Effect of morphology on the large-amplitude flapping dynamics of an inverted flag in a uniform flow

The stability of a cantilevered elastic sheet in a uniform flow has been studied extensively due to its importance in engineering and its prevalence in natural structures. Varying the flow speed can give rise to a range of dynamics including limit cycle behaviour and chaotic motion of the cantilevered sheet. Recently, the "inverted flag" configuration - a cantilevered elastic sheet aligned with the flow impinging on its free edge - has been observed to produce large-amplitude flapping over a finite band of flow speeds. This flapping phenomenon has been found to be a vortex-induced vibration, and only occurs at sufficiently large Reynolds numbers. In all cases studied, the inverted flag has been formed from a cantilevered sheet of rectangular morphology, i.e. the planform of its elastic sheet is a rectangle. Here, we investigate the effect of the inverted flag's morphology on its resulting stability and dynamics. We choose a trapezoidal planform which is explored using experiment and an analytical theory for the divergence instability of an inverted flag of arbitrary morphology. Strikingly, for this planform we observe that the flow speed range over which flapping occurs scales approximately with the flow speed at which the divergence instability occurs. This provides a means by which to predict and control flapping. In a biological setting, leaves in a wind can also align themselves in an inverted flag configuration. Motivated by this natural occurrence we also study the effect of adding an artificial "petiole" (a thin elastic stalk that connects the sheet to the clamp) on the inverted flag's dynamics. We find that the petiole serves to partially decouple fluid forces from elastic forces and increases the freedom by which the flapping dynamics can be tuned. These results highlight the intricacies of the flapping instability and account for some of the varied dynamics of leaves in nature.Comment: 21 pages, 10 figures, 1 tabl

Position and Mode Dependent Optical Detection Back-Action in Cantilever Beam Resonators

Optical detection back-action in cantilever resonant or static detection presents a challenge when striving for state-of-the-art performance. The origin and possible routes for minimizing optical back-action have received little attention in literature. Here, we investigate the position and mode dependent optical back-action on cantilever beam resonators. A high power heating laser (100 {\mu}W) is scanned across a silicon nitride cantilever while its effect on the first three resonance modes is detected via a low-power readout laser (1 {\mu}W) positioned at the cantilever tip. We find that the measured effect of back-action is not only dependent on position but also the shape of the resonance mode. Relevant silicon nitride material parameters are extracted by fitting the temperature-dependent frequency response of the first three modes to finite element (FE) simulations. In a second round of simulations, using the extracted parameters, we successfully fit the FEM results with the measured mode and position dependent back-action. Finally, different routes for minimizing the effect of this optical detection back-action are described, allowing further improvements of cantilever-based sensing in general

Asymptotic analysis of the Boltzmann–BGK equation for oscillatory flows

Kinetic theory provides a rigorous foundation for calculating the dynamics of gas flow at arbitrary degrees of rarefaction, with solutions of the Boltzmann equation requiring numerical methods in many cases of practical interest. Importantly, the near-continuum regime can be examined analytically using asymptotic techniques. These asymptotic analyses often assume steady flow, for which analytical slip models have been derived. Recently, developments in nanoscale fabrication have stimulated research into the study of oscillatory non-equilibrium flows, drawing into question the applicability of the steady flow assumption. In this article, we present a formal asymptotic analysis of the unsteady linearized Boltzmann–BGK equation, generalizing existing theory to the oscillatory (time-varying) case. We consider the near-continuum limit where the mean free path and oscillation frequency are small. The complete set of hydrodynamic equations and associated boundary conditions are derived for arbitrary Stokes number and to second order in the Knudsen number. The first-order steady boundary conditions for the velocity and temperature are found to be unaffected by oscillatory flow. In contrast, the second-order boundary conditions are modified relative to the steady case, except for the velocity component tangential to the solid wall. Application of this general asymptotic theory is explored for the oscillatory thermal creep problem, for which unsteady effects manifest themselves at leading order

Attraction between like-charged colloidal particles induced by a surface a density - functional analysis

We show that the first non-linear correction to the linearised Poisson-Boltzman n (or DLVO) theory of effective pair interactions between charge-stabilised, co lloidal particles near a charged wall leads to an attractive component of entro pic origin. The position and depth of the potential compare favourably with rec ent experimental measurementsComment: 12 pages including 2 figures. submitted to physical review letter

Wrinkling of Transversely Loaded Spinning Membranes

Spinning membrane structures provide a mass-efficient solution for large space apertures. This paper presents a detailed study of the wrinkling of spinning circular membranes loaded by transverse, uniform loads. Experimental measurements of the angular velocities at which different membranes become wrinkled, and of the wrinkling mode transitions that occur upon spin down of the membrane, are presented. A theoretical formulation of the problem is presented, from which pairs of critical angular velocities and critical transverse loads are determined. A general stability chart is presented, which identifies the stability limits in terms of only two dimensionless parameters, for any membrane. The transition between bending dominated behavior and in-plane dominated behavior is identified, and it is shown that in the bending-dominated case the critical non-dimensional transverse load is independent from the non-dimensional angular velocity

Energy dissipation in microfluidic beam resonators: Dependence on mode number

Energy dissipation experienced by vibrating microcantilever beams immersed in fluid is strongly dependent on the mode of vibration, with quality factors typically increasing with mode number. Recently, we examined energy dissipation in a new class of cantilever device that embeds a microfluidic channel in its interior—the fundamental mode of vibration only was considered. Due to its importance in practice, we examine the effect of mode number on energy dissipation in these microfluidic beam resonators. Interestingly, and in contrast to other cantilever devices, we find that the quality factor typically decreases with increasing mode number. We explore the underlying physical mechanisms leading to this counterintuitive behavior, and provide a detailed comparison to experimental measurements for which good agreement is found.United States. Army Research Office (Institute for Collaborative Biotechnologies Contract No. W911NF-09-D-0001)National Institutes of Health (U.S.) (NIH Cell Decision Process Center P50-GM68762)Australian Research Council (Grants Scheme

Comment on "Long-range electrostatic interactions between like-charged colloids: Steric and confinement effects"

In a recent study [Phys. Rev. E 60, 6530 (1999)], Trizac and Raimbault showed that the effective pair interaction between like charged colloids immersed in a cylindrically confined electrolyte remains repulsive even when the size of the micro-ions or the finite longitudinal extension of the confining cylinder are taken into account. Contrary to their claim, we argue that the case of finite longitudinal confinement doesn't always generate repulsive interactions and to illustrate this point we also provide a simple example.Comment: 3 pages, 1 figure. Accepted for publication in Phys. Rev. E 200