the trajectories of droplets flowing in this microchannel are strongly affected by the deformations: drops carried by swelling oils are pushed towards the edges of the channel while those carried by non-swelling oils remain in the channel center.

Dynamics of microfluidic droplets.

This critical review discusses the current understanding of the formation, transport, and merging of drops in microfluidics. We focus on the physical ingredients which determine the flow of drops in microchannels and recall classical results of fluid dynamics which help explain the observed behaviour. We begin by introducing the main physical ingredients that differentiate droplet microfluidics from single-phase microfluidics, namely the modifications to the flow and pressure fields that are introduced by the presence of interfacial tension. Then three practical aspects are studied in detail: (i) The formation of drops and the dominant interactions depending on the geometry in which they are formed. (ii) The transport of drops, namely the evaluation of drop velocity, the pressure-velocity relationships, and the flow field induced by the presence of the drop. (iii) The fusion of two drops, including different methods of bridging the liquid film between them which enables their merging.

Laser-induced force on a microfluidic drop: origin and magnitude.

The localized heating produced by a tightly focused infrared laser leads to surface tension gradients at the interface of microfluidic drops covered with surfactants, resulting in a net force on the drop whose origin and magnitude are the focus of this paper. First, by colocalization of the surfactant micelles with a fluorescent dye, we demonstrate that the heating alters their spatial distribution, driving the interface out of equilibrium. This soluto-capillary effect opposes and overcomes the purely thermal dependence of the surface tension, leading to reversed interfacial flows. As the surface of the drop is set into motion, recirculation rolls are created outside and inside the drop, which we measure using time-resolved micro-Particle Image Velocimetry. Second, the net force produced on the drop is measured using an original microfluidic design. For a drop 300 microm-long and 100 microm-wide, we obtain a force of 180 nN for a laser power of 100 mW. This micro-dynanometer further shows that the magnitude of the heating, which is determined by the laser power and its absorption in the water, sets the magnitude of the net force on the drop. On the other hand, the dynamics of the force generation is limited by the time scale for heating, which has independently been measured to be tau(Theta) = 4 ms. This time scale sets the maximum velocity that the drops can have and still be blocked, by requiring that the interface passes the laser spot in a time longer than tau(Theta). The maximum velocity is measured at U(max) = 0.7 mm/s for our geometric conditions. Finally, a scaling model is derived that describes the blocking force in a confined geometry as the result of the viscous stresses produced by the shear between the drop and the lateral walls.