An unrecognized inertial force induced by flow curvature in microfluidics.

Modern inertial microfluidics routinely employs oscillatory flows around localized solid features or microbubbles for controlled, specific manipulation of particles, droplets, and cells. It is shown that theories of inertial effects that have been state of the art for decades miss major contributions and strongly underestimate forces on small suspended objects in a range of practically relevant conditions. An analytical approach is presented that derives a complete set of inertial forces and quantifies them in closed form as easy-to-use equations of motion, spanning the entire range from viscous to inviscid flows. The theory predicts additional attractive contributions toward oscillating boundaries, even for density-matched particles, a previously unexplained experimental observation. The accuracy of the theory is demonstrated against full-scale, three-dimensional direct numerical simulations throughout its range.

Rotation-translation coupling of soft objects in lubricated contact.

We study the coupling between rotation and translation of a submerged cylinder in lubricated contact with a soft elastic substrate. Using numerical solutions and asymptotic theory, we analyze the elastohydrodynamic problem over the entire range of substrate deformations relative to the thickness of the intervening fluid film. We find a strong coupling between the rotation and translation of the cylinder when the surface deformation of the substrate is comparable to the thickness of the lubricating fluid layer. In the limit of large deformations, we show that the bodies are in near-Hertzian contact and cylinder rolls without slip, reminiscent of dry frictional contact. When the surface deformation is small relative to the separation between the surfaces, the coupling persists but is weaker, and the rotation rate scales with the translation speed to the one-third power. We then show how the external application of a torque modifies these behaviors by generating different combinations of rotational and translational motions, including back-spinning and top-spinning states. We demonstrate that these behaviors are robust regardless of whether the elastic substrate is thick or thin relative to the length scales of the flow.

Self-sustained three-dimensional beating of a model eukaryotic flagellum.

Flagella and cilia are common features of a wide variety of biological cells and play important roles in locomotion and feeding at the microscale. The beating of flagella is controlled by molecular motors that exert forces along the length of the flagellum and are regulated by a feedback mechanism coupled to the flagella deformation. We develop a three-dimensional (3D) flagellum beating model based on sliding-controlled motor feedback, accounting for both bending and twist, as well as differential bending resistances along and orthogonal to the major bending plane of the flagellum. We show that beating is generated and sustained spontaneously for a sufficiently high motor activity through an instability mechanism. Isotropic bending rigidities in the flagellum lead to 3D helical beating patterns. By contrast, anisotropic flagella present a rich variety of wave-like beating dynamics, including both 3D beating patterns as well as planar beating patterns. We show that the ability to generate nearly planar beating despite the 3D beating machinery requires only a modest degree of bending anisotropy, and is a feature observed in many eukaryotic flagella such as mammalian spermatozoa.

Electrostatic wrapping of a microfiber around a curved particle.

The dynamics of the wrapping of a charged flexible microfiber around an oppositely charged curved particle immersed in a viscous fluid is investigated. We observe that the wrapping behavior varies with the radius and Young's modulus of the fiber, the radius of the particle, and the ionic strength of the surrounding solution. We find that wrapping is primarily a function of the favorable interaction energy due to electrostatics and the unfavorable deformation energy needed to conform the fiber to the curvature of the particle. We perform an energy balance to predict the critical particle radius for wrapping, finding reasonably good agreement with experimental observations. In addition, we use mathematical modeling and observations of the deflected shape of the free end of the fiber during wrapping to extract a measurement of the Young's modulus of the fiber. We evaluate the accuracy and potential limitations of this in situ measurement when compared to independent mechanical tests.

CO2-Driven diffusiophoresis for maintaining a bacteria-free surface.

Dissolution and dissociation of CO2 in an aqueous phase induce diffusiophoretic motion of suspended particles with a nonzero surface charge. We report CO2-driven diffusiophoresis of colloidal particles and bacterial cells in a circular Hele-Shaw geometry. Combining experiments and model calculations, we identify the characteristic length and time scales of CO2-driven diffusiophoresis in relation to system dimensions and CO2 diffusivity. The motion of colloidal particles driven by a CO2 gradient is characterized by measuring the average velocities of particles as a function of distance from the CO2 sources. In the same geometrical configurations, we demonstrate that the directional migration of wild-type V. cholerae and a mutant lacking flagella, as well as S. aureus and P. aeruginosa, near a dissolving CO2 source is diffusiophoresis, not chemotaxis. Such a directional response of the cells to CO2 (or an ion) concentration gradient shows that diffusiophoresis of bacteria is achieved independent of cell shape, motility and the Gram stain (cell surface structure). Long-time experiments suggest potential applications for bacterial diffusiophoresis to cleaning systems or anti-biofouling surfaces, by reducing the population of the cells near CO2 sources.

Foam-driven fracture.

In hydraulic fracturing, water is injected at high pressure to crack shale formations. More sustainable techniques use aqueous foams as injection fluids to reduce the water use and wastewater treatment of conventional hydrofractures. However, the physical mechanism of foam fracturing remains poorly understood, and this lack of understanding extends to other applications of compressible foams such as fire-fighting, energy storage, and enhanced oil recovery. Here we show that the injection of foam is much different from the injection of incompressible fluids and results in striking dynamics of fracture propagation that are tied to the compressibility of the foam. An understanding of bubble-scale dynamics is used to develop a model for macroscopic, compressible flow of the foam, from which a scaling law for the fracture length as a function of time is identified and exhibits excellent agreement with our experimental results.

Silver-Based Self-Powered pH-Sensitive Pump and Sensor.

Nonmechanical nano/microscale pumps that provide precise control over flow rate without the aid of an external power source and that are capable of turning on in response to specific analytes in solution are needed for the next generation of smart micro- and nanoscale devices. Herein, a self-powered chemically driven silver micropump is reported that is based on the two-step catalytic decomposition of hydrogen peroxide, H2O2. The pumping direction and speed can be controlled by modulating the solution pH, and modeling and theory allow for the kinetics of the reaction steps to be connected to the fluid velocity. In addition, by changing the pH dynamically using glucose oxidase (GOx)-catalyzed oxidation of glucose to gluconic acid, the direction of fluid pumping can be altered in situ, allowing for the design of a glucose sensor. This work underscores the versatility of catalytic pumps and their ability to function as sensors.

Rotation of a submerged finite cylinder moving down a soft incline.

A submerged finite cylinder moving under its own weight along a soft incline lifts off and slides at a steady velocity while also spinning. Here, we experimentally quantify the steady spinning of the cylinder and show theoretically that it is due to a combination of an elastohydrodynamic torque generated by flow in the variable gap, and the viscous friction on the edges of the finite-length cylinder. The relative influence of the latter depends on the aspect ratio of the cylinder, the angle of the incline, and the deformability of the substrate, which we express in terms of a single scaled compliance parameter. By independently varying these quantities, we show that our experimental results are consistent with a transition from an edge-effect dominated regime for short cylinders to a gap-dominated elastohydrodynamic regime when the cylinder is very long.

Curvature Regularization near Contacts with Stretched Elastic Tubes.

Inserting a rigid object into a soft elastic tube produces conformal contact between the two, resulting in contact lines. The curvature of the tube walls near these contact lines is often large and is typically regularized by the finite bending rigidity of the tube. Here, it is demonstrated using experiments and a Föppl-von Kármán-like theory that a second, independent, mechanism of curvature regularization occurs when the tube is axially stretched. In contrast with the effects of finite bending rigidity, the radius of curvature obtained increases with the applied stretching force and decreases with sheet thickness. The dependence of the curvature on a suitably rescaled stretching force is found to be universal, independent of the shape of the intruder, and results from an interplay between the longitudinal stresses due to the applied stretch and hoop stresses characteristic of curved geometry. These results suggest that curvature measurements can be used to infer the mechanical properties of stretched tubular structures.

Migration of ferrofluid droplets in shear flow under a uniform magnetic field.

Manipulation of droplets based on physical properties (e.g., size, interfacial tension, electrical, and mechanical properties) is a critical step in droplet microfluidics. Manipulations based on magnetic fields have several benefits compared to other active methods. While traditional magnetic manipulations require spatially inhomogeneous fields to apply forces, the fast spatial decay of the magnetic field strength from the source makes these techniques difficult to scale up. In this work, we report the observation of lateral migration of ferrofluid (or magnetic) droplets under the combined action of a uniform magnetic field and a pressure-driven flow in a microchannel. While the uniform magnetic field exerts negligible net force on the droplet, the Maxwell stresses deform the droplet to achieve elongated shapes and modulate the orientation relative to the fluid flow. Hydrodynamic interactions between the droplets and the channel walls result in a directional lateral migration. We experimentally study the effects of field strength and direction, and interfacial tension, and use analytical and numerical modeling to understand the lateral migration mechanism.

Enhanced Boiling Heat Transfer using Self-Actuated Nanobimorphs.

We present a new concept of a structured surface for enhanced boiling heat transfer that is capable of self-adapting to the local thermal conditions. An array of freestanding nanoscale bimorphs, a structure that consists of two adjoining materials with a large thermal expansion mismatch, is able to deform under local temperature change. Such a surface gradually deforms as the nucleate boiling progresses due to the increase in the wall superheat. The deformation caused by the heated surface is shown to be favorable for boiling heat transfer, leading to about 10% of increase in the critical heat flux compared to a regular nanowire surface. A recently developed theoretical model that accounts for the critical instability wavelength of the vapor film and the capillary wicking force successfully describes the critical heat flux enhancement for the nanobimorph surface with a good quantitative agreement.

Wind-Driven Formation of Ice Bridges in Straits.

Ice bridges are static structures composed of tightly packed sea ice that can form during the course of its flow through a narrow strait. Despite their important role in local ecology and climate, the formation and breakup of ice bridges is not well understood and has proved difficult to predict. Using long-wave approximations and a continuum description of sea ice dynamics, we develop a one-dimensional theory for the wind-driven formation of ice bridges in narrow straits, which is verified against direct numerical simulations. We show that for a given wind stress and minimum and maximum channel widths, a steady-state ice bridge can only form beyond a critical value of the thickness and the compactness of the ice field. The theory also makes quantitative predictions for ice fluxes, which are particularly useful to estimate the ice export associated with the breakup of ice bridges. We note that similar ideas are applicable to dense granular flows in confined geometries.

In situ enzymatic control of colloidal phoresis and catalysis through hydrolysis of ATP.

The ability to sense chemical gradients and respond with directional motility and chemical activity is a defining feature of complex living systems. There is a strong interest among scientists to design synthetic systems that emulate these properties. Here, we realize and control such behaviors in a synthetic system by tailoring multivalent interactions of adenosine nucleotides with catalytic microbeads. We first show that multivalent interactions of the bead with gradients of adenosine mono-, di- and trinucleotides (AM/D/TP) control both the phoretic motion and a proton-transfer catalytic reaction, and find that both effects are diminished greatly with increasing valence of phosphates. We exploit this behavior by using enzymatic hydrolysis of ATP to AMP, which downregulates multivalent interactivity in situ. This produces a sudden increase in transport of the catalytic microbeads (a phoretic jump), which is accompanied by increased catalytic activity. Finally, we show how this enzymatic activity can be systematically tuned, leading to simultaneous in situ spatial and temporal control of the location of the microbeads, as well as the products of the reaction that they catalyze. These findings open up new avenues for utilizing multivalent interaction-mediated programming of complex chemo-mechanical behaviors into active systems.

Representative subsampling of sedimenting blood.

It is often necessary to extract a small amount of a suspension, such as blood, from a larger sample of the same material for the purposes of diagnostics, testing or imaging. A practical challenge is that the cells in blood sediment noticeably on the time scale of a few minutes, making a representative subsampling of the original sample challenging. Guided by experimental data, we develop a Kynch sedimentation model to discuss design considerations that ensure a representative subsampling of blood, from a container of constant cross-sectional area, for the entire range of physiologically relevant hematocrit over a specified time of interest. Additionally, we show that this design may be modified to exploit the sedimentation and perform subsampling to achieve either higher or lower hematocrit relative to that of the original sample. Thus, our method provides a simple tool to either concentrate or dilute small quantities of blood or other sedimenting suspensions.

Particle migration and sorting in microbubble streaming flows.

Ultrasonic driving of semicylindrical microbubbles generates strong streaming flows that are robust over a wide range of driving frequencies. We show that in microchannels, these streaming flow patterns can be combined with Poiseuille flows to achieve two distinctive, highly tunable methods for size-sensitive sorting and trapping of particles much smaller than the bubble itself. This method allows higher throughput than typical passive sorting techniques, since it does not require the inclusion of device features on the order of the particle size. We propose a simple mechanism, based on channel and flow geometry, which reliably describes and predicts the sorting behavior observed in experiment. It is also shown that an asymptotic theory that incorporates the device geometry and superimposed channel flow accurately models key flow features such as peak speeds and particle trajectories, provided it is appropriately modified to account for 3D effects caused by the axial confinement of the bubble.