In this paper we present a comprehensive study of the step-emulsification process for high-throughput production of (sub-)$mu$m-size monodisperse droplets. The microfluidic device combines a Hele-Shaw nanofluidic cell with a step-like outlet to a dee
p and wide reservoir. The proposed theory based on Hele-Shaw hydrodynamics provides the quasi-static shape of the free boundary between the disperse liquid phase engulfed by the co-flowing continuous phase prior to transition to oscillatory step-emulsification at low enough capillary number. At the transition the proposed theory anticipates a simple condition for critical capillary number as a function of the Hele-Shaw cell geometry. The transition threshold is in excellent agreement with experimental data. A simple closed-form expression for the size of the droplets generated in step-emulsification regime derived using simple geometric arguments also shows a very good agreement with the experimental results.
In this communication we address some hydrodynamic aspects of recently revisited drift mechanism of biogenic mixing in the ocean (Katija and Dabiri, Nature vol. 460, pp. 624-626, 2009). The relevance of the locomotion gait at various spatial scales w
ith 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.
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 qua
litative 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 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.
