We study the interaction between a pair of particles suspended in a uniform oscillatory flow. The time-averaged behaviour of particles under these conditions, which arises from an interplay of inertial and viscous forces, is explored through a theoretical framework relying on small oscillation amplitude. We approximate the oscillatory flow in terms of dual multipole expansions, with which we compute time-averaged interaction forces using the Lorentz reciprocal theorem. We then develop analytic approximations for the force in the limit where Stokes layers surrounding the particles do not overlap. Finally, we show how the same formalism can be generalised to the situation where the particles are free to oscillate and drift in response to the applied flow. The results are shown to be in agreement with existing numerical data for forces and particle velocities. The theory thus provides an efficient means to quantify nonlinear particle interactions in oscillatory flows.

We study the lubricated contact of sliding soft surfaces that are locally patterned but globally cylindrical, held together under an external normal force. We consider gently engineered sinusoidal patterns with small slopes. Three dimensionless parameters govern the system: a speed, and the amplitude and wavelength of the pattern. Using numerical solutions of the Reynolds lubrication equation, we investigate the effects of these dimensionless parameters on key variables such as contact pressure and the coefficient of friction of the lubricated system. For small pattern amplitudes, the coefficient of friction increases with the amplitude. However, our findings reveal that increasing pattern amplitude beyond a critical value can decrease the friction coefficient, a result that contradicts conventional intuition and classical studies on the lubrication of rigid surfaces. For very large amplitudes, we show that the coefficient of friction drops even below the corresponding smooth case. We support these observations with a combination of perturbation theory and physical arguments, identifying scaling laws for large and small speeds, and for large and small pattern amplitudes. This study provides a quantitative understanding of friction in the contact of soft, wet objects and lays theoretical foundations for incorporating the friction coefficient into haptic feedback systems in soft robotics and haptic engineering.

The interaction between deformable surfaces and oscillatory driving is known to produce complex secondary time-averaged flows due to inertial and elastic nonlinearities. Here, we revisit the problem of oscillatory flow in a cylindrical tube with a deformable wall, and analyse it under a long-wave theory for small deformations, but for arbitrary Womersley numbers. We find that the oscillatory pressure does not vary linearly along the length of a deformable channel, but instead decays exponentially with spatial oscillations. We show that this decay occurs over an elasto-visco-inertial length scale that depends on the material properties of the fluid and the elastic walls, the geometry of the system, and the frequency of the oscillatory flow, but is independent of the amplitude of deformation. Inertial and geometric nonlinearities associated with the elastic deformation of the channel drive a time-averaged secondary flow. We quantify the flow using numerical solutions of the perturbation theory, and gain insight by developing analytic approximations. The theory identifies a complex non-monotonic dependence of the time-averaged flux on the elastic compliance and inertia, including a reversal of the flow. Finally, we show that our analytic theory is in excellent quantitative agreement with the three-dimensional direct numerical simulations of Pande et al. (Phys. Rev. Fluids, vol. 8, no. 12, 2023, 124102).

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.

Acoustic fields are widely used to manipulate suspended particles, by rectifying the inertia of rapid oscillations into steady transport. We develop an analytic theory of this particle motion, systematically unifying inviscid acoustophoresis with viscous streaming effects. By applying the Lorentz reciprocal theorem, we obtain a Faxén-like relationship that relates particle motion to a generalized version of the secondary radiation force that depends on the thickness of the oscillatory Stokes layer around the particle, and the density and compressibility contrast between the particle and the fluid. The theory identifies a reversal of particle motion when inertial and viscous forces are comparable, which we validate quantitatively with numerical solutions of the timescale-separated hydrodynamics. We discuss the implications of our findings for practical applications seeking to sort or focus particles by size or material properties.

Interactions between fluid flow and elastic structures are important in many naturally occurring and engineered systems. This review collects and organizes recent theoretical and experimental developments in understanding fluid-structure interactions at low Reynolds numbers. Particular attention is given to the motion of objects moving in close proximity to deformable soft materials and the ensuing interplay between fluid flow and elastic deformation. We discuss how this interplay can be understood in terms of forces and torques, and harnessed in applications such as microrheometry, tribology, and soft robotics. We then discuss the interaction of soft and wet objects close to contact, where intermolecular forces and surface roughness effects become important and are sources of complexity and opportunity.

Solute–surface interactions have garnered considerable interest in recent years as a novel control mechanism for driving unique fluid dynamics and particle transport with potential applications in fields such as biomedicine, the development of microfluidic devices and enhanced oil recovery. In this study, we will discuss dispersion induced by the diffusioosmotic motion near a charged wall in the presence of a solute concentration gradient. Here, we introduce a plug of salt with a Gaussian distribution at the centre of a channel with no background flow. As the solute diffuses, the concentration gradient drives a diffusioosmotic slip flow at the walls, which results in a recirculating flow in the channel; this, in turn, drives an advective flux of the solute concentration. This effect leads to cross-stream diffusion of the solute, altering the effective diffusivity of the solute as it diffuses along the channel. We derive theoretical predictions for the solute dynamics using a multiple-time-scale analysis to quantify the dispersion driven by the solute–surface interactions. Furthermore, we derive a cross-sectionally averaged concentration equation with an effective diffusivity analogous to that from Taylor dispersion. In addition, we use numerical simulations to validate our theoretical predictions.

Driving oscillatory flow around an obstacle generates, due to inertial rectification, a steady ‘streaming’ flow that is useful in a host of microfluidic applications. While theory has focused largely on two-dimensional flows, streaming in many practical microfluidic devices is three-dimensional due to confinement. We develop a three-dimensional streaming theory around an obstacle in a microchannel with a Hele-Shaw-like geometry, where one dimension (depth) is much shorter than the other two dimensions. Utilizing inertial lubrication theory, we demonstrate that the time-averaged streaming flow has a three-dimensional structure. Notably, the flow reverses direction across the depth of the channel, which is a feature not observed in less confined streaming set-ups. This feature is confirmed by our experiments of streaming around a cylinder sandwiched in a microchannel. Our theory also predicts that the streaming velocity decays as the inverse cube of the distance from the cylinder, faster than that expected from previous two-dimensional approaches. We verify this velocity decay quantitatively using particle tracking measurements from experiments of streaming around cylinders with different aspect ratios at different driving frequencies.

We study the coupling between rotation and translation of a submerged cylinder in lubricated contact with a soft elastic substrate. 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.

We develop a three-dimensional flagellum beating model based on sliding-controlled motor feedback accounting for bending and twist, and find a rich variety of beating patterns. 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.

The motion of finite-length cylindrical rods moving near a planar rigid surface is a scenario common across many engineering and natural settings. We study the low-Reynolds-number flow around finite rods that are allowed to rotate or translate in directions perpendicular or parallel to the plane. We develop a three-dimensional lubrication theory to characterize the pressure and hydrodynamic resistances of the cylinders through a special consideration of the cylinder's end effects. In addition, we use three-dimensional numerical simulations to solve these Stokes flows for cylinders of varying lengths and with varying gap sizes between the cylinder and plane, and the numerical results support the developed analytical descriptions. We also use visualizations of the flow to provide qualitative insights and rationalize the effect of the ends on the dynamics of the cylinders. The numerical simulations and theoretical predictions show good agreement in the long (isolated ends) and short (disk-like) limits.

We consider the translation of a rigid, axisymmetric, tightly fitting object through a cylindrical elastic tube filled with viscous fluid, using a combination of theory and direct numerical simulations. The intruding object is assumed to be wider than the undeformed tube radius, forcing solid–solid contact in the absence of relative motion. The motion of the object establishes a thin fluid film that lubricates this contact. Our theory couples lubrication theory to a geometrically nonlinear membrane description of the tube's elasticity, and applies to a slender intruding object and a thin tube with negligible bending rigidity. We show using asymptotic and numerical solutions of the theory, that the thickness of the thin fluid film scales with the square root of the relative speed for small speeds, set by a balance of hoop stresses, membrane tension and fluid pressure. While membrane tension is relatively small at the entrance of the film, it dominates near the exit and produces undulations of the film thickness, even in the limit of vanishing speeds and slender objects. We find that the drag force on the intruding object depends on the slope of its surface at the entrance to the thin fluid film, and scales as the square root of the relative speed. The predictions of the lubricated membrane theory for the shape of the film and the force on the intruder are in quantitative agreement with three-dimensional direct numerical simulations of the coupled fluid–elastic problem.

When an object suspended in fluid moves past a soft substrate it experiences an additional lift force due to the deformability of the substrate. In this work we find this lift force analytically for a general deformable substrate in the limit of small deformations. In particular we employ Lorentz's reciprocal theorem to obtain a general integral relation between the lift force and the linear response function of the soft substrate. We apply these results to an elastic layer, and discuss the behavior of the lift force as a function of Poisson's ratio and the thickness of the layer, obtaining analytic results for thin and thick layers. Then we generalize the theory to a linear viscoelastic response of the substrate. For oscillatory relative motion between the surfaces we find that the resulting lift force is a superposition of steady and oscillating modes whose amplitude and phase contain information about the elastic and viscous components of the material response. Our theory makes transparent the connection between the elastohydrodynamic lift force and the underlying response of the substrate and can be used to characterize the mechanical properties of an arbitrary soft material without solid-to-solid contact via lift force measurements.

The Maxey–Riley equation describes the motion of a spherical particle suspended in a spatially nonuniform, time-dependent flow, and finds applications in a wide range of flow situations. We reexamine the hydrodynamics underlying the Maxey–Riley equation to find additional inertial forces associated with second gradients of the background flow velocity, not accounted for in the original framework. These forces amplify inertial Faxén terms threefold, while also contributing advective terms that are quadratic in fluid velocity and may exceed Faxén forces in some flows. We present a more comprehensive form of the Maxey–Riley equation that includes these contributions, and discuss its implications for particle dynamics in flows with curvature.

Using experiments and modeling, we study the spontaneous wrapping of a negatively charged microfiber around a positively charged disk-shaped particle immersed in a liquid. 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.

Dissolution and dissociation of CO₂ in an aqueous phase induce diffusiophoretic motion of charged particles. Such phenomenon can be applied to maintaining a surface free of bacteria, by migrating the nearby cells away from a CO₂ source. 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.

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.

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.

Acoustically actuated sessile bubbles can be used as a tool to manipulate microparticles, vesicles, and cells. In this work, using acoustically actuated sessile semicylindrical microbubbles, we demonstrate experimentally that finite-sized microparticles undergo size-sensitive migration and trapping toward specific spatial positions in three dimensions with high reproducibility. The particle trajectories are successfully reproduced by passive advection of the particles in a steady three-dimensional streaming flow field augmented with volume exclusion from the confining boundaries. For different particle sizes, this volume exclusion mechanism leads to three regimes of qualitatively different migratory behavior, suggesting applications for separating, trapping, and sorting of particles in three dimensions.

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.

We demonstrated a simple and novel approach to manipulate droplet migration in microfluidics by using 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.

Diffusiophoresis and diffusioosmosis are electrokinetic phenomena where relative motion is induced between a charged surface and a surrounding electrolyte due to a concentration gradient of ions. In the literature, a relative velocity between a surface and the electrolyte has been derived for a valence-symmetric (z:z) electrolyte. In this article, we reformulate the governing equations in a convenient form based on a systematic generalization of the nonlinear Poisson-Boltzmann equations in the limit of a thin double layer, which allows us to derive results for diffusiophoretic and diffusioosmotic velocities for a mixture of electrolytes with a general combination of cation and anion valences. We find that the relative motion depends significantly on ion valences. We also provide analytical approximations for the diffusiophoretic and diffusioosmotic velocities and discuss their accuracy and applicability. Further, we tabulate diffusiphoretic velocities for some common cases, which highlights the importance of asymmetry in cation and anion valences. Finally, we discuss the validity of our assumptions and the importance of effects such as finite ion size, dielectric decrement, and surface conduction for typical experimental conditions.

Flow instabilities can occur in a fluid system with two components that have significantly different diffusivities and that have opposite effects on the fluid density, as is the scenario in traditional double-diffusive convection. Here, we experimentally show that an oil-in-water emulsion exposed to salt concentration gradients generates a flowerlike pattern driven by vertical and azimuthal instabilities. We also report numerical and analytical studies to elaborate on the mechanism, the instability criteria, and the most unstable modes that determine the details of the observed patterns. We find that the instability is driven by buoyancy and stems from the differential transport between the dissolved salt and the suspended oil droplets, which have opposing effects on the density of the medium. Consequently, we identify a criterion for the development of the instability that involves the relative densities and concentrations of the salt and oil droplets. We also argue that the typical wave number of the pattern formed scales with the Péclet number of the salt, which here is equivalent to the Rayleigh number since the flow is driven by buoyancy. We find good agreement of these predictions with both experiments and numerical simulations.

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.

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.

Classical diffusiophoresis describes the motion of particles in an electrolyte or non-electrolyte solution with an imposed concentration gradient. We investigate the autophoresis of two particles in an electrolyte solution where the concentration gradient is produced by either adsorption or desorption of ions at the particle surfaces. We find that when the sorption fluxes are large, the ion concentration near the particle surfaces, and consequently the Debye length, is strongly modified, resulting in a nonlinear dependence of the phoretic speed on the sorption flux. In particular, we show that the phoretic velocity saturates at a finite value for large desorption fluxes, but depends superlinearly on the flux for adsorption fluxes, where both conclusions are in contrast with previous results that predict a linear relationship between autophoretic velocity and sorption flux. Our theory can also be applied to precipitation/dissolution and other surface chemical processes.

Understanding the hydrodynamics of self-propelled organisms is critical to evaluate the role of migrating zooplankton aggregations in sustaining marine ecosystems via the transport of nutrients and mixing of fluid properties. Analysis of transport and mixing during swimming is thus essential to assess whether biomixing is a relevant source of kinetic energy in the upper ocean. In this study, dilute swarms of the ephyral Aurelia aurita were simulated under different configurations to analyze the effects of inter-organism spacing and structure of a migrating aggregation on fluid transport. By using velocimetry data instead of numerically simulated velocity fields, our study integrates the effects of the near- and far-field flows. Lagrangian analysis of simulated fluid particles, both in homogeneous and stratified fluid, shows that the near-field flow ultimately dictates fluid dispersion. The discrepancy between our results and predictions made using low-order models (both in idealized fluid and within the Stokes limit) highlights the need to correctly represent the near-field flow resulting from swimming kinematics and organism morphology. Derived vertical stirring coefficients for all cases suggest that even in the limit of dilute aggregations, self-propelled organisms can play an important role in transporting fluid against density gradients.

Hydraulic fracturing plays an important role in meeting today's energy demands. However, the substantial use of fresh water in fracturing and wastewater returning to the surface pose risks to the environment. Alternative technology has been developed that reduces the water-related risks by injecting aqueous foam instead of water to fracture shale formations, but the mechanism is poorly understood. Here, we show, using laboratory experiments, that the injection of foam instead of water dramatically changes the fracture dynamics when the foam compressibility is important. We develop a scaling argument for the fracture dynamics that exhibits excellent agreement with the experimental results. Our findings extend to other systems involving compressible foams, including fire-fighting, energy storage using compressed foams, and enhanced oil recovery. 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.

While coupling between fluid flow and soft elastic surfaces is common in biology and engineering, an analytical description is challenging as it often involves non-linear dynamics. Here we show using theory and experiments that a small particle moving along an elastic membrane through a viscous fluid is repelled from the membrane due to hydroelastic forces. The flow field produces an elastic disturbance in the membrane leading to particle-wave coupling. We derive an analytic expression for the particle trajectory and find that the normal migration velocity of the particle is quadratic in its speed and depends on a combination of the tension and bending resistance of the membrane. Experimentally, we measure the normal displacement of spheres sedimenting under gravity along a suspended elastic membrane and find quantitative agreement with the theoretical predictions with no fitting parameters. We experimentally demonstrate that the effect is strong enough for separation and sorting of particles on the basis of both their size and density. We discuss the significance of our results for particles interacting with biological membranes, and propose the use of our model for membrane elasticity measurements.

When an elastic object is dragged through a viscous fluid tangent to a rigid boundary, it experiences a lift force perpendicular to its direction of motion. An analogous lift occurs when a rigid symmetric object translates parallel to an elastic interface or a soft substrate. The induced lift force is attributed to an elastohydrodynamic coupling that arises from the breaking of the flow reversal symmetry produced by the elastic deformation of the translating object or the interface. Here we derive explicit analytical expressions for the quasi-steady-state lift force exerted on a rigid spherical particle translating parallel to a finite-sized membrane exhibiting a resistance toward both shear and bending. Our analytical approach applies the Lorentz reciprocal theorem so as to obtain the solution of the flow problem using a perturbation technique for small deformations of the membrane. We find that the shear-related contribution to the normal force leads to an attractive interaction between the particle and the membrane. This emerging attractive force decreases quadratically with the system size to eventually vanish in the limit of an infinitely extended membrane. In contrast, membrane bending leads to a repulsive interaction whose effect becomes more pronounced upon increasing the system size, where the lift force is found to diverge logarithmically for an infinitely large membrane. The unphysical divergence of the bending-induced lift force can be rendered finite by regularizing the solution with a cutoff length beyond which the bending forces become subdominant to an external body force.

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.

Due to the inherent nonlinearity of fluid dynamics, a large class of oscillating flows gives rise to rectified effects of steady motion. It has recently been shown that particle transport in such flows leads to differential displacement and efficient sorting of microparticles. Here we present a model that generalizes a Maxey-Riley-like equation for particle motion, incorporating important viscous and inviscid effects near oscillating interfaces and efficiently bridging the acoustofluidic and microfluidic approaches. Resulting in direct predictions for particle motion on slower timescales, the model predicts a richer and qualitatively different behavior from that expected from simplified radiation-force formalisms: depending on experimental control parameters, the net effect of interfacial oscillation can be either an attraction to or a repulsion from the interface, and particles can be captured at a fixed distance or released. These results are verified in comparison with experiments.

Ice bridges are rigid structures composed of sea ice that form seasonally in the many straits and channels of the Canadian Arctic Archipelago. Driven primarily by atmospheric stresses, these ice bridges are formed when sufficiently thick ice ``jams'' during the course of its flow between land masses, resulting in a region of stationary compacted ice that is separated from a region of flowing open water (a polynya) by a static arch. Using a continuum description of sea ice that is widely used in climate modeling, we present an asymptotic theory of the process of formation of such bridges in slender channels when the motion of the ice is driven by external wind and water stresses. We show that for an arbitrary channel shape, ice bridges can only form within a range of ice properties that is determined by the channel geometry and the external stress. We then compare the results of our theory with direct numerical simulations and observational evidence. Finally, we provide simple analytical expressions for the mean velocity of the ice flow as a function of the channel shape, the properties of the ice, and the wind and water stresses along the channel.

For a small sphere suspended in a background fluid flow near an obstacle, we calculate the hydrodynamic force on the sphere in the direction normal to the boundary of the obstacle. Using the Lorentz reciprocal theorem, we obtain analytical expressions for the normal force in the Stokes flow limit, valid for arbitrary separations of the particle from the obstacle, both for solid obstacles and those with free surfaces. The main effect of the boundary is to produce a normal force proportional to extensional flow gradients in the vicinity of the particle. The strength of this force is greatest when the separation between the surfaces of the particle and the obstacle is small relative to the particle size. While the magnitude of the force weakens for large separations between the sphere and the obstacle (decaying quadratically with separation distance), it can significantly modify Faxén's law even at modestly large separation distances. In addition, we find a second force contribution due to the curvature of the background flow normal to the obstacle, which is also important when the sphere is close to the obstacle. The results of the theory are of importance to the dynamics of particles in confined geometries, whether bounded by a solid obstacle, the wall of a channel or a gas bubble.

Solutions are presented for both laminar developing flow in a curved pipe with a parabolic inlet velocity and laminar transitional flow downstream of a curved pipe into a straight outlet. Scalings and linearized analyses about appropriate base states are used to show that both cases obey the same governing equations and boundary conditions. In particular, the governing equations in the two cases are linearized about fully developed Poiseuille flow in cylindrical coordinates and about Dean's velocity profile for curved pipe flow in toroidal coordinates respectively. Subsequently, we identify appropriate scalings of the axial coordinate and disturbance velocities that eliminate dependence on the Reynolds number $\text{Re}$ and dimensionless pipe curvature $\alpha$ from the governing equations and boundary conditions in the limit of small $\alpha$ and large $\text{Re}$. Direct numerical simulations confirm the scaling arguments and theoretical solutions for a range of Re and $\alpha$. Maximum values of the axial velocity, secondary velocity and pressure perturbations are determined along the curved pipe section. Results collapse when the scalings are applied, and the theoretical solutions are shown to be valid up to Dean numbers of $D=\text{Re}^2 \alpha = O(100)$. The developing flows are shown numerically and analytically to contain spatial oscillations. The numerically determined decay of the velocity perturbations is also used to determine entrance/development lengths for both flows, which are shown to scale linearly with the Reynolds number, but with a prefactor $\sim 60\%$ larger than the textbook case of developing flow in a straight pipe.

It is known that an object translating parallel to a soft wall in a viscous fluid produces hydrodynamic stresses that deform the wall, which in turn results in a lift force on the object. Recent experiments with cylinders sliding under gravity near a soft incline, which confirmed theoretical arguments for the lift force, also reported an unexplained steady-state rotation of the cylinders [B. Saintyves et al., Proc. Natl. Acad. Sci. USA 113, 5847 (2016)]. Motivated by these observations, we show, in the lubrication limit, that an infinite cylinder that translates in a viscous fluid parallel to a soft wall at constant speed and separation distance must also rotate in order to remain free of torque. Using the Lorentz reciprocal theorem, we show analytically that for small deformations of the elastic layer, the angular velocity of the cylinder scales with the cube of the sliding speed. These predictions are confirmed numerically. We then apply the theory to the gravity-driven motion of a cylinder near a soft incline and find qualitative agreement with the experimental observations, namely, that a softer elastic layer results in a greater angular speed of the cylinder.

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.

It is demonstrated that micron-sized particles suspended in fluid near oscillating interfaces experience strong inertial displacements above and beyond the fluid streaming. Experiments with oscillating bubbles show rectified particle lift over extraordinarily short (millisecond) times. A quantitative model on both the oscillatory and the steady time scales describes the particle displacement relative to the fluid motion. The formalism yields analytical predictions confirming the observed scaling behavior with particle size and experimental control parameters. It applies to a large class of oscillatory flows with applications from particle trapping to size sorting.

In this work, a systematic approach to efficient open flow mixing is introduced, using general theoretical concepts to identify optimized parameters of a deliberately introduced unsteady flow component. The method is applied in detail to two-dimensional (2D) advective mixing in flows resulting from the superposition of a transport flow through a channel and secondary localized cross-flows, here the vortical streaming due to a microbubble array. A simple description of stirring in a steady 2D vortex identifies the characteristic time beyond which vortex stirring becomes ineffective, with slow algebraic decay of the mix-variance. Duty cycling of the vortices introduces flow unsteadiness, for which optimum duty cycling protocols are identified, following analytically from a few selected Eulerian properties of the combined transport and vortex stirring flow. In comparison with experiments and simulations, it is shown that this simple formalism allows for the accurate prediction of optimal advective mixing, exponential in time, in the microbubble streaming case and, by extension, for any open-flow mixer with modulated secondary flow. Taking into account the effect of diffusion, estimated residence times required for complete mixing in such optimized devices are obtained.

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.

Steady streaming vortex flow from microbubbles has been developed into a versatile tool for microfluidic sample manipulation. For ease of manufacture and quantitative control, set-ups have focused on approximately two-dimensional flow geometries based on semi-cylindrical bubbles. The present work demonstrates how the necessary flow confinement perpendicular to the cylinder axis gives rise to non-trivial three-dimensional flow components. This is an important effect in applications such as sorting and micromixing. Using asymptotic theory and numerical integration of fluid trajectories, it is shown that the two-dimensional flow dynamics is modified in two ways: (i) the vortex motion is punctuated by bursts of strong axial displacement near the bubble, on time scales smaller than the vortex period; and (ii) the vortex trajectories drift over time scales much longer than the vortex period, forcing fluid particles onto three-dimensional paths of toroidal topology. Both effects are verified experimentally by quantitative comparison with astigmatism particle tracking velocimetry (APTV) measurements of streaming flows. It is further shown that the long-time flow patterns obey a Hamiltonian description that is applicable to general confined Stokes flows beyond microstreaming.

Ultrasound-driven oscillating microbubbles are used as active actuators in microfluidic devices to perform manifold tasks such as mixing, sorting, and manipulation of microparticles. A common configuration consists of side bubbles created by trapping air pockets in blind channels perpendicular to the main channel direction. This configuration consists of acoustically excited bubbles with a semicylindrical shape that generate significant streaming flow. Because of the geometry of the channels, such flows are generally considered as quasi-two-dimensional. Similar assumptions are often made in many other microfluidic systems based on flat microchannels. However, in this Letter we show that microparticle trajectories actually present a much richer behavior, with particularly strong out-of-plane dynamics in regions close to the microbubble interface. Using astigmatism particle-tracking velocimetry, we reveal that the apparent planar streamlines are actually projections of a stream surface with a pseudotoroidal shape. We, therefore, show that acoustic streaming cannot generally be assumed as a two-dimensional phenomenon in confined systems. The results have crucial consequences for most of the applications involving acoustic streaming such as particle trapping, sorting, and mixing.

Steady streaming flow from oscillating sessile bubbles at walls is the centrepiece of many microstreaming experiments. A complete asymptotic theory of the flow is developed, requiring only the oscillatory driving frequency and material parameters as input, and properly accounting for bubble and wall boundary conditions. It is shown that mixed-mode streaming of neighbouring bubble oscillation modes is responsible for the robustness of the generic 'fountain' vortex pair flow pattern, and that the pattern reverses for high frequencies when wall-induced streaming becomes dominant. The far-field flow and its dependence on control parameters are in agreement with experimental data and can be understood considering just a few asymptotic coefficients.

Steady streaming from oscillating microbubbles is a powerful actuating mechanism in microfluidics, enjoying increased use due to its simplicity of manufacture, ease of integration, low heat generation, and unprecedented control over the flow field and particle transport. As the streaming flow patterns are caused by oscillations of microbubbles in contact with walls of the set-up, an understanding of the bubble dynamics is crucial. Here we experimentally characterize the oscillation modes and the frequency response spectrum of such cylindrical bubbles, driven by a pressure variation resulting from ultrasound in the range of $1\, \text{kHz} \lesssim f \lesssim 100\, \text{kHz}$. We find that (i) the appearance of 2D streaming flow patterns is governed by the relative amplitudes of bubble azimuthal surface modes (normalized by the volume response), (ii) distinct, robust resonance patterns occur independent of details of the set-up, and (iii) the position and width of the resonance peaks can be understood using an asymptotic theory approach. This theory describes, for the first time, the shape oscillations of a pinned cylindrical bubble at a wall and gives insight into necessary mode couplings that shape the response spectrum. Having thus correlated relative mode strengths and observed flow patterns, we demonstrate that the performance of a bubble micromixer can be optimized by making use of such flow variations when modulating the driving frequency.