Quartz Crystal Microbalance Frequency Response to Discrete Adsorbates in Liquids.

Quartz crystal microbalance with dissipation monitoring (QCM-D) has become a major tool enabling accurate investigation of the adsorption kinetics of nanometric objects such as DNA fragments, polypeptides, proteins, viruses, liposomes, polymer, and metal nanoparticles. However, in liquids, a quantitative analysis of the experimental results is often intricate because of the complex interplay of hydrodynamic and adhesion forces varying with the physicochemical properties of adsorbates and functionalized QCM-D sensors. In the present paper, we dissect the role of hydrodynamics for the analytically tractable case of stiff contact, whereas the adsorbed rigid particles oscillate with the resonator without rotation. Under the assumption of the low surface coverage, we theoretically study the excess shear force exerted on the resonator, which has two contributions: (i) the fluid-mediated force due to flow disturbance created by the particle and (ii) the force exerted on the particle by the fluid and transmitted to the sensor via contact. The theoretical analysis enables an accurate interpretation of the QCM-D impedance measurements. It is demonstrated inter alia that for particles of the size comparable with protein molecules, the hydrodynamic force dominates over the inertial force and that the apparent mass derived from QCM independently of the overtone is about 10 times the Sauerbrey (inertial) mass. The theoretical results show excellent agreement with the results of experiments and advanced numerical simulations for a wide range of particle sizes and oscillation frequencies.

Gas-assisted microfluidic step-emulsification for generating micron- and submicron-sized droplets.

Micron- and submicron-sized droplets have extensive applications in biomedical diagnosis and drug delivery. Moreover, accurate high-throughput analysis requires a uniform droplet size distribution and high production rates. Although the previously reported microfluidic coflow step-emulsification method can be used to generate highly monodispersed droplets, the droplet diameter (d) is constrained by the microchannel height (b), d≳3b, while the production rate is limited by the maximum capillary number of the step-emulsification regime, impeding emulsification of highly viscous liquids. In this paper, we report a novel, gas-assisted coflow step-emulsification method, where air serves as the innermost phase of a precursor hollow-core air/oil/water emulsion. Air gradually diffuses out, producing oil droplets. The size of the hollow-core droplets and the ultrathin oil layer thickness both follow the scaling laws of triphasic step-emulsification. The minimal droplet size attains d≈1.7b, inaccessible in standard all-liquid biphasic step-emulsification. The production rate per single channel is an order-of-magnitude higher than that in the standard all-liquid biphasic step-emulsification and is also superior to alternative emulsification methods. Due to low gas viscosity, the method can also be used to generate micron- and submicron-sized droplets of high-viscosity fluids, while the inert nature of the auxiliary gas offers high versatility.

Correction: Shape-controlled anisotropy of superparamagnetic micro-/nanohelices.

Correction for 'Shape-controlled anisotropy of superparamagnetic micro-/nanohelices' by Alexander M. Leshansky et al., Nanoscale, 2016, 8, 14127-14138, https://doi.org/10.1039/C6NR01803C.

Fluid flow induced by helical microswimmers in bulk and near walls.

Magnetic nano- and microswimmers provide a powerful platform to study driven colloidal systems in fluidic media and are relevant to futuristic medical technologies requiring precise yet minimally invasive motion control at small scales. Upon the action of a rotating magnetic field, the helical microswimmers rotate and translate, generating flow in the surrounding fluid. In this paper, we study the fluid flow induced by the rotating helices using a combination of experiments, numerical simulations, and theory. The microhelices are actuated either in a fluid bulk or in proximity to the bottom wall using typical microfluidic device setup. We conclude that the mean hydrodynamic flow due to the helix actuation can be closely approximated by a system of rotlets line distributed along the helical axis (i.e., representing the flow due to rotating cylinder) which gets modified close to a wall through appropriate contributions from image multipoles. As the mean flow can be obtained in closed form, this study can be further applied towards modeling of the dynamics in a swarm of driven microswimmers interacting hydrodynamically near a bounding surface.

Double emulsions with ultrathin shell by microfluidic step-emulsification.

Double emulsions with ultrathin shells are important in some biomedical applications, such as controlled drug release. However, the existing production techniques require two or more manipulation steps, or more complicated channel geometry, to form thin-shell double emulsions. This work presents a novel microfluidic tri-phasic step-emulsification device, with an easily fabricated double-layer PDMS channel, for production of oil-in-oil-in-water and water-in-water-in-oil double emulsions in a single step. The shell thickness is controlled by the flow rates and can reach 1.4% of the µm-size droplet diameter. Four distinct emulsification regimes are observed depending on the experimental conditions. A theoretical model for the tri-phasic step-emulsification is proposed to predict the boundaries separating the four regimes of emulsification in plane of two dimensionless capillary numbers, Ca. The theory yields two coupled nonlinear differential equations that can be solved numerically to find the approximate shape of the free interfaces in the shallow (Hele-Shaw) microfluidic channel. This approximation is then used as the initial guess for the more accurate finite element method solution, showing very good agreement with the experimental findings. This study demonstrates the feasibility of co-flow step-emulsification as a promising method to production of double (and multiple) emulsions and micro-capsules with ultrathin shells of controllable thickness.

Fluid-Mediated Force on a Particle Due to an Oscillating Plate and Its Effect on Deposition Measurements by a Quartz Crystal Microbalance.

Interaction of particles with boundaries is a fundamental problem in many fields of physics. In this Letter, we theoretically examine the fluid-mediated interaction between a horizontally oscillating plate and a spherical particle, revealing emergence of the novel nonlinear vertical force exerted on the particle. Although we demonstrate that the phenomenon only slightly alters deposition of colloidal (sub-)µm-sized particles measured by quartz crystal microbalance, it can result in levitation of larger particles above the plate, considerably hindering their deposition.

Towards focusing of a swarm of magnetic micro/nanomotors.

Magnetic micro- and nanoparticles propelled by a rotating magnetic field provide a new technology for targeted drug delivery. The therapeutic effect of the technology is achievable with the collective action of large groups (swarms) of the motors. Narrowing of the swarm width before it reaches the target or, vice versa, its expansion prior to deposition on the channel walls are of high importance. Here we show how such swarm tuning can be achieved using a combination of the in-plane rotating and static magnetic field acting in the same plane. Although for this asymmetric actuating field the steady synchronous solutions of the problem do not materialize, the developed approach admits an analytical consideration for the average motor orientation and propulsion. The unique property of an average motion in the actuation by an asymmetric magnetic field is the emergence of propeller's net drift in plane of the field rotation. The drift velocity can be comparable in magnitude to the propulsion velocity along the axis of the field rotation. The field-induced drift is studied in detail for achiral V-shaped and chiral helical propellers, depending on their magnetization. Finally, we suggest spatial configuration of the constant magnetic field capable of focusing/defocusing swarms of magnetic motors.

Modeling Propulsion of Soft Magnetic Nanowires.

The emergent interest in artificial nanostructures that can be remotely navigated a specific location in a fluidic environment is motivated by the enormous potential this technology offers to biomedical applications. Originally, bio-inspired micro-/nanohelices driven by a rotating magnetic field were proposed. However, fabrication of 3D helical nanostructures is complicated. One idea to circumvent complex microfabrication is to use 1D soft magnetic nanowires that acquire chiral shape when actuated by a rotating field. The paper describes the comprehensive numerical approach for modeling propulsion of externally actuated soft magnetic nanowires. The proposed bead-spring model allows for arbitrary filament geometry and flexibility and takes rigorous account of intra-filament hydrodynamic interactions. The comparison of the numerical predictions with the previous experimental results on propulsion of composite two-segment (Ni-Ag) nanowires shows an excellent agreement. Using our model we could substantiate and rationalize important and previously unexplained details, such as bidirectional propulsion of three-segment (Ni-Ag-Au) nanowires.

Photonics of Template-Mediated Lattices of Colloidal Clusters.

The recent progress in microfluidic microfabrication enables mass production of "colloidal molecules" with a preprogrammed geometry (e.g., dumbbells, tetrahedrons, etc.). Such colloids can be used as elementary building blocks in the fabrication of colloidal crystals with unique optical properties. Anisotropic clusters, however, cannot be readily assembled into regular lattices. In this paper, we study photonic properties of compact cubic templates of microdrops encapsulating complex "colloidal molecules". Because monodisperse droplets can be easily packed into dense cubic lattices and encapsulation techniques (e.g., using microfluidics) are well developed, such a material is experimentally feasible. The rationale behind such a methodology is that for a particular alignment of the encapsulated "colloidal molecules" (e.g., by applying an external magnetic or electric field), the resulting structures resemble a diamond lattice, which is known to exhibit a wide complete photonic band gap. The photonic properties of two cubic templates encapsulating dumbbells (symmetric and asymmetric) and tetrahedrons are investigated numerically. In particular, we show the emergence of the complete 3D band gap (∼8% wide for the dielectric contrast ε = 14) for symmetric dumbbells embedded within a face-centered cubic template and oriented along the space diagonal of the elementary cubic cell.

Geometric constraints and optimization in externally driven propulsion.

Micro/nanomachines capable of propulsion through fluidic environments provide diverse opportunities in important biomedical applications. In this paper, we present a theoretical study on micromotors steered through liquid by an external rotating magnetic field. A purely geometric tight upper bound on the propulsion speed normalized with field frequency, known as propulsion efficiency, δ, for an arbitrarily shaped object is derived. Using this bound, we estimate the maximum propulsion efficiency of previously reported random magnetic aggregates. We introduce a complementary definition of the propulsion efficiency, δ*, that ranks propellers according to their maximal speed in body lengths per unit time and that appears to be preferable over the standard definition in a search for fastest machines. Using a bead-based hydrodynamic model combined with genetic algorithms, we determine that δ*-optimal propeller deviates strongly from the bioinspired slim helix and has a surprising chubby skew-symmetric shape. It is also shown that optimized propellers with preprogrammed shape are substantially more efficient than random magnetic aggregates. We anticipate that the results of the present study will provide guidance toward prospective experimental design of more efficient magnetic micro/nanomachines.

Highly Efficient Freestyle Magnetic Nanoswimmer.

The unique swimming strategies of natural microorganisms have inspired recent development of magnetic micro/nanorobots powered by artificial helical or flexible flagella. However, as artificial nanoswimmers with unique geometries are being developed, it is critical to explore new potential modes for kinetic optimization. For example, the freestyle stroke is the most efficient of the competitive swimming strokes for humans. Here we report a new type of magnetic nanorobot, a symmetric multilinked two-arm nanoswimmer, capable of efficient "freestyle" swimming at low Reynolds numbers. Excellent agreement between the experimental observations and theoretical predictions indicates that the powerful "freestyle" propulsion of the two-arm nanorobot is attributed to synchronized oscillatory deformations of the nanorobot under the combined action of magnetic field and viscous forces. It is demonstrated for the first time that the nonplanar propulsion gait due to the cooperative "freestyle" stroke of the two magnetic arms can be powered by a plane oscillatory magnetic field. These two-arm nanorobots are capable of a powerful propulsion up to 12 body lengths per second, along with on-demand speed regulation and remote navigation. Furthermore, the nonplanar propulsion gait powered by the consecutive swinging of the achiral magnetic arms is more efficient than that of common chiral nanohelical swimmers. This new swimming mechanism and its attractive performance opens new possibilities in designing remotely actuated nanorobots for biomedical operation at the nanoscale.

Integral representation of channel flow with interacting particles.

We construct a boundary integral representation for the low-Reynolds-number flow in a channel in the presence of freely suspended particles (or droplets) of arbitrary size and shape. We demonstrate that lubrication theory holds away from the particles at horizontal distances exceeding the channel height and derive a multipole expansion of the flow which is dipolar to the leading approximation. We show that the dipole moment of an arbitrary particle is a weighted integral of the stress and the flow at the particle surface, which can be determined numerically. We introduce the equation of motion that describes hydrodynamic interactions between arbitrary, possibly different, distant particles, with interactions determined by the product of the mobility matrix and the dipole moment. Further, the problem of three identical interacting spheres initially aligned in the streamwise direction is considered and the experimentally observed "pair exchange" phenomenon is derived analytically and confirmed numerically. For nonaligned particles, we demonstrate the formation of a configuration with one particle separating from a stable pair. Our results suggest that in a dilute initially homogenous particulate suspension flowing in a channel the particles will eventually separate into singlets and pairs.

Shape-controlled anisotropy of superparamagnetic micro-/nanohelices.

Micro-/nanopropellers can be actuated remotely by a rotating magnetic field and steered at high precision through various fluidic environments. Recent progress comprises microfabrication of superparamagnetic microhelices not possessing remanent magnetization, but rather magnetized by an applied magnetic field. In this article we present a numerical approach for computing, from first principles, the effective susceptibility of polarizable helical micro-/nanopropellers. We show that nanopropeller geometry, in particular, filament cross-section elongation and orientation, play a central role in determining its magnetic anisotropy and polarizability. The numerical predictions are in qualitative agreement with the previously reported experiments, showing that tight polarizable helices are propulsive. The numerical results are also supported by the approximate slender-body theory. Finally, we propose a semi-quantitative energy criterion to rank polarizable helices with different geometries of the filament by their propulsive capacity and also estimate their maximal propulsion speed.

Droplets in Microchannels: Dynamical Properties of the Lubrication Film.

We study the motion of droplets in a confined, micrometric geometry, by focusing on the lubrication film between a droplet and a wall. When capillary forces dominate, the lubrication film thickness evolves nonlinearly with the capillary number due to the viscous dissipation between the meniscus and the wall. However, this film may become thin enough (tens of nanometers) that intermolecular forces come into play and affect classical scalings. Our experiments yield highly resolved topographies of the shape of the interface and allow us to bring new insights into droplet dynamics in microfluidics. We report the novel characterization of two dynamical regimes as the capillary number increases: (i) at low capillary numbers, the film thickness is constant and set by the disjoining pressure, while (ii) above a critical capillary number, the interface behavior is well described by a viscous scenario. At a high surfactant concentration, structural effects lead to the formation of patterns on the interface, which can be used to trace the interface velocity, that yield direct confirmation of the boundary condition in the viscous regime.

Phytoplankton's motion in turbulent ocean.

We study the influence of turbulence on upward motion of phytoplankton. Interaction with the flow is described by the Pedley-Kessler model considering spherical microorganisms. We find a range of parameters when the upward drift is only weakly perturbed or when turbulence completely randomizes the drift direction. When the perturbation is small, the drift is either determined by the local vorticity or is Gaussian. We find a range of parameters where the phytoplankton interaction with the flow can be described consistently as diffusion of orientation in effective potential. By solving the corresponding Fokker-Planck equation we find exponential steady-state distribution of phytoplankton's propulsion orientation. We further identify the range of parameters where phytoplankton's drift velocity with respect to the flow is determined uniquely by its position. In this case, one can describe phytoplankton's motion by a smooth flow and phytoplankton concentrates on fractal. We find fractal dimensions and demonstrate that phytoplankton forms vertical stripes in space with a nonisotropic pair-correlation function of concentration increased in the vertical direction. The probability density function of the distance between two particles obeys power law with the negative exponent given by the ratio of integrals of the turbulent energy spectrum. We find the regime of strong clustering where the exponent is of order one so that turbulence increases the rate of collisions by a large factor. The predictions hold for Navier-Stokes turbulence and stand for testing.

Convective stability of turbulent Boussinesq flow in the dissipative range and flow around small particles.

We consider arbitrary, possibly turbulent, Boussinesq flow which is smooth below a dissipative scale l_{d}. It is demonstrated that the stability of the flow with respect to growth of fluctuations with scale smaller than l_{d} leads to a nontrivial constraint. That involves the dimensionless strength of fluctuations of the gradients of the scalar in the direction of gravity Fl and the Rayleigh scale L depending on the Rayleigh number Ra, the Nusselt number Nu, and l_{d}. The constraint implies that the stratified fluid at rest, which is linearly stable, develops instability in the limit of large Ra. This limits observability of solution for the flow around small swimmer in quiescent stratified fluid that has closed streamlines at scale L [A. M. Ardekani and R. Stocker, Phys. Rev. Lett. 105, 084502 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.084502]. Correspondingly, to study the flow at scale L one has to take turbulence into account. We demonstrate that the resulting turbulent flow around small particles or swimmers can be described by a scalar integro-differential advection-diffusion equation. Describing the solutions, we show that closed streamlines persist with finite probability. Our results seem to be the necessary basis in understanding flows around small particles and swimmers in natural marine environments.

Swimming by reciprocal motion at low Reynolds number.

Biological microorganisms swim with flagella and cilia that execute nonreciprocal motions for low Reynolds number (Re) propulsion in viscous fluids. This symmetry requirement is a consequence of Purcell's scallop theorem, which complicates the actuation scheme needed by microswimmers. However, most biomedically important fluids are non-Newtonian where the scallop theorem no longer holds. It should therefore be possible to realize a microswimmer that moves with reciprocal periodic body-shape changes in non-Newtonian fluids. Here we report a symmetric 'micro-scallop', a single-hinge microswimmer that can propel in shear thickening and shear thinning (non-Newtonian) fluids by reciprocal motion at low Re. Excellent agreement between our measurements and both numerical and analytical theoretical predictions indicates that the net propulsion is caused by modulation of the fluid viscosity upon varying the shear rate. This reciprocal swimming mechanism opens new possibilities in designing biomedical microdevices that can propel by a simple actuation scheme in non-Newtonian biological fluids.

Dynamics and polarization of superparamagnetic chiral nanomotors in a rotating magnetic field.

Externally powered magnetic nanomotors are of particular interest due to their potential use for in vivo biomedical applications. Here we develop a theory for dynamics and polarization of recently fabricated superparamagnetic chiral nanomotors powered by a rotating magnetic field. We study in detail various experimentally observed regimes of the nanomotor dynamic orientation and propulsion and establish the dependence of these properties on polarization and geometry of the propellers. Based on the proposed theory we introduce a novel "steerability" parameter γ that can be used to rank polarizable nanomotors by their propulsive capability. The theoretical predictions of the nanomotor orientation and propulsion speed are in excellent agreement with available experimental results. Finally, we apply slender-body approximation to estimate the polarization anisotropy and orientation of the easy-axis of superparamagnetic helical propellers.

Nanopropellers and their actuation in complex viscoelastic media.

Tissue and biological fluids are complex viscoelastic media with a nanoporous macromolecular structure. Here, we demonstrate that helical nanopropellers can be controllably steered through such a biological gel. The screw-propellers have a filament diameter of about 70 nm and are smaller than previously reported nanopropellers as well as any swimming microorganism. We show that the nanoscrews will move through high-viscosity solutions with comparable velocities to that of larger micropropellers, even though they are so small that Brownian forces suppress their actuation in pure water. When actuated in viscoelastic hyaluronan gels, the nanopropellers appear to have a significant advantage, as they are of the same size range as the gel's mesh size. Whereas larger helices will show very low or negligible propulsion in hyaluronan solutions, the nanoscrews actually display significantly enhanced propulsion velocities that exceed the highest measured speeds in Newtonian fluids. The nanopropellers are not only promising for applications in the extracellular environment but small enough to be taken up by cells.

Direct measurement of helical cell motion of the spirochete leptospira.

Leptospira are spirochete bacteria distinguished by a short-pitch coiled body and intracellular flagella. Leptospira cells swim in liquid with an asymmetric morphology of the cell body; the anterior end has a long-pitch spiral shape (S-end) and the posterior end is hook-shaped (H-end). Although the S-end and the coiled cell body called the protoplasmic cylinder are thought to be responsible for propulsion together, most observations on the motion mechanism have remained qualitative. In this study, we analyzed the swimming speed and rotation rate of the S-end, protoplasmic cylinder, and H-end of individual Leptospira cells by one-sided dark-field microscopy. At various viscosities of media containing different concentrations of Ficoll, the rotation rate of the S-end and protoplasmic cylinder showed a clear correlation with the swimming speed, suggesting that these two helical parts play a central role in the motion of Leptospira. In contrast, the H-end rotation rate was unstable and showed much less correlation with the swimming speed. Forces produced by the rotation of the S-end and protoplasmic cylinder showed that these two helical parts contribute to propulsion at nearly equal magnitude. Torque generated by each part, also obtained from experimental motion parameters, indicated that the flagellar motor can generate torque >4000 pN nm, twice as large as that of Escherichia coli. Furthermore, the S-end torque was found to show a markedly larger fluctuation than the protoplasmic cylinder torque, suggesting that the unstable H-end rotation might be mechanically related to changes in the S-end rotation rate for torque balance of the entire cell. Variations in torque at the anterior and posterior ends of the Leptospira cell body could be transmitted from one end to the other through the cell body to coordinate the morphological transformations of the two ends for a rapid change in the swimming direction.