A note on the stability of slip channel flows

We consider the influence of slip boundary conditions on the modal and non-modal stability of pressure-driven channel flows. In accordance with previous results by Gersting (1974) (Phys. Fluids, 17) but in contradiction with the recent investigation of Chu (2004) (C.R. Mecanique, 332), we show that slip increases significantly the value of the critical Reynolds number for linear instability. The non-modal stability analysis however reveals that the slip has a very weak influence on the maximum transient energy growth of perturbations at subcritical Reynolds numbers. Slip boundary conditions are therefore not likely to have a significant effect on the transition to turbulence in channel flows

Micro-Tug-of-War: A Selective Control Mechanism for Magnetic Swimmers

One of the aspirations for artificial microswimmers is their application in noninvasive medicine. For any practical use, adequate mechanisms enabling control of multiple artificial swimmers will be of paramount importance. Here we theoretically propose a multihelical, freely jointed motor as a selective control mechanism. We show that the nonlinear step-out behavior of a magnetized helix driven by a rotating magnetic field can be exploited when used in conjunction with other helices to obtain a velocity profile that is non-negligible only within a chosen interval of operating frequencies. Specifically, the force balance between the competing opposite-handed helices is tuned to give no net motion at low frequencies (tug-of-war), while in the middle-frequency range, the magnitude and, potentially, the sign of the swimming velocity can be adjusted by varying the driving frequency. We illustrate this idea on a two-helix system and demonstrate how to generalize to $\textit{N}$ helices, both numerically and theoretically. We then explain how to solve the inverse problem and design an artificial swimmer with an arbitrarily complex velocity vs frequency relationship. We finish by discussing potential experimental implementation.This work is funded in part by the European Union through a Marie Curie CIG Grant (E. L.) and by the Engineering and Physical Sciences Research Council (P. K.).This is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevApplied.5.06401

Low-Reynolds number swimming in gels

Many microorganisms swim through gels, materials with nonzero zero-frequency elastic shear modulus, such as mucus. Biological gels are typically heterogeneous, containing both a structural scaffold (network) and a fluid solvent. We analyze the swimming of an infinite sheet undergoing transverse traveling wave deformations in the "two-fluid" model of a gel, which treats the network and solvent as two coupled elastic and viscous continuum phases. We show that geometric nonlinearities must be incorporated to obtain physically meaningful results. We identify a transition between regimes where the network deforms to follow solvent flows and where the network is stationary. Swimming speeds can be enhanced relative to Newtonian fluids when the network is stationary. Compressibility effects can also enhance swimming velocities. Finally, microscopic details of sheet-network interactions influence the boundary conditions between the sheet and network. The nature of these boundary conditions significantly impacts swimming speeds.Comment: 6 pages, 5 figures, submitted to EP

Slip flow over structured surfaces with entrapped microbubbles

On hydrophobic surfaces, roughness may lead to a transition to a superhydrophobic state, where gas bubbles at the surface can have a strong impact on a detected slip. We present two-phase lattice Boltzmann simulations of a Couette flow over structured surfaces with attached gas bubbles. Even though the bubbles add slippery surfaces to the channel, they can cause negative slip to appear due to the increased roughness. The simulation method used allows the bubbles to deform due to viscous stresses. We find a decrease of the detected slip with increasing shear rate which is in contrast to some recent experimental results implicating that bubble deformation cannot account for these experiments. Possible applications of bubble surfaces in microfluidic devices are discussed.Comment: 4 pages, 4 figures. v2: revised version, to appear in Phys. Rev. Let

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

A note on the effective slip properties for microchannel flows with ultra-hydrophobic surfaces

A type of super-hydrophobic surface consists of a solid plane boundary with an array of grooves which, due to the effect of surface tension, prevent a complete wetting of the wall. The effect is greatest when the grooves are aligned with the flow. The pressure difference between the liquid and the gas in the grooves causes a curvature of the liquid surface resisted by surface tension. The effects of this surface deformation are studied in this paper. The corrections to the effective slip length produced by the curvature are analyzed theoretically and a comparison with available data and related mathematical models is presented.Comment: 19 pages, 5 figure

Shear-dependent apparent slip on hydrophobic surfaces: The Mattress Model

Recent experiments (Zhu & Granick (2001) Phys. Rev. Lett. 87 096105) have measured a large shear dependent fluid slip at partially wetting fluid-solid surfaces. We present a simple model for such slip, motivated by the recent observations of nanobubbles on hydrophobic surfaces. The model considers the dynamic response of bubbles to change in hydrodynamic pressure due to the oscillation of a solid surface. Both the compression and diffusion of gas in the bubbles decrease the force on the oscillating surface by a ``leaking mattress'' effect, thereby creating an apparent shear-dependent slip. With bubbles similar to those observed by atomic force microscopy to date, the model is found to lead to force decreases consistent with the experimental measurements of Zhu & Granick

Slippage of water past superhydrophobic carbon nanotube forests in microchannels

We present in this letter an experimental characterization of liquid flow slippage over superhydrophobic surfaces made of carbon nanotube forests, incorporated in microchannels. We make use of a micro-PIV (Particule Image Velocimetry) technique to achieve the submicrometric resolution on the flow profile necessary for accurate measurement of the surface hydrodynamic properties. We demonstrate boundary slippage on the Cassie superhydrophobic state, associated with slip lengths of a few microns, while a vanishing slip length is found in the Wenzel state, when the liquid impregnates the surface. Varying the lateral roughness scale L of our carbon nanotube forest-based superhydrophobic surfaces, we demonstrate that the slip length varies linearly with L in line with theoretical predictions for slippage on patterned surfaces.Comment: under revie