Transverse flow in thin superhydrophobic channels

We provide some general theoretical results to guide the optimization of transverse hydrodynamic phenomena in superhydrophobic channels. Our focus is on the canonical micro- and nanofluidic geometry of a parallel-plate channel with an arbitrary two-component (low-slip and high-slip) coarse texture, varying on scales larger than the channel thickness. By analyzing rigorous bounds on the permeability, over all possible patterns, we optimize the area fractions, slip lengths, geometry and orientation of the surface texture to maximize transverse flow. In the case of two aligned striped surfaces, very strong transverse flows are possible. Optimized superhydrophobic surfaces may find applications in passive microfluidic mixing and amplification of transverse electrokinetic phenomena.Comment: 4 page

Force calculation on walls and embedded particles in multiparticle collision dynamics simulations

Colloidal solutions posses a wide range of time and length scales, so that it is unfeasible to keep track of all of them within a single simulation. As a consequence some form of coarse-graining must be applied. In this work we use the Multi-Particle Collision Dynamics scheme. We describe a particular implementation of no-slip boundary conditions upon a solid surface, capable of providing correct force s on the solid bypassing the calculation of the velocity profile or the stre ss tensor in the fluid near the surface. As an application we measure the friction on a spherical particle, when it is placed in a bulk fluid and when it is confined in a slit. We show that the implementation of the no-slip boundary conditions leads to an enhanced Ensko g friction, which can be understood analytically. Because of the long-range nature of hydrodynamic interactions, the Stokes friction obtained from the simulations is sensitive of the simulation box size. We address this topic for the slit geometry, showing that that the dependence on the system size differs very much from what is expected in a 3D system, where periodic boundary conditions are used in all directions.Comment: To appear in Physical Review

Measurement of Newtonian fluid slip using a torsional ultrasonic oscillator

The composite torsional ultrasonic oscillator, a versatile experimental system, can be used to investigate slip of Newtonian fluid at a smooth surface. A rigorous analysis of slip-dependent damping for the oscillator is presented. Initially, the phenomenon of finite surface slip and the slip length are considered for a half-space of Newtonian fluid in contact with a smooth, oscillating solid surface. Definitions are revisited and clarified in light of inconsistencies in the literature. We point out that, in general oscillating flows, Navier's slip length b is a complex number. An intuitive velocity discontinuity parameter of unrestricted phase is used to describe the effect of slip on measurement of viscous shear damping. The analysis is applied to the composite oscillator and preliminary experimental work for a 40 kHz oscillator is presented. The Non-Slip Boundary Condition (NSBC) has been verified for a hydrophobic surface in water to within ~60 nm of |b|=0 nm. Experiments were carried out at shear rate amplitudes between 230 and 6800 /s, corresponding to linear displacement amplitudes between 3.2 and 96 nm.Comment: Revised with minor edits for revie

Electrophoresis of a polyelectrolyte through a nanopore

A hydrodynamic model for determining the electrophoretic speed of a polyelectrolyte through a nanopore is presented. It is assumed that the speed is determined by a balance of electrical and viscous forces arising from within the pore and that classical continuum electrostatics and hydrodynamics may be considered applicable. An explicit formula for the translocation speed as a function of the pore geometry and other physical parameters is obtained and is shown to be consistent with experimental measurements on DNA translocation through nanopores in silicon membranes. Experiments also show a weak dependence of the translocation speed on polymer length that is not accounted for by the present model. It is hypothesized that this is due to secondary effects that are neglected here.Comment: 5 pages, 2 column, 2 figure

Bundling of elastic filaments induced by hydrodynamic interactions

Peritrichous bacteria swim in viscous fluids by rotating multiple helical flagellar filaments. As the bacterium swims forward, all its flagella rotate in synchrony behind the cell in a tight helical bundle. When the bacterium changes its direction, the flagellar filaments unbundle and randomly reorient the cell for a short period of time before returning to their bundled state and resuming swimming. This rapid bundling and unbundling is, at its heart, a mechanical process whereby hydrodynamic interactions balance with elasticity to determine the time-varying deformation of the filaments. Inspired by this biophysical problem, we present in this paper what is perhaps the simplest model of bundling whereby two, or more, straight elastic filaments immersed in a viscous fluid rotate about their centreline, inducing rotational flows which tend to bend the filaments around each other. We derive an integro-differential equation governing the shape of the filaments resulting from mechanical balance in a viscous fluid at low Reynolds number. We show that such equation may be evaluated asymptotically analytically in the long-wavelength limit, leading to a local partial differential equation governed by a single dimensionless Bundling number. A numerical study of the dynamics predicted by the model reveals the presence of two configuration instabilities with increasing Bundling numbers: first to a crossing state where filaments touch at one point and then to a bundled state where filaments wrap along each other in a helical fashion. We also consider the case of multiple filaments, and the unbundling dynamics. We next provide an intuitive physical model for the crossing instability and show that it may be used to predict analytically its threshold, and adapted to address the transition to a bundling state. We then use a macro-scale experimental implementation of the two-filament configuration in order to validate our theoretical predictions and obtain excellent agreement. This long-wavelength model of bundling will be applicable to other problems in biological physics and provides the groundwork for further, more realistic, models of flagellar bundling

Tuning gastropod locomotion: Modeling the influence of mucus rheology on the cost of crawling

Common gastropods such as snails crawl on a solid substrate by propagating muscular waves of shear stress on a viscoelastic mucus. Producing the mucus accounts for the largest component in the gastropod's energy budget, more than twenty times the amount of mechanical work used in crawling. Using a simple mechanical model, we show that the shear-thinning properties of the mucus favor a decrease in the amount of mucus necessary for crawling, thereby decreasing the overall energetic cost of locomotion.Comment: Corrected typo

Scattering series in mobility problem for suspensions

The mobility problem for suspension of spherical particles immersed in an arbitrary flow of a viscous, incompressible fluid is considered in the regime of low Reynolds numbers. The scattering series which appears in the mobility problem is simplified. The simplification relies on the reduction of the number of types of single-particle scattering operators appearing in the scattering series. In our formulation there is only one type of single-particle scattering operator.Comment: 11 page

Low Reynolds number hydrodynamics of asymmetric, oscillating dumbbell pairs

Active dumbbell suspensions constitute one of the simplest model system for collective swimming at low Reynolds number. Generalizing recent work, we derive and analyze stroke-averaged equations of motion that capture the effective hydrodynamic far-field interaction between two oscillating, asymmetric dumbbells in three space dimensions. Time-averaged equations of motion, as those presented in this paper, not only yield a considerable speed-up in numerical simulations, they may also serve as a starting point when deriving continuum equations for the macroscopic dynamics of multi-swimmer suspensions. The specific model discussed here appears to be particularly useful in this context, since it allows one to investigate how the collective macroscopic behavior is affected by changes in the microscopic symmetry of individual swimmers.Comment: 10 pages, to appear in EPJ Special Topic

Generic flow profiles induced by a beating cilium

We describe a multipole expansion for the low Reynolds number fluid flows generated by a localized source embedded in a plane with a no-slip boundary condition. It contains 3 independent terms that fall quadratically with the distance and 6 terms that fall with the third power. Within this framework we discuss the flows induced by a beating cilium described in different ways: a small particle circling on an elliptical trajectory, a thin rod and a general ciliary beating pattern. We identify the flow modes present based on the symmetry properties of the ciliary beat.Comment: 12 pages, 6 figures, to appear in EPJ

Viscous Flow Over a Chemically Patterned Surface

The classical fluid dynamics boundary condition of no-slip suggests that variation in the wettability of a solid should not affect the flow of an adjacent liquid. However experiments and molecular dynamics simulations indicate that this is not the case. In this paper we show how flow over a solid substrate with variations of wettability can be described in a continuum framework using the interface formation theory developed earlier. Results demonstrate that a shear flow over a perfectly flat solid surface is disturbed by a change in its wettability, i.e. by a change in the chemistry of the solid substrate. The magnitude of the effect is shown to be proportional to cos(t1)-cos(t2) where t1 and t2 are the equilibrium contact angles that a liquid-gas free surface would form with the two chemically different parts of the solid surface