Microfluidic step-emulsification in axisymmetric geometry.

Biphasic step-emulsification (Z. Li et al., Lab Chip, 2015, 15, 1023) is a promising microfluidic technique for high-throughput production of µm and sub-µm highly monodisperse droplets. The step-emulsifier consists of a shallow (Hele-Shaw) microchannel operating with two co-flowing immiscible liquids and an abrupt expansion (i.e., step) to a deep and wide reservoir. Under certain conditions the confined stream of the disperse phase, engulfed by the co-flowing continuous phase, breaks into small highly monodisperse droplets at the step. Theoretical investigation of the corresponding hydrodynamics is complicated due to the complex geometry of the planar device, calling for numerical approaches. However, direct numerical simulations of the three dimensional surface-tension-dominated biphasic flows in confined geometries are computationally expensive. In the present paper we study a model problem of axisymmetric step-emulsification. This setup consists of a stable core-annular biphasic flow in a cylindrical capillary tube connected co-axially to a reservoir tube of a larger diameter through a sudden expansion mimicking the edge of the planar step-emulsifier. We demonstrate that the axisymmetric setup exhibits similar regimes of droplet generation to the planar device. A detailed parametric study of the underlying hydrodynamics is feasible via inexpensive (two dimensional) simulations owing to the axial symmetry. The phase diagram quantifying the different regimes of droplet generation in terms of governing dimensionless parameters is presented. We show that in qualitative agreement with experiments in planar devices, the size of the droplets generated in the step-emulsification regime is independent of the capillary number and almost insensitive to the viscosity ratio. These findings confirm that the step-emulsification regime is solely controlled by surface tension. The numerical predictions are in excellent agreement with in-house experiments with the axisymmetric step-emulsifier.

Flexible helical yarn swimmers.

We investigate the motion of a flexible Stokesian flagellar swimmer realised as a yarn made of two intertwined elastomer fibres, one active, that can reversibly change its length in response to a local excitation causing transition to the nematic state or swelling, and the other one, a passive isotropic elastomer with identical mechanical properties. A propagating chemical wave may provide an excitation mechanism ensuring a constant length of the excited region. Generally, the swimmer moves along a helical trajectory, and the propagation and rotation velocity are very sensitive to the ratio of the excited region to the pitch of the yarn, as well as to the size of a carried load. External excitation by a moving actuating beam is less effective, unless the direction of the beam is adjusted to rotation of the swimmer.

Optimal Length of Low Reynolds Number Nanopropellers.

Locomotion in fluids at the nanoscale is dominated by viscous drag. One efficient propulsion scheme is to use a weak rotating magnetic field that drives a chiral object. From bacterial flagella to artificial drills, the corkscrew is a universally useful chiral shape for propulsion in viscous environments. Externally powered magnetic micro- and nanomotors have been recently developed that allow for precise fuel-free propulsion in complex media. Here, we combine analytical and numerical theory with experiments on nanostructured screw-propellers to show that the optimal length is surprisingly short-only about one helical turn, which is shorter than most of the structures in use to date. The results have important implications for the design of artificial actuated nano- and micropropellers and can dramatically reduce fabrication times, while ensuring optimal performance.

Correction: Step-emulsification in a microfluidic device.

Correction for 'Step-emulsification in a microfluidic device' by Z. Li et al., Lab Chip, 2015, 15, 1023-1031.

Step-emulsification in a microfluidic device.

We present a comprehensive study of the step-emulsification process for high-throughput production of colloidal monodisperse droplets. The 'microfluidic step emulsifier' combines a shallow microchannel operating with two co-flowing immiscible fluids and an abrupt (step-like) opening to a deep and wide reservoir. Based on Hele-Shaw hydrodynamics, we determine the quasi-static shape of the fluid interface prior to transition to oscillatory step-emulsification at low capillary numbers. The theoretically derived transition threshold yields an excellent agreement with experimental data. A closed-form expression for the size of the droplets generated in the step-emulsification regime and derived using geometric arguments also shows a very good agreement with the experiment.

Obstructed breakup of slender drops in a microfluidic T junction.

In this Letter we present a theoretical analysis of the droplet breakup with "permanent obstruction" in a microfluidic T junction [M.-C. Jullien et al., Phys. Fluids 21, 072001 (2009)]. The proposed theory is based on a simple geometric construction for the interface shape combined with Tanner's law for the local contact angle. The resulting scaling of the droplet deformation with time and capillary number is in excellent agreement with the results of direct numerical simulations and prior experiments. More rigorous analysis based on the lubrication approximation reveals a self-similar behavior analogous to the classical problem of a droplet spreading over a preexisting liquid film.

Rupture of thin liquid films: generalization of weakly nonlinear theory.

In this paper, we investigate the rupture dynamics of thin liquid films driven by intermolecular forces via weakly nonlinear bifurcation analysis. The dynamic equations governing slow dynamics of the perturbation amplitude of the near-critical mode corresponding to several models describing the evolution of thin liquid films in different physical situations appear to have the same structure. When antagonistic (attractive and repulsive) molecular forces are considered, nonlinear saturation of the instability becomes possible, while the boundary of this supercritical bifurcation is determined solely by the form of the intermolecular potential. The rupture time estimate obtained in closed form shows an excellent agreement with the results of the previously reported numerical simulations of the strongly nonlinear coupled evolution equations upon fitting the amplitude of the small initial perturbation. We further extend the weakly nonlinear analysis of the film dynamics and apply the Galerkin approximation to derive the amplitude equation(s) governing the dynamics of the fastest growing linear mode far from the instability threshold. The comparison of the rupture time derived from this theory with the results of numerical simulations of the original nonlinear evolution equations shows a very good agreement without any adjustable parameters.

Do small swimmers mix the ocean?

In this communication we address some hydrodynamic aspects of recently proposed drift mechanism of biogenic mixing in the ocean [K. Katija and J. O. Dabiri, Nature (London) 460, 624 (2009)10.1038/nature 08207]. The relevance of the locomotion gait at various spatial scales with respect to the drift is discussed. A hydrodynamic scenario of the drift based on unsteady inertial propulsion, typical for most small marine organisms, is proposed. We estimate its effectiveness by taking into account interaction of a swimmer with the turbulent marine environment. Simple scaling arguments are derived to estimate the comparative role of drift-powered mixing with respect to the turbulence. The analysis indicates substantial biomixing effected by relatively small but numerous drifters, such as krill or jellyfish.

Enhanced low-Reynolds-number propulsion in heterogeneous viscous environments.

It has been known for some time that some microorganisms can swim faster in high-viscosity gel-forming polymer solutions. These gel-like media come to mimic highly viscous heterogeneous environment that these microorganisms encounter in-vivo. The qualitative explanation of this phenomena first offered by Berg and Turner [Nature (London) 278, 349 (1979)], suggests that propulsion enhancement is a result of flagellum pushing on quasi-rigid loose polymer network formed in some polymer solutions. Inspired by these observations, inertia-less propulsion in a heterogeneous viscous medium composed of sparse array of stationary obstacles embedded into a incompressible Newtonian liquid is considered. It is demonstrated that for prescribed propulsion gaits, including propagating surface distortions and rotating helical filament, the propulsion speed is enhanced when compared to swimming in purely viscous solvent. It is also shown that the locomotion in heterogenous viscous media is characterized by improved hydrodynamic efficiency. The results of the rigorous numerical simulation of the rotating helical filament propelled through a random sparse array of stationary obstructions are in close agreement with predictions of the proposed resistive force theory based on effective media approximation.

Efficiency of cargo towing by a microswimmer.

We study the properties of an arbitrary microswimmer towing a passive load through a viscous liquid. The simple close-form expression for the dragging efficiency of a microswimmer dragging a distant load is found, and the approximation for finite mutual proximity is derived. We show that, while the swimmer can be arbitrarily efficient, the dragging efficiency is always bounded from above. It is also demonstrated, that opposite to Purcell's assumption [E. M. Purcell, Proc. Natl. Acad. Sci. U.S.A. 94, 11307 (1997)], the hydrodynamic coupling can "help" the propeller to tow the load. We support our conclusions by rigorous numerical calculations for the rotary swimmer, towing a spherical cargo positioned at a finite distance.

Tunable nonlinear viscoelastic "focusing" in a microfluidic device.

In this Letter we describe a novel method for tunable viscoelastic focusing of particles flowing in a microchannel. It is proposed that some elasticity, inherently present in dilute polymer solutions, may be responsible for highly nonuniform spatial distribution of flowing particles across the channel cross section, yielding their "focusing" in the midplane of the channel. A theory based on scaling arguments is presented to explain the lateral migration and is found to be in a very good agreement with the experimental observations. It was found that, in agreement with the theoretical prediction, the particles would have different spatial distribution depending on their size and rheology of the suspending medium. We demonstrate how the viscoelastic focusing can be precisely controlled by proper rheological design of the carrier solution.

Actin-based propulsion of a microswimmer.

A simple hydrodynamic model of actin-based propulsion of microparticles in dilute cell-free cytoplasmic extracts is presented. Under the basic assumption that actin polymerization at the particle surface acts as a force dipole, pushing apart the load and the free (nonanchored) actin tail, the propulsive velocity of the microparticle is determined as a function of the tail length, porosity, and particle shape. The anticipated velocities of the cargo displacement and the rearward motion of the tail are in good agreement with recently reported results of biomimetic experiments. A more detailed analysis of the particle-tail hydrodynamic interaction is presented and compared to the prediction of the simplified model.

Chaos and threshold for irreversibility in sheared suspensions.

Systems governed by time reversible equations of motion often give rise to irreversible behaviour. The transition from reversible to irreversible behaviour is fundamental to statistical physics, but has not been observed experimentally in many-body systems. The flow of a newtonian fluid at low Reynolds number can be reversible: for example, if the fluid between concentric cylinders is sheared by boundary motion that is subsequently reversed, then all fluid elements return to their starting positions. Similarly, slowly sheared suspensions of solid particles, which occur widely in nature and science, are governed by time reversible equations of motion. Here we report an experiment showing precisely how time reversibility fails for slowly sheared suspensions. We find that there is a concentration dependent threshold for the deformation or strain beyond which particles do not return to their starting configurations after one or more cycles. Instead, their displacements follow the statistics of an anisotropic random walk. By comparing the experimental results with numerical simulations, we demonstrate that the threshold strain is associated with a pronounced growth in the Lyapunov exponent (a measure of the strength of chaotic particle interactions). The comparison illuminates the connections between chaos, reversibility and predictability.

Nonlinear rupture of thin liquid films on solid surfaces.

In this letter we investigate the rupture instability of thin liquid films by means of a bifurcation analysis in the vicinity of the short-scale instability threshold. The rupture time estimate obtained in closed form as a function of the relevant dimensionless groups is in striking agreement with the results of the numerical simulations of the original nonlinear evolution equations. This suggests that the weakly nonlinear theory adequately captures the underlying physics of the instability. When antagonistic (attractive/repulsive) molecular forces are considered, nonlinear saturation of the instability becomes possible. We show that the stability boundaries are determined by the van der Waals potential alone.